| Title: | Wavelet Routines for Global and Local Multiple Regression and Correlation |
|---|---|
| Description: | Wavelet routines that calculate single sets of wavelet multiple regressions and correlations, and cross-regressions and cross-correlations from a multivariate time series. Dynamic versions of the routines allow the wavelet local multiple (cross-)regressions and (cross-)correlations to evolve over time. |
| Authors: | Javier Fernandez-Macho [aut, cre]
|
| Maintainer: | Javier Fernandez-Macho <[email protected]> |
| License: | GPL-3 |
| Version: | 3.1.2 |
| Built: | 2024-11-29 09:06:21 UTC |
| Source: | CRAN |
Wavelet routines that calculate single sets of wavelet multiple regressions and correlations, and cross-regressions and cross-correlations from a multivariate time series. Dynamic versions of the routines allow the wavelet local multiple (cross-)regressions and (cross-)correlations to evolve over time.
Wavelet routines that calculate single sets of wavelet multiple regressions and correlations (WMR and WMC), and cross-regressions and cross-correlations (WMCR and WMCC) from a multivariate time series. Dynamic versions of the routines allow the wavelet local multiple (cross-)regressions (WLMR and WLMCR) and (cross-)correlations (WLMC and WLMCC) to evolve over time. The output from these Wavelet statistics can later be plotted in single graphs, as an alternative to trying to make sense out of several sets of wavelet correlations or wavelet cross-correlations. The code is based on the calculation, at each wavelet scale, of the square root of the coefficient of determination in a linear combination of variables for which such coefficient of determination is a maximum. The code provided here is based on the wave.correlation routine in Brandon Whitcher's waveslim R package Version: 1.6.4, which in turn is based on wavelet methodology developed in Percival and Walden (2000), Gençay, Selçuk and Whitcher (2002) and others. Version 2 incorporates wavelet local multiple correlations (WLMC). These are like the previous global WMC but consisting in one single set of multiscale correlations along time. That is, at each time t, they are calculated by letting a window of weighted wavelet coefficients around t move along time. Six weight functions are provided. Namely, the uniform window, Cleveland's tricube window, Epanechnikov's parabolic window, Bartlett's triangular window and Wendland's truncated power window and the Gaussian window. Version 2.2 incorporates auxiliary functions that calculate local multiple correlations and cross-correlations (LMC, LMCC). They are calculated by letting move along time a window of weighted time series values around t. Any of the six weight functions mentioned above can be used. They also feed a new routine to compute wavelet local multiple cross-correlation (WLMCC). Version 3 extends all the previous correlation routines (WMC, WMCC, LMC, WLMC, WLMCC) to handle wavelet regressions (WMR, WMCR, LMR, WLMR, WLMCR) that provide regression coefficients and statistics across wavelet scales. Auxiliary plot_ and heatmap_ routines are also provided to visualize the wavmulcor statistics.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a heatmap of wave local multiple correlations.
heatmap_wave.local.multiple.correlation(Lst, xaxt="s", ci=NULL, pdf.write=NULL)heatmap_wave.local.multiple.correlation(Lst, xaxt="s", ci=NULL, pdf.write=NULL)
Lst |
A list from wave.local.multiple.regression. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
ci |
value to plot: "center" value of confidence interval (i.e. the estimated correlation), the "lower" bound, or the "upper" bound. Default is "center". |
pdf.write |
Optional name leader to save files to pdf format. The actual name of the file is "heat_<pdf.write>_WLMC.pdf". |
The routine produces a time series vs. wavelet periods heatmap of wave local multiple correlations.
Heat map.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces heatmaps of wave local multiple cross-correlations.
heatmap_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE, xaxt="s", ci=NULL, pdf.write=NULL)heatmap_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE, xaxt="s", ci=NULL, pdf.write=NULL)
Lst |
A list from wave.local.multiple.cross.regression. |
lmax |
maximum lag (and lead). |
lag.first |
if TRUE, it produces lag-lead pages with |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
ci |
value to plot: "center" value of confidence interval (i.e. the estimated cross-correlation), the "lower" bound, or the "upper" bound. Default is "center". |
pdf.write |
Optional name leader to save files to pdf format. The actual name of the file is either "heat_<pdf.write>_WLMCC_lags.pdf" or, "heat_<pdf.write>_WLMCC_levels.pdf". |
The routine produces a set of time series vs. wavelet periods heatmaps of wave local multiple cross-correlations at different lags and leads.
Heat map.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces heatmaps of wave multiple cross-correlations.
heatmap_wave.multiple.cross.correlation(Lst, lmax, by=3, ci=NULL, pdf.write=NULL)heatmap_wave.multiple.cross.correlation(Lst, lmax, by=3, ci=NULL, pdf.write=NULL)
Lst |
A list from wave.multiple.cross.regression or wave.multiple.cross.correlation. |
lmax |
maximum lag (and lead). |
by |
labels are printed every lmax/by. Default is 3. |
ci |
value to plot: "center" value of confidence interval (i.e. the estimated cross-correlation), the "lower" bound, or the "upper" bound. Default is "center". |
pdf.write |
Optional name leader to save files to pdf format. The actual name of the file is either "heat_<pdf.write>_WLMCC_lags.pdf" or, "heat_<pdf.write>_WLMCC_levels.pdf". |
The routine produces a set of time series vs. wavelet periods heatmaps of wave local multiple cross-correlations at different lags and leads.
Heat map.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
Produces an estimate of local multiple correlations (as defined below) along with approximate confidence intervals.
local.multiple.correlation(xx, M, window="gauss", p = .975, ymaxr=NULL)local.multiple.correlation(xx, M, window="gauss", p = .975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level lmc chooses the one maximizing the multiple correlation. |
The routine calculates a time series of multiple correlations out of variables.
The code is based on the calculation of the square root of the coefficient of
determination in that linear combination of locally weighted values for which such coefficient of determination is a maximum.
List of four elements:
val: |
numeric vector (rows = #observations) providing the point estimates for the local multiple correlation. |
lo: |
numeric vector (rows = #observations) providing the lower bounds of the confidence interval. |
up: |
numeric vector (rows = #observations) providing the upper bounds of the confidence interval. |
YmaxR: |
numeric vector (rows = #observations) giving, at each value in time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, lmc chooses at each value in time the variable maximizing the multiple correlation. |
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) xrand1 <- wavemulcor::xrand1 xrand2 <- wavemulcor::xrand2 N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gaussian" J <- trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xx <- data.frame(xrand1,xrand2) # --------------------------- xy.mulcor <- local.multiple.correlation(xx, M, window=window) val <- as.matrix(xy.mulcor$val) lo <- as.matrix(xy.mulcor$lo) up <- as.matrix(xy.mulcor$up) YmaxR <- as.matrix(xy.mulcor$YmaxR) # --------------------------- old.par <- par() # ##Producing line plots with CI title <- paste("Local Multiple Correlation") sub <- paste("first",b,"obs:",round(100*cor1,1),"% correlation;","middle",b,"obs:", round(100*cor2,1),"%","rest:",round(100*cor3,1),"%") xlab <- "time" ylab <- "correlation" matplot(1:N,cbind(val,lo,up), main=title, sub=sub, xlab=xlab, ylab=ylab, type="l", lty=1, col= c(1,2,2), cex.axis=0.75) abline(h=0) ##Add Straight horiz and vert Lines to a Plot #reset graphics parameters par(old.par)## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) xrand1 <- wavemulcor::xrand1 xrand2 <- wavemulcor::xrand2 N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gaussian" J <- trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xx <- data.frame(xrand1,xrand2) # --------------------------- xy.mulcor <- local.multiple.correlation(xx, M, window=window) val <- as.matrix(xy.mulcor$val) lo <- as.matrix(xy.mulcor$lo) up <- as.matrix(xy.mulcor$up) YmaxR <- as.matrix(xy.mulcor$YmaxR) # --------------------------- old.par <- par() # ##Producing line plots with CI title <- paste("Local Multiple Correlation") sub <- paste("first",b,"obs:",round(100*cor1,1),"% correlation;","middle",b,"obs:", round(100*cor2,1),"%","rest:",round(100*cor3,1),"%") xlab <- "time" ylab <- "correlation" matplot(1:N,cbind(val,lo,up), main=title, sub=sub, xlab=xlab, ylab=ylab, type="l", lty=1, col= c(1,2,2), cex.axis=0.75) abline(h=0) ##Add Straight horiz and vert Lines to a Plot #reset graphics parameters par(old.par)
Produces an estimate of local multiple cross-correlations (as defined below) along with approximate confidence intervals.
local.multiple.cross.correlation(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)local.multiple.cross.correlation(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level lmc chooses the one maximizing the multiple correlation. |
The routine calculates a set of time series of multiple cross-correlations, one per lag and lead) out of variables.
List of four elements:
vals: |
numeric matrix (rows = #observations, cols = #lags and leads) providing the point estimates for the local multiple cross-correlation. |
lower: |
numeric vmatrix (rows = #observations, cols = #lags and leads) providing the lower bounds from the confidence interval. |
upper: |
numeric matrix (rows = #observations, cols = #lags and leads) providing the upper bounds from the confidence interval. |
YmaxR: |
numeric matrix (rows = #observations, cols = #lags and leads) giving, at each value in time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, lmcc chooses at each value in time the variable maximizing the multiple correlation. |
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] M <- 30 window <- "gauss" lmax <- 1 demusd <- returns[,"DEM.USD"] jpyusd <- returns[,"JPY.USD"] set.seed(140859) xrand <- rnorm(N) xx <- data.frame(demusd, jpyusd, xrand) ##exchange.names <- c(colnames(returns), "RAND") Lst <- local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax) val <- Lst$vals low.ci <- Lst$lower upp.ci <- Lst$upper YmaxR <- Lst$YmaxR # --------------------------- ##Producing correlation plot colnames(val) <- paste("Lag",-lmax:lmax) xvar <- seq(1,N,M) par(mfcol=c(lmax+1,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(i in c(-lmax:0,lmax:1)+lmax+1) { matplot(1:N,val[,i], type="l", lty=1, ylim=c(ymin,1), #xaxt="n", xlab="", ylab="", main=colnames(val)[i]) # if(i==lmax+1) {axis(side=1, at=seq(0,N+50,50))} #axis(side=2, at=c(-.2, 0, .5, 1)) abline(h=0) ##Add Straight horiz lines(low.ci[,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(upp.ci[,i], lty=1, col=2) text(xvar,1, labels=names(xx)[YmaxR][xvar], adj=0.25, cex=.8) } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Local Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5)## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] M <- 30 window <- "gauss" lmax <- 1 demusd <- returns[,"DEM.USD"] jpyusd <- returns[,"JPY.USD"] set.seed(140859) xrand <- rnorm(N) xx <- data.frame(demusd, jpyusd, xrand) ##exchange.names <- c(colnames(returns), "RAND") Lst <- local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax) val <- Lst$vals low.ci <- Lst$lower upp.ci <- Lst$upper YmaxR <- Lst$YmaxR # --------------------------- ##Producing correlation plot colnames(val) <- paste("Lag",-lmax:lmax) xvar <- seq(1,N,M) par(mfcol=c(lmax+1,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(i in c(-lmax:0,lmax:1)+lmax+1) { matplot(1:N,val[,i], type="l", lty=1, ylim=c(ymin,1), #xaxt="n", xlab="", ylab="", main=colnames(val)[i]) # if(i==lmax+1) {axis(side=1, at=seq(0,N+50,50))} #axis(side=2, at=c(-.2, 0, .5, 1)) abline(h=0) ##Add Straight horiz lines(low.ci[,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(upp.ci[,i], lty=1, col=2) text(xvar,1, labels=names(xx)[YmaxR][xvar], adj=0.25, cex=.8) } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Local Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5)
Produces an estimate of local multiple cross-regressions (as defined below) along with approximate confidence intervals.
local.multiple.cross.regression(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)local.multiple.cross.regression(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level lmc chooses the one maximizing the multiple correlation. |
The routine calculates a set of time series of multiple cross-regressions, one per lag and lead) out of variables.
List of four elements:
cor: |
List of three elements: |
vals: numeric matrix (rows = #observations, cols = #lags and leads) providing the point estimates for the local multiple cross-correlation.
lower: numeric vmatrix (rows = #observations, cols = #lags and leads) providing the lower bounds from the confidence interval.
upper: numeric matrix (rows = #observations, cols = #lags and leads) providing the upper bounds from the confidence interval.
reg: |
List of seven elements: |
rval: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of local regression estimates.
rstd: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their standard deviations.
rlow: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their lower bounds.
rupp: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their upper bounds.
rtst: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their t statistic values.
rord: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their index order when sorted by significance.
rpva: numeric array (1st_dim = #observations, 2nd_dim = #lags and leads, 3rd_dim = #regressors+1) of their p values.
YmaxR: |
numeric matrix (rows = #observations, cols = #lags and leads) giving, at each value in time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, lmcr chooses at each value in time the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #observations, cols = #regressors) of original data. |
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] M <- 30 window <- "gauss" lmax <- 1 demusd <- returns[,"DEM.USD"] jpyusd <- returns[,"JPY.USD"] set.seed(140859) xrand <- rnorm(N) # --------------------------- xx <- data.frame(demusd, jpyusd, xrand) ##exchange.names <- c(colnames(returns), "RAND") Lst <- local.multiple.cross.regression(xx, M, window=window, lag.max=lmax) # --------------------------- ##Producing correlation plot plot_local.multiple.cross.correlation(Lst, lmax) #, xaxt="s") ##Producing regression plot plot_local.multiple.cross.regression(Lst, lmax) #, nsig=2, xaxt="s")## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] M <- 30 window <- "gauss" lmax <- 1 demusd <- returns[,"DEM.USD"] jpyusd <- returns[,"JPY.USD"] set.seed(140859) xrand <- rnorm(N) # --------------------------- xx <- data.frame(demusd, jpyusd, xrand) ##exchange.names <- c(colnames(returns), "RAND") Lst <- local.multiple.cross.regression(xx, M, window=window, lag.max=lmax) # --------------------------- ##Producing correlation plot plot_local.multiple.cross.correlation(Lst, lmax) #, xaxt="s") ##Producing regression plot plot_local.multiple.cross.regression(Lst, lmax) #, nsig=2, xaxt="s")
Produces an estimate of local multiple regressions (as defined below) along with approximate confidence intervals.
local.multiple.regression(xx, M, window="gauss", p=.975, ymaxr=NULL)local.multiple.regression(xx, M, window="gauss", p=.975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level lmc chooses the one maximizing the multiple correlation. |
The routine calculates a set of time series of multiple regression coefficients out of variables.
List of four elements:
cor: |
List of three elements: |
val: numeric vector (rows = #observations) of point estimates for the local multiple correlation.
lo: numeric vector (rows = #observations) of lower bounds of the confidence interval.
up: numeric vector (rows = #observations) of upper bounds of the confidence interval.
reg: |
List of seven elements: |
rval: numeric matrix (rows = #observations, cols = #regressors+1) of local regression estimates.
rstd: numeric matrix (rows = #observations, cols = #regressors+1) of their standard deviations.
rlow: numeric matrix (rows = #observations, cols = #regressors+1) of their lower bounds.
rupp: numeric matrix (rows = #observations, cols = #regressors+1) of their upper bounds.
rtst: numeric matrix (rows = #observations, cols = #regressors+1) of their t statistic values.
rord: numeric matrix (rows = #observations, cols = #regressors+1) of their index order when sorted by significance.
rpva: numeric matrix (rows = #observations, cols = #regressors+1) of their p values.
YmaxR: |
numeric vector (rows = #observations) giving, at each value in time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, lmr chooses at each value in time the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #observations, cols = #regressors) of original data. |
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) xrand1 <- wavemulcor::xrand1 xrand2 <- wavemulcor::xrand2 N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gaussian" J <- trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xx <- data.frame(xrand1,xrand2) # --------------------------- Lst <- local.multiple.regression(xx, M, window=window) #, ymax=1) # --------------------------- ##Producing correlation plot plot_local.multiple.correlation(Lst) ##Producing regression plot plot_local.multiple.regression(Lst)## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) xrand1 <- wavemulcor::xrand1 xrand2 <- wavemulcor::xrand2 N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gaussian" J <- trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xx <- data.frame(xrand1,xrand2) # --------------------------- Lst <- local.multiple.regression(xx, M, window=window) #, ymax=1) # --------------------------- ##Producing correlation plot plot_local.multiple.correlation(Lst) ##Producing regression plot plot_local.multiple.regression(Lst)
Produces a plot of local multiple correlations.
plot_local.multiple.correlation(Lst, xaxt="s")plot_local.multiple.correlation(Lst, xaxt="s")
Lst |
A list from local.multiple.regression or local.multiple.correlation. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces a time series plot of local multiple correlations with its confidence interval. Also, at every upturn and downturn, the name of the variable that maximizes its multiple correlation against the rest is shown. Note that the routine is optimize for local.multiple.regression. If you want to use output from the legacy local.multiple.correlation function then you must create an empty list and put that output into a list element named cor like this: Lst <- list(); Lst$cor <- local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax); Lst$YmaxR <- Lst2$cor$YmaxR; Lst$cor$YmaxR <- NULL.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of local multiple cross-correlations.
plot_local.multiple.cross.correlation(Lst, lmax, xaxt="s")plot_local.multiple.cross.correlation(Lst, lmax, xaxt="s")
Lst |
A list from local.multiple.cross.regression or local.multiple.cross.correlation. |
lmax |
maximum lag (and lead). |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces a set of time series plots of local multiple cross-correlations, one per lag and lead, each with its confidence interval. Also, at every upturn and downturn, the name of the variable that maximizes its multiple correlation against the rest is shown. Note that the routine is optimize for local.multiple.cross.regression. If you want to use output from local.multiple.cross.correlation function then you must create an empty list and put that output into a list element named cor like this: Lst <- list(); Lst$cor <- local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax); Lst$YmaxR <- Lst2$cor$YmaxR; Lst$cor$YmaxR <- NULL.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of local multiple cross-regressions.
plot_local.multiple.cross.regression(Lst, lmax, nsig=2, xaxt="s")plot_local.multiple.cross.regression(Lst, lmax, nsig=2, xaxt="s")
Lst |
A list from local.multiple.cross.regression. |
lmax |
maximum lag (and lead). |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces time series plots of local multiple cross-regressions with their confidence interval for every lag and lead. Also, at every upturn and downturn of the corresponding local multiple cross-correlation, the name of the variable that maximizes that multiple correlation against the rest is shown on top. The others are named ordered by significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of local multiple regressions.
plot_local.multiple.regression(Lst, nsig=2, xaxt="s")plot_local.multiple.regression(Lst, nsig=2, xaxt="s")
Lst |
A list from local.multiple.regression. |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces a time series plot of local multiple regressions with its confidence interval. Also, at every upturn and downturn of the corresponding local multiple correlation, the name of the variable that maximizes that multiple correlation against the rest is shown on top. The others are named ordered by significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of wave local multiple correlations.
plot_wave.local.multiple.correlation(Lst, xaxt="s")plot_wave.local.multiple.correlation(Lst, xaxt="s")
Lst |
A list from local.multiple.regression. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces time series plots of wave local multiple correlations with their confidence intervals. Also, at every upturn and downturn, the name of the variable that maximizes its multiple correlation against the rest is shown.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of wave local multiple cross-correlations.
plot_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE, xaxt="s", pdf.write=NULL)plot_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE, xaxt="s", pdf.write=NULL)
Lst |
A list from local.multiple.cross.regression. |
lmax |
maximum lag (and lead). |
lag.first |
if TRUE, it produces lag-lead pages with |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
pdf.write |
Optional name leader to save files to pdf format.
The actual filename of each page is either
"plot_<pdf.write>_WLMCC_<i>.pdf", where "i" is the lag/lead |
The routine produces time series plots of wave local multiple cross-correlations with their confidence intervals. Also, at every upturn and downturn, the name of the variable that maximizes its multiple cross-correlation against the rest is shown.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a set of plots of wave local multiple cross-regressions.
plot_wave.local.multiple.cross.regression(Lst, lmax, nsig=2, xaxt="s", pdf.write=NULL)plot_wave.local.multiple.cross.regression(Lst, lmax, nsig=2, xaxt="s", pdf.write=NULL)
Lst |
A list from wave.multiplecross.regression. |
lmax |
maximum lag (and lead). |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
pdf.write |
Optional name leader to save files to pdf format.
The actual filename of each page
"plot_<pdf.write>_WLMCC_<j>.pdf", where "j" is the wavelet level |
The routine produces pages, one per wavelet level, each with time series plots of wave multiple cross-regressions at different lags and leads, each with their confidence interval.
Also, the name of the variable that maximizes that multiple correlation against the rest is shown on top.
The others are named with their order of significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a set of plots of wave local multiple regressions.
plot_wave.local.multiple.regression(Lst,nsig=2, xaxt="s")plot_wave.local.multiple.regression(Lst,nsig=2, xaxt="s")
Lst |
A list from wave.multiple.regression. |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
xaxt |
An optional vector of labels for the "x" axis. Default is 1:n. |
The routine produces time series plots of wave multiple regressions, each with their confidence interval.
Also, the name of the variable that maximizes that multiple correlation against the rest is shown on top.
The others are named with their order of significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of wave multiple correlations.
plot_wave.multiple.correlation(Lst)plot_wave.multiple.correlation(Lst)
Lst |
A list from wave.multiple.regression or wave.multiple.correlation. |
The routine produces a plot of wave multiple correlations, at each wavelet level, with its confidence interval. Also, at each wavelet level, the name of the variable that maximizes its multiple correlation against the rest is shown.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
Produces a plot of wave multiple cross-correlations.
plot_wave.multiple.cross.correlation(Lst, lmax, by=3)plot_wave.multiple.cross.correlation(Lst, lmax, by=3)
Lst |
A list from wave.multiple.cross.regression or wave.multiple.cross.correlation. |
lmax |
maximum lag (and lead). |
by |
labels are printed every lmax/by. Default is 3. |
The routine produces a set of plots of wave multiple cross-correlations, one per wavelet level, with their confidence intervals. Also, at each wavelet level, the name of the variable that maximizes its multiple cross-correlation against the rest is shown.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
Produces a plot of wave multiple cross.regressions.
plot_wave.multiple.cross.regression(Lst, lmax, nsig=2, by=3)plot_wave.multiple.cross.regression(Lst, lmax, nsig=2, by=3)
Lst |
A list from wave.multiple.cross.regression. |
lmax |
maximum lag (and lead). |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
by |
labels are printed every lmax/by. Default is 3. |
The routine produces a plot of wave multiple regressions, one per wavelet level, with their confidence intervals. Also, the name of the variable that maximizes that multiple correlation against the rest is shown on top. The others are named with their order of significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces a plot of wave multiple regressions.
plot_wave.multiple.regression(Lst, nsig=2)plot_wave.multiple.regression(Lst, nsig=2)
Lst |
A list from wave.multiple.regression. |
nsig |
An optional value for the number of significant variables to plot_ Default is 2. |
The routine produces a plot of wave multiple regressions with their confidence interval. Also, the name of the variable that maximizes that multiple correlation against the rest is shown on top. The others are named with their order of significance when they are relevant.
Plot.
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
Produces an estimate of the multiscale local multiple correlation (as defined below) along with approximate confidence intervals.
wave.local.multiple.correlation(xx, M, window="gauss", p = .975, ymaxr=NULL)wave.local.multiple.correlation(xx, M, window="gauss", p = .975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wlmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple correlations out of variables
that can be plotted in in either single heatmap or line graphs (the former is usually the best graphic option but the latter is useful if confidence intervals are explicitly needed),
as an alternative to trying to make sense out of sets of local wavelet correlations.
The code is based on the calculation, at each wavelet scale, of the square root of the coefficient of
determination in that linear combination of locally weighted wavelet coefficients for which such coefficient of determination is a maximum.
The code provided here is based on the wave.multiple.correlation routine in this package
which in turn is based on the wave.correlation routine in Brandon Whitcher's waveslim R package Version: 1.6.4, which in turn is based on wavelet methodology
developed in Percival and Walden (2000); Gençay, Selçuk and Whitcher (2001) and others.
List of four elements:
val: |
numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the point estimates for the wavelet local multiple correlation. |
lo: |
numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the lower bounds from the confidence interval. |
up: |
numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the upper bounds from the confidence interval. |
YmaxR: |
numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) giving, at each wavelet level and time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wlmc chooses at each wavelet level and value in time the variable maximizing the multiple correlation. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) data(xrand) N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gauss" J <- 3 #trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xrand1.modwt <- modwt(xrand1, wf, J) xrand1.modwt.bw <- brick.wall(xrand1.modwt, wf) xrand2.modwt <- modwt(xrand2, wf, J) xrand2.modwt.bw <- brick.wall(xrand2.modwt, wf) xx <- list(xrand1.modwt.bw,xrand2.modwt.bw) # --------------------------- xy.mulcor <- wave.local.multiple.correlation(xx, M, window=window) val <- as.matrix(xy.mulcor$val) lo <- as.matrix(xy.mulcor$lo) up <- as.matrix(xy.mulcor$up) YmaxR <- as.matrix(xy.mulcor$YmaxR) # --------------------------- old.par <- par() # ##Producing heat plot scale.names <- paste0("(",c("2-4","4-8","8-16","16-32","32-64","64-128","128-256","256-512", "512-1024","1024-2048"),"]") scale.names <- c(scale.names[1:J],"smooth") title <- paste("Wavelet Local Multiple Correlation") sub <- paste("first",b,"obs:",round(100*cor1,1),"% correlation;","middle",b,"obs:", round(100*cor2,1),"%","rest:",round(100*cor3,1),"%") xlab <- "time" ylab <- "periods" plot3D::image2D(z=val, x=1:nrow(val), y=1:ncol(val), main=title, #sub=sub, xlab=xlab, ylab=ylab, axes=FALSE, clab = expression(varphi), rasterImage = TRUE, contour = list(lwd = 2, col = plot3D::jet.col(11))) axis(side=1, at=seq(10,nrow(val),by=10), cex.axis=0.75) axis(side=2, at=1:ncol(val),labels=scale.names, las=1,cex.axis=0.75) # --------------------------- ##Producing line plots with confidence intervals colnames(val)[1:J] <- paste0("level",1:J) par(mfrow=c(3,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) for(i in J:1) { matplot(1:N,val[,i], type="l", lty=1, ylim=c(-1,1), xaxt="n", xlab="", ylab="", main=colnames(val)[i]) if(i<3) {axis(side=1, at=seq(10,N,by=10))} #axis(side=2, at=c(-.2, 0, .5, 1)) lines(lo[,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(up[,i], lty=1, col=2) abline(h=0) ##Add Straight horiz and vert Lines to a Plot } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Wavelet Local Multiple Correlation', side=2, outer=TRUE, adj=0.5) #reset graphics parameters par(old.par)## Based on Figure 4 showing correlation structural breaks in Fernandez-Macho (2018). library(wavemulcor) options(warn = -1) data(xrand) N <- length(xrand1) b <- trunc(N/3) t1 <- 1:b t2 <- (b+1):(2*b) t3 <- (2*b+1):N wf <- "d4" M <- N/2^3 #sharper with N/2^4 window <- "gauss" J <- 3 #trunc(log2(N))-3 # --------------------------- cor1 <- cor(xrand1[t1],xrand2[t1]) cor2 <- cor(xrand1[t2],xrand2[t2]) cor3 <- cor(xrand1[t3],xrand2[t3]) cortext <- paste0(round(100*cor1,0),"-",round(100*cor2,0),"-",round(100*cor3,0)) ts.plot(cbind(xrand1,xrand2),col=c("red","blue"),xlab="time") xrand1.modwt <- modwt(xrand1, wf, J) xrand1.modwt.bw <- brick.wall(xrand1.modwt, wf) xrand2.modwt <- modwt(xrand2, wf, J) xrand2.modwt.bw <- brick.wall(xrand2.modwt, wf) xx <- list(xrand1.modwt.bw,xrand2.modwt.bw) # --------------------------- xy.mulcor <- wave.local.multiple.correlation(xx, M, window=window) val <- as.matrix(xy.mulcor$val) lo <- as.matrix(xy.mulcor$lo) up <- as.matrix(xy.mulcor$up) YmaxR <- as.matrix(xy.mulcor$YmaxR) # --------------------------- old.par <- par() # ##Producing heat plot scale.names <- paste0("(",c("2-4","4-8","8-16","16-32","32-64","64-128","128-256","256-512", "512-1024","1024-2048"),"]") scale.names <- c(scale.names[1:J],"smooth") title <- paste("Wavelet Local Multiple Correlation") sub <- paste("first",b,"obs:",round(100*cor1,1),"% correlation;","middle",b,"obs:", round(100*cor2,1),"%","rest:",round(100*cor3,1),"%") xlab <- "time" ylab <- "periods" plot3D::image2D(z=val, x=1:nrow(val), y=1:ncol(val), main=title, #sub=sub, xlab=xlab, ylab=ylab, axes=FALSE, clab = expression(varphi), rasterImage = TRUE, contour = list(lwd = 2, col = plot3D::jet.col(11))) axis(side=1, at=seq(10,nrow(val),by=10), cex.axis=0.75) axis(side=2, at=1:ncol(val),labels=scale.names, las=1,cex.axis=0.75) # --------------------------- ##Producing line plots with confidence intervals colnames(val)[1:J] <- paste0("level",1:J) par(mfrow=c(3,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) for(i in J:1) { matplot(1:N,val[,i], type="l", lty=1, ylim=c(-1,1), xaxt="n", xlab="", ylab="", main=colnames(val)[i]) if(i<3) {axis(side=1, at=seq(10,N,by=10))} #axis(side=2, at=c(-.2, 0, .5, 1)) lines(lo[,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(up[,i], lty=1, col=2) abline(h=0) ##Add Straight horiz and vert Lines to a Plot } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Wavelet Local Multiple Correlation', side=2, outer=TRUE, adj=0.5) #reset graphics parameters par(old.par)
Produces an estimate of the multiscale local multiple cross-correlation (as defined below) along with approximate confidence intervals.
wave.local.multiple.cross.correlation(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)wave.local.multiple.cross.correlation(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wlmc chooses the one maximizing the multiple correlation. |
The routine calculates sets of wavelet multiple cross-correlations,one per wavelet level, out of variables, that can be plotted each as lags and leads time series plots.
List of four elements:
val: |
list of |
lo: |
list of |
up: |
list of |
YmaxR: |
numeric matrix (rows = #observations, columns = #levels) giving, at each wavelet level and time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wlmc chooses at each wavelet level and value in time the variable maximizing the multiple correlation. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 lmax <- 2 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) ##xx <- list(demusd.modwt.bw, jpyusd.modwt.bw) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") ## Not run: # Note: WLMCC may take more than 10 seconds of CPU time on some systems Lst <- wave.local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax) val <- Lst$val low.ci <- Lst$lo upp.ci <- Lst$up YmaxR <- Lst$YmaxR # --------------------------- ##Producing cross-correlation plot xvar <- seq(1,N,M) level.lab <- c(paste("Level",1:J),paste("Smooth",J)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(j in 1:(J+1)) { par(mfcol=c(lmax+1,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,1.2,0)) # xaxt <- c(rep("n",lmax),"s",rep("n",lmax)) for(i in c(-lmax:0,lmax:1)+lmax+1) { matplot(1:N,val[[j]][,i], type="l", lty=1, ylim=c(ymin,1), #xaxt=xaxt[i], xlab="", ylab="", main=paste("Lag",i-lmax-1)) abline(h=0) ##Add Straight horiz lines(low.ci[[j]][,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(upp.ci[[j]][,i], lty=1, col=2) text(xvar,1, labels=names(xx)[YmaxR[[j]]][xvar], adj=0.25, cex=.8) } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Local Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5) mtext(level.lab[j], side=3, outer=TRUE, adj=0.5) } ## End(Not run)## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 lmax <- 2 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) ##xx <- list(demusd.modwt.bw, jpyusd.modwt.bw) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") ## Not run: # Note: WLMCC may take more than 10 seconds of CPU time on some systems Lst <- wave.local.multiple.cross.correlation(xx, M, window=window, lag.max=lmax) val <- Lst$val low.ci <- Lst$lo upp.ci <- Lst$up YmaxR <- Lst$YmaxR # --------------------------- ##Producing cross-correlation plot xvar <- seq(1,N,M) level.lab <- c(paste("Level",1:J),paste("Smooth",J)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(j in 1:(J+1)) { par(mfcol=c(lmax+1,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,1.2,0)) # xaxt <- c(rep("n",lmax),"s",rep("n",lmax)) for(i in c(-lmax:0,lmax:1)+lmax+1) { matplot(1:N,val[[j]][,i], type="l", lty=1, ylim=c(ymin,1), #xaxt=xaxt[i], xlab="", ylab="", main=paste("Lag",i-lmax-1)) abline(h=0) ##Add Straight horiz lines(low.ci[[j]][,i], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(upp.ci[[j]][,i], lty=1, col=2) text(xvar,1, labels=names(xx)[YmaxR[[j]]][xvar], adj=0.25, cex=.8) } par(las=0) mtext('time', side=1, outer=TRUE, adj=0.5) mtext('Local Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5) mtext(level.lab[j], side=3, outer=TRUE, adj=0.5) } ## End(Not run)
Produces an estimate of the multiscale local multiple cross-regression (as defined below) along with approximate confidence intervals.
wave.local.multiple.cross.regression(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)wave.local.multiple.cross.regression(xx, M, window="gauss", lag.max=NULL, p=.975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wlmc chooses the one maximizing the multiple correlation. |
The routine calculates sets of wavelet multiple cross-regressions, one per wavelet level, out of variables, that can be plotted each as lags and leads time series plots.
List of four elements:
cor: |
List of three elements: |
val: list of dataframes, each (rows = #observations, columns = #levels)
providing the point estimates for the wavelet local multiple correlation.
lo: list of dataframes, each (rows = #observations, columns = #lags and leads) providing the lower bounds from the confidence interval.
up: list of dataframes, each (rows = #observations, columns = #lags and leads) providing the upper bounds from the confidence interval.
reg: |
List of |
rval: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of local regression estimates.
rstd: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their standard deviations.
rlow: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their lower bounds.
rupp: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their upper bounds.
rtst: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their t statistic values.
rord: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their index order when sorted by significance.
rpva: numeric array (1st_dim = #observations, 2nd-dim = #lags and leads, 3rd_dim = #regressors+1) of their p values.
YmaxR: |
dataframe (rows = #observations, columns = #levels) giving, at each wavelet level and time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wlmcr chooses at each wavelet level and value in time the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #observations, cols = #regressors) of original data. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 lmax <- 2 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") ## Not run: # Note: WLMCR may take more than 10 seconds of CPU time on some systems Lst <- wave.local.multiple.cross.regression(xx, M, window=window, lag.max=lmax) #, ymaxr=1) # --------------------------- ##Producing cross-correlation plot plot_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE) #, xaxt="s") ##Producing cross-regression plot plot_wave.local.multiple.cross.regression(Lst, lmax, nsig=2) #, xaxt="s") ## End(Not run)## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 lmax <- 2 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") ## Not run: # Note: WLMCR may take more than 10 seconds of CPU time on some systems Lst <- wave.local.multiple.cross.regression(xx, M, window=window, lag.max=lmax) #, ymaxr=1) # --------------------------- ##Producing cross-correlation plot plot_wave.local.multiple.cross.correlation(Lst, lmax, lag.first=FALSE) #, xaxt="s") ##Producing cross-regression plot plot_wave.local.multiple.cross.regression(Lst, lmax, nsig=2) #, xaxt="s") ## End(Not run)
Produces an estimate of the multiscale local multiple regression (as defined below) along with approximate confidence intervals.
wave.local.multiple.regression(xx, M, window="gauss", p = .975, ymaxr=NULL)wave.local.multiple.regression(xx, M, window="gauss", p = .975, ymaxr=NULL)
xx |
A list of |
M |
length of the weight function or rolling window. |
window |
type of weight function or rolling window. Six types are allowed, namely the uniform window, Cleveland or tricube window, Epanechnikov or parabolic window, Bartlett or triangular window, Wendland window and the gaussian window. The letter case and length of the argument are not relevant as long as at least the first four characters are entered. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wlmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple regressions out of variables
that can be plotted in in line graphs with explicit confidence intervals.
List of four elements:
cor: |
List of |
val: numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the point estimates for the wavelet local multiple correlation.
lo: numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the lower bounds from the confidence interval.
up: numeric matrix (rows = #observations, columns = #levels in the wavelet transform object) providing the upper bounds from the confidence interval.
reg: |
List of |
rval: numeric matrix (rows = #observations, cols = #regressors+1) of local regression estimates.
rstd: numeric matrix (rows = #observations, cols = #regressors+1) of their standard deviations.
rlow: numeric matrix (rows = #observations, cols = #regressors+1) of their lower bounds.
rupp: numeric matrix (rows = #observations, cols = #regressors+1) of their upper bounds.
rtst: numeric matrix (rows = #observations, cols = #regressors+1) of their t statistic values.
rord: numeric matrix (rows = #observations, cols = #regressors+1) of their index order when sorted by significance.
rpva: numeric matrix (rows = #observations, cols = #regressors+1) of their p values.
YmaxR: |
dataframe (rows = #observations, columns = #levels in the wavelet transform object) giving, at each wavelet level and time, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wlmr chooses at each wavelet level and value in time the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #observations, cols = #regressors) of original data. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus two random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) xrand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, xrand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.local.multiple.regression(xx, M, window=window) #, ymaxr=1) # --------------------------- ##Producing line plots with CI plot_wave.local.multiple.correlation(Lst) #, xaxt="s") ##Producing regression plots plot_wave.local.multiple.regression(Lst) #, xaxt="s")## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus two random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" M <- 30 window <- "gauss" J <- 3 #trunc(log2(N))-3 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) xrand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, xrand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.local.multiple.regression(xx, M, window=window) #, ymaxr=1) # --------------------------- ##Producing line plots with CI plot_wave.local.multiple.correlation(Lst) #, xaxt="s") ##Producing regression plots plot_wave.local.multiple.regression(Lst) #, xaxt="s")
Produces an estimate of the multiscale multiple correlation (as defined below) along with approximate confidence intervals.
wave.multiple.correlation(xx, N, p = 0.975, ymaxr=NULL)wave.multiple.correlation(xx, N, p = 0.975, ymaxr=NULL)
xx |
A list of |
N |
length of the time series |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple correlations out of variables
that can be plotted in a single graph, as an
alternative to trying to make sense out of sets of wavelet correlations. The code is
based on the calculation, at each wavelet scale, of the square root of the coefficient of
determination in the linear combination of variables for which such coefficient of determination
is a maximum. The code provided here is based on the wave.correlation routine in Brandon
Whitcher's waveslim R package Version: 1.6.4, which in turn is based on wavelet methodology
developed in Percival and Walden (2000); Gençay, Selçuk and Whitcher (2001) and others.
List of two elements:
xy.mulcor: |
numeric matrix with as many rows as levels in the wavelet transform object. The first column provides the point estimate for the wavelet multiple correlation, followed by the lower and upper bounds from the confidence interval. |
YmaxR: |
numeric vector giving, at each wavelet level, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wmc chooses at each wavelet level the variable maximizing the multiple correlation. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) Lst <- wave.multiple.correlation(xx, N = length(xx[[1]][[1]])) returns.modwt.cor <- Lst$xy.mulcor[1:J,] YmaxR <- Lst$YmaxR exchange.names <- c("DEM.USD", "JPY.USD", "RAND") ##Producing plot par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) matplot(2^(0:(J-1)), returns.modwt.cor[-(J+1),], type="b", log="x", pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", ylab="Wavelet Multiple Correlation") axis(side=1, at=2^(0:7)) abline(h=0) text(2^(0:7), min(returns.modwt.cor[-(J+1),])-0.03, labels=exchange.names[YmaxR], adj=0.5, cex=.5)## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) Lst <- wave.multiple.correlation(xx, N = length(xx[[1]][[1]])) returns.modwt.cor <- Lst$xy.mulcor[1:J,] YmaxR <- Lst$YmaxR exchange.names <- c("DEM.USD", "JPY.USD", "RAND") ##Producing plot par(mfrow=c(1,1), las=0, mar=c(5,4,4,2)+.1) matplot(2^(0:(J-1)), returns.modwt.cor[-(J+1),], type="b", log="x", pch="*LU", xaxt="n", lty=1, col=c(1,4,4), xlab="Wavelet Scale", ylab="Wavelet Multiple Correlation") axis(side=1, at=2^(0:7)) abline(h=0) text(2^(0:7), min(returns.modwt.cor[-(J+1),])-0.03, labels=exchange.names[YmaxR], adj=0.5, cex=.5)
Produces an estimate of the multiscale multiple cross-correlation (as defined below).
wave.multiple.cross.correlation(xx, lag.max=NULL, p=.975, ymaxr=NULL)wave.multiple.cross.correlation(xx, lag.max=NULL, p=.975, ymaxr=NULL)
xx |
A list of |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple cross-correlations out of variables
that can be plotted as one single set of graphs (one per wavelet level), as an
alternative to trying to make sense out of sets of wavelet cross-correlations.
The code is based on the calculation, at each wavelet scale, of the square root of the coefficient of
determination in a linear combination of variables that includes a lagged variable for which such coefficient of determination
is a maximum.
List of two elements:
xy.mulcor: numeric matrix with as many rows as levels in the wavelet transform object. The columns provide the point estimates for the wavelet multiple cross-correlations at different lags (and leads). The central column (lag=0) replicates the wavelet multiple correlations. Columns to the right (lag>0) give wavelet multiple cross-correlations with positive lag, i.e. with y=var[Pimax] lagging behind a linear combination of the rest: x[t]hat –> y[t+j]. Columns to the left (lag<0) give wavelet multiple cross-correlations with negative lag, i.e. with y=var[Pimax] leading a linear combination of the rest: y[t-j] –> x[t]hat.
ci.mulcor: list of two elements:
lower: numeric matrix of the same dimensions as xy.mulcor giving the lower bounds of the corresponding confidence interval.
upper: idem for the upper bounds.
YmaxR: numeric vector giving, at each wavelet level, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wmcc chooses at each wavelet level the variable maximizing the multiple correlation.
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2012. Wavelet multiple correlation and cross-correlation: A multiscale analysis of Eurozone stock markets. Physica A: Statistical Mechanics and its Applications 391, 1097–1104. <DOI:10.1016/j.physa.2011.11.002>
## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 lmax <- 36 n <- dim(returns)[1] demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) ##xx <- list(demusd.modwt.bw, jpyusd.modwt.bw) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) Lst <- wave.multiple.cross.correlation(xx, lmax) returns.cross.cor <- Lst$xy.mulcor[1:J,] returns.lower.ci <- Lst$ci.mulcor$lower[1:J,] returns.upper.ci <- Lst$ci.mulcor$upper[1:J,] YmaxR <- Lst$YmaxR # --------------------------- ##Producing correlation plot rownames(returns.cross.cor) <- rownames(returns.cross.cor, do.NULL = FALSE, prefix = "Level ") par(mfrow=c(3,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(i in J:1) { matplot((1:(2*lmax+1)),returns.cross.cor[i,], type="l", lty=1, ylim=c(ymin,1), xaxt="n", xlab="", ylab="", main=rownames(returns.cross.cor)[[i]][1]) if(i<3) {axis(side=1, at=seq(1, 2*lmax+1, by=12), labels=seq(-lmax, lmax, by=12))} #axis(side=2, at=c(-.2, 0, .5, 1)) abline(h=0,v=lmax+1) ##Add Straight horiz and vert Lines to a Plot lines(returns.lower.ci[i,], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(returns.upper.ci[i,], lty=1, col=2) text(1,1, labels=names(xx)[YmaxR[i]], adj=0.25, cex=.8) } par(las=0) mtext('Lag (months)', side=1, outer=TRUE, adj=0.5) mtext('Wavelet Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5)## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 lmax <- 36 n <- dim(returns)[1] demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) ##xx <- list(demusd.modwt.bw, jpyusd.modwt.bw) xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) Lst <- wave.multiple.cross.correlation(xx, lmax) returns.cross.cor <- Lst$xy.mulcor[1:J,] returns.lower.ci <- Lst$ci.mulcor$lower[1:J,] returns.upper.ci <- Lst$ci.mulcor$upper[1:J,] YmaxR <- Lst$YmaxR # --------------------------- ##Producing correlation plot rownames(returns.cross.cor) <- rownames(returns.cross.cor, do.NULL = FALSE, prefix = "Level ") par(mfrow=c(3,2), las=1, pty="m", mar=c(2,3,1,0)+.1, oma=c(1.2,1.2,0,0)) ymin <- -0.1 if (length(xx)<3) ymin <- -1 for(i in J:1) { matplot((1:(2*lmax+1)),returns.cross.cor[i,], type="l", lty=1, ylim=c(ymin,1), xaxt="n", xlab="", ylab="", main=rownames(returns.cross.cor)[[i]][1]) if(i<3) {axis(side=1, at=seq(1, 2*lmax+1, by=12), labels=seq(-lmax, lmax, by=12))} #axis(side=2, at=c(-.2, 0, .5, 1)) abline(h=0,v=lmax+1) ##Add Straight horiz and vert Lines to a Plot lines(returns.lower.ci[i,], lty=1, col=2) ##Add Connected Line Segments to a Plot lines(returns.upper.ci[i,], lty=1, col=2) text(1,1, labels=names(xx)[YmaxR[i]], adj=0.25, cex=.8) } par(las=0) mtext('Lag (months)', side=1, outer=TRUE, adj=0.5) mtext('Wavelet Multiple Cross-Correlation', side=2, outer=TRUE, adj=0.5)
Produces an estimate of the multiscale multiple cross-regression (as defined below).
wave.multiple.cross.regression(xx, lag.max=NULL, p = .975, ymaxr=NULL)wave.multiple.cross.regression(xx, lag.max=NULL, p = .975, ymaxr=NULL)
xx |
A list of |
lag.max |
maximum lag (and lead). If not set, it defaults to half the square root of the length of the original series. |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple cross-regressions out of variables that can be plotted as one single set of graphs (one per wavelet level).
List of four elements:
xy.mulcor |
List of three elements: |
wavemulcor: numeric matrix (rows = #levels, #cols = #lags and leads) with as many rows as levels in the wavelet transform object. The columns provide the point estimates for the wavelet multiple cross-correlations at different lags (and leads). The central column (lag=0) replicates the wavelet multiple correlations. Columns to the right (lag>0) give wavelet multiple cross-correlations with positive lag, i.e. with y=var[Pimax] lagging behind a linear combination of the rest: x[t]hat –> y[t+j]. Columns to the left (lag<0) give wavelet multiple cross-correlations with negative lag, i.e. with y=var[Pimax] leading a linear combination of the rest: y[t-j] –> x[t]hat.
lower: numeric matrix (rows = #levels, #cols = #lags and leads) of lower bounds of the confidence interval.
upper: numeric matrix (rows = #levels, #cols = #lags and leads) of upper bounds of the confidence interval.
xy.mulreg: |
List of seven elements: |
rval: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of regression estimates.
rstd: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their standard deviations.
rlow: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their lower bounds.
rupp: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their upper bounds.
rtst: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their t statistic values.
rord: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their index order when sorted by significance.
rpva: numeric array (1stdim = #levels, 2nddim = #lags and leads, 3rddim = #regressors+1) of their p values.
YmaxR: |
numeric vector giving, at each wavelet level, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wmcr chooses at each wavelet level the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #levels, cols = #regressors) of original data. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 lmax <- 36 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.multiple.cross.regression(xx, lmax) # --------------------------- ##Producing correlation plot plot_wave.multiple.cross.correlation(Lst, lmax) #, by=2) ##Producing regression plot plot_wave.multiple.cross.regression(Lst, lmax) #, by=2)## Based on data from Figure 7.9 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(exchange)) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 lmax <- 36 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) rand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, rand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.multiple.cross.regression(xx, lmax) # --------------------------- ##Producing correlation plot plot_wave.multiple.cross.correlation(Lst, lmax) #, by=2) ##Producing regression plot plot_wave.multiple.cross.regression(Lst, lmax) #, by=2)
Produces an estimate of the multiscale multiple regression (as defined below) along with approximate confidence intervals.
wave.multiple.regression(xx, N, p = 0.975, ymaxr=NULL)wave.multiple.regression(xx, N, p = 0.975, ymaxr=NULL)
xx |
A list of |
N |
length of the time series |
p |
one minus the two-sided p-value for the confidence interval, i.e. the cdf value. |
ymaxr |
index number of the variable whose correlation is calculated against a linear combination of the rest, otherwise at each wavelet level wmc chooses the one maximizing the multiple correlation. |
The routine calculates one single set of wavelet multiple regressions out of variables
that can be plotted in a single graph.
List of four elements:
xy.mulcor: |
numeric matrix with as many rows as levels in the wavelet transform object. The first column provides the point estimate for the wavelet multiple correlation, followed by the lower and upper bounds from the confidence interval. |
xy.mulreg: |
List of seven elements: |
rval: numeric matrix (rows = #levels, cols = #regressors+1) of regression estimates.
rstd: numeric matrix (rows = #levels, cols = #regressors+1) of their standard deviations.
rlow: numeric matrix (rows = #levels, cols = #regressors+1) of their lower bounds.
rupp: numeric matrix (rows = #levels, cols = #regressors+1) of their upper bounds.
rtst: numeric matrix (rows = #levels, cols = #regressors+1) of their t statistic values.
rord: numeric matrix (rows = #levels, cols = #regressors+1) of their index order when sorted by significance.
rpva: numeric matrix (rows = #levels, cols = #regressors+1) of their p values.
YmaxR: |
numeric vector giving, at each wavelet level, the index number of the variable whose correlation is calculated against a linear combination of the rest. By default, wmc chooses at each wavelet level the variable maximizing the multiple correlation. |
data: |
dataframe (rows = #levels, cols = #regressors) of original data. |
Needs waveslim package to calculate dwt or modwt coefficients as inputs to the routine (also for data in the example).
Javier Fernández-Macho, Dpt. of Quantitative Methods, University of the Basque Country, Agirre Lehendakari etorb. 83, E48015 BILBAO, Spain. (email: javier.fernandezmacho at ehu.eus).
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A: Statistical Mechanics, vol. 490, p. 1226–1238. <DOI:10.1016/j.physa.2017.11.050>
## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) xrand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, xrand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.multiple.regression(xx) # --------------------------- ##Producing correlation plot plot_wave.multiple.correlation(Lst) ##Producing regression plot plot_wave.multiple.regression(Lst)## Based on data from Figure 7.8 in Gencay, Selcuk and Whitcher (2001) ## plus one random series. library(wavemulcor) data(exchange) returns <- diff(log(as.matrix(exchange))) returns <- ts(returns, start=1970, freq=12) N <- dim(returns)[1] wf <- "d4" J <- trunc(log2(N))-3 set.seed(140859) demusd.modwt <- brick.wall(modwt(returns[,"DEM.USD"], wf, J), wf) jpyusd.modwt <- brick.wall(modwt(returns[,"JPY.USD"], wf, J), wf) xrand.modwt <- brick.wall(modwt(rnorm(length(returns[,"DEM.USD"])), wf, J), wf) # --------------------------- xx <- list(demusd.modwt, jpyusd.modwt, xrand.modwt) names(xx) <- c("DEM.USD","JPY.USD","rand") Lst <- wave.multiple.regression(xx) # --------------------------- ##Producing correlation plot plot_wave.multiple.correlation(Lst) ##Producing regression plot plot_wave.multiple.regression(Lst)
Simulated data showing correlation structural breaks in Figure 4 of Fernández-Macho (2018).
data("xrand")data("xrand")
A data frame with 512 observations on the following 2 variables.
xrand1a numeric vector
xrand2a numeric vector
and
are highly correlated at low frequencies (long timescales) but uncorrelated at high frequencies (short timescales).
However, during a period of time spanning the second third of the sample () that behavior is reversed so that data become highly correlated at short timescales but uncorrelated at low frequencies.
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A, 492, https://doi.org/10.1016/j.physa.2017.11.050
data(xrand) ## maybe str(xrand) ; plot(xrand) ...data(xrand) ## maybe str(xrand) ; plot(xrand) ...
Simulated data showing correlation structural breaks in Figure 4 of Fernández-Macho (2018).
data("xrand")data("xrand")
A data frame with 512 observations on 1 variables.
xrand1a numeric vector
and
are highly correlated at low frequencies (long timescales) but uncorrelated at high frequencies (short timescales).
However, during a period of time spanning the second third of the sample () that behavior is reversed so that data become highly correlated at short timescales but uncorrelated at low frequencies.
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A, 492, https://doi.org/10.1016/j.physa.2017.11.050
data(xrand) ## maybe str(xrand) ; plot(xrand) ...data(xrand) ## maybe str(xrand) ; plot(xrand) ...
Simulated data showing correlation structural breaks in Figure 4 of Fernández-Macho (2018).
data("xrand")data("xrand")
A data frame with 512 observations on 1 variables.
xrand2a numeric vector
and
are highly correlated at low frequencies (long timescales) but uncorrelated at high frequencies (short timescales).
However, during a period of time spanning the second third of the sample () that behavior is reversed so that data become highly correlated at short timescales but uncorrelated at low frequencies.
Fernández-Macho, J., 2018. Time-localized wavelet multiple regression and correlation, Physica A, 492, https://doi.org/10.1016/j.physa.2017.11.050
data(xrand) ## maybe str(xrand) ; plot(xrand) ...data(xrand) ## maybe str(xrand) ; plot(xrand) ...