| Title: | Asymmetric Price Transmission |
|---|---|
| Description: | The transmission between two time-series prices is assessed. It contains several functions for linear and nonlinear threshold co-integration, and furthermore, symmetric and asymmetric error correction models. |
| Authors: | Changyou Sun [aut, cre] |
| Maintainer: | Changyou Sun <[email protected]> |
| License: | GPL (>= 2) |
| Version: | 4.0 |
| Built: | 2024-12-01 07:58:29 UTC |
| Source: | CRAN |
The transmission between two time-series prices is assessed. The names of functions and datasets reveal the categories they belong to. A prefix of da is for datasets, ci for cointegration, and ecm for error correction model.
The focus is on the price transmission between two price variables. Therefore, objectives like fitting an error correction model for more than two variables are beyond the scope of this package.
| Package: | apt |
| Type: | Package |
| Version: | 4.0 |
| Date: | 2024-09-30 |
| Depends: | R (>= 3.0.0), erer |
| Imports: | car, urca |
| License: | GPL |
| LazyLoad: | yes |
Changyou Sun ([email protected])
Fit a threshold cointegration regression between two time series.
ciTarFit(y, x, model = c('tar','mtar'), lag = 1, thresh = 0, small.win = NULL)ciTarFit(y, x, model = c('tar','mtar'), lag = 1, thresh = 0, small.win = NULL)
y |
dependent or left-side variable for the long-run model; must be a time series object. |
x |
independent or right-side variable for the long-run model; must be a time series object. |
model |
a choice of two models: |
lag |
number of lags for the threshold cointegration regression. |
thresh |
a threshold value (default of zero). |
small.win |
value of a small window for fitting the threshold
cointegration regression; used mainly for lag selection in
|
This is the main function for threshold autoregression regression (TAR) in assessing the nonlinear threshold relation between two time series variables. It can be used to estimate four types of threshold cointegration regressions. These four types are TAR with a threshold value of zero; consistent TAR with a nonzero threshold; MTAR (momentum TAR) with a threshold value of zero; and consistent MTAR with a nonzero threshold. The option of small window will be used in lag selection because a comparison of AIC and BIC values should be based on the same number of regression observations.
Return a list object of class "ciTarFit" with these components:
y |
dependend variable |
x |
independent variable |
model |
model choice |
lag |
number of lags |
thresh |
threshold value |
data.LR |
data used in the long-run regression |
data.CI |
data used in the threshold cointegration regression |
z |
residual from the long-run regression |
lz |
lagged residual from the long-run regression |
ldz |
lagged residual with 1st difference from long-run model |
LR |
long-run regression |
CI |
threshold cointegration regression |
f.phi |
test with a null hypothesis of no threshold cointegration |
f.apt |
test with a null hypothesis of no asymmetric price transmission in the long run |
sse |
value of sum of squared errors |
aic |
value of Akaike Information Criterion |
bic |
value of Bayesian Information Criterion. |
One method is defined as follows:
print:Four main outputs from threshold cointegration regression are shown: long-run regression between the two price variables, threshold cointegration regression, hypothesis test of no cointegration, and hypothesis test of no asymmetric adjustment.
Changyou Sun ([email protected])
Balke, N.S., and T. Fomby. 1997. Threshold cointegration. International Economic Review 38(3):627-645.
Enders, W., and C.W.J. Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16(3):304-311.
Enders, W., and P.L. Siklos. 2001. Cointegration and threshold adjustment. Journal of Business and Economic Statistics 19(2):166-176.
summary.ciTarFit;
ciTarLag for lag selection; and
ciTarThd for threshold selection.
# see example at daVich# see example at daVich
Select the best lag for threshold cointegration regression by AIC and BIC
ciTarLag(y, x, model = c("tar", "mtar"), maxlag = 4, thresh = 0, adjust = TRUE)ciTarLag(y, x, model = c("tar", "mtar"), maxlag = 4, thresh = 0, adjust = TRUE)
y |
dependent or left-side variable for the long-run regression. |
x |
independent or right-side variable for the long-run regression. |
model |
a choice of two models, either tar or mtar. |
maxlag |
maximum number of lags allowed in the search process. |
thresh |
a threshold value. |
adjust |
logical value (default of TRUE) of whether to adjust the window widths so all regressions by lag have the same number of observations |
Estimate the threshold cointegration regressions by lag and then select the best regression by AIC or BIC value. The longer the lag, the smaller the number of observations availabe for estimation. If the windows of regressions by lag are not ajusted, the maximum lag is usually the best lag by AIC or BIC. Theorectially, AIC and BIC from different models should be compared on the basis of the same observation numbers (Ender 2004). adjust shows the effect of this adjustment on the estimation window. By default, the value of adjust should be TRUE.
Return a list object of class "ciTarLag" with the following components:
path |
a data frame of model criterion values by lag, including |
out |
a data frame of the final model selection, including the values of model, maximum lag, threshold value, best lag by AIC, best lag by BIC |
Two methods are defined as follows:
print: This shows the out component in the returned list.
plot:This demonstrates the trend of AIC and BIC changes of threshold cointegration regressions by lag. It facilitates the selection of the best lag for a threshold cointegration model.
Changyou Sun ([email protected])
Enders, W. 2004. Applied Econometric Time Series. John Wiley & Sons, Inc., New York. 480 P.
Enders, W., and C.W.J. Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16(3):304-311.
# see example at daVich# see example at daVich
Select the best threshold for threshold cointegration regression by sum of squared errors
ciTarThd(y, x, model = c('tar', 'mtar'), lag = 1, th.range = 0.15, digits = 3)ciTarThd(y, x, model = c('tar', 'mtar'), lag = 1, th.range = 0.15, digits = 3)
y |
dependent or left-side variable for the long-run regression. |
x |
independent or right-side variable for the long-run regression. |
model |
a choice of two models, either tar or mtar. |
lag |
number of lags. |
th.range |
the percentage of observations to be excluded from the search. |
digits |
number of digits used in rounding outputs. |
The best threshold is determined by fitting the regression for possible threshold values, sorting the results by sum of squared errors (SSE), and selecting the best with the lowest SSE. To have sufficient observations on either side of the threshold value, certain percentage of observations on the top and bottoms are excluded from the search path. This is usually set as 0.15 by the th.range (Chan 1993).
Return a list object of class "ciTarThd" with the following components:
model |
model choice |
lag |
number of lags |
th.range |
the percentage of observations excluded |
th.final |
the best threshold value |
ssef |
the best (i.e., lowest) value of SSE |
obs.tot |
total number of observations in the raw data |
obs.CI |
number of observations used in the threshold cointegration regression |
basic |
a brief summary of the major outputs |
path |
a data frame of the search record (number of regression, threshold value, SSE, AIC, and BIC values). |
Two methods are defined as follows:
print: This shows the basic component in the returned list object.
plot:plotting three graphs in one window; they reveals the relationship between SSE (sum of squared errors), AIC, BIC and the threshold values. The best threshold value is associated with the lowest SSE value.
Changyou Sun ([email protected])
Chan, K.S. 1993. Consistency and limiting distribution of the least squares estimator of a threshold autoregressive model. The Annals of Statistics 21(1):520-533.
Enders, W., and C.W.J. Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16(3):304-311.
# see example at daVich# see example at daVich
This data set contains two unit import prices (dollar per piece) and values (million dollars) of wooden beds from Vietnam and China to the United States.
price.vi |
Monthly price over Janurary 2002 to Janurary 2010 from Vietnam. |
price.ch |
Monthly price over Janurary 2002 to Janurary 2010 from China. |
price.vi |
Monthly value over Janurary 2002 to Janurary 2010 from Vietnam. |
price.ch |
Monthly value over Janurary 2002 to Janurary 2010 from China. |
data(daVich)data(daVich)
A monthly time series from Janurary 2002 to Janurary 2010 with 97 observations for each of the four series.
Under the Harmonized Tariff Schedule (HTS) system, the commodity of wooden beds is classified as HTS 9403.50.9040. The monthly cost-insurance-freight values in dollar and quantities in piece are reported by country from U.S. ITC (2010). The unit price (dollar per piece) is calculated as the ratio of value over quantity by country.
U.S. ITC, 2010. Interactive tariff and trade data web. US International Trade Commision (Assecced on March 1, 2010).
Sun, C. 2011. Price dynamics in the import wooden bed market of the United States. Forest Policy and Economics 13(6): 479-487.
# The following codes reproduce the main results in Sun (2011 FPE). # All the codes have been tested and should work. # 1. Data preparation __________________________________________________________ library(urca); data(daVich) head(daVich); tail(daVich); str(daVich) prVi <- y <- daVich[, 1] prCh <- x <- daVich[, 2] # 2. EG cointegration _________________________________________________________ LR <- lm(y ~ x); summary(LR) (LR.coef <- round(summary(LR)$coefficients, 3)) (ry <- ts(residuals(LR), start=start(prCh), end=end(prCh), frequency =12)) summary(eg <- ur.df(ry, type=c("none"), lags=1)); plot(eg) (eg4 <- Box.test(eg@res, lag = 4, type="Ljung") ) (eg8 <- Box.test(eg@res, lag = 8, type="Ljung") ) (eg12 <- Box.test(eg@res, lag = 12, type="Ljung")) # 3. TAR + Cointegration ______________________________________________________ # best threshold t3 <- ciTarThd(y=prVi, x=prCh, model="tar", lag=0) (th.tar <- t3$basic); plot(t3) for (i in 1:12) { # 20 seconds t3a <- ciTarThd(y=prVi, x=prCh, model="tar", lag=i) th.tar[i+2] <- t3a$basic[,2] } th.tar t4 <- ciTarThd(y=prVi, x=prCh, model="mtar", lag=0); (th.mtar <- t4$basic) plot(t4) for (i in 1:12) { t4a <- ciTarThd(y=prVi, x=prCh, model="mtar", lag=i) th.mtar[i+2] <- t4a$basic[,2] } th.mtar # The following threshold values are specific to this data. They HAVE TO be # revised for another data set. Otherwise, various errors will occur. t.tar <- -8.041; t.mtar <- -0.451 # lag = 0 to 4 # t.tar <- -8.701 ; t.mtar <- -0.451 # lag = 5 to 12 # lag selection mx <- 12 (g1 <-ciTarLag(y=prVi, x=prCh, model="tar", maxlag=mx, thresh= 0)); plot(g1) (g2 <-ciTarLag(y=prVi, x=prCh, model="mtar",maxlag=mx, thresh= 0)); plot(g2) (g3 <-ciTarLag(y=prVi, x=prCh, model="tar", maxlag=mx, thresh=t.tar)); plot(g3) (g4 <-ciTarLag(y=prVi, x=prCh, model="mtar",maxlag=mx, thresh=t.mtar)); plot(g4) # Table 3 Results of EG and threshold cointegration tests # Note: Some results in Table 3 in the published paper were incorrect because # of a mistake made when the paper was done in 2009. I found the mistake when # the package was build in later 2010. For example, for the consistent MTAR, # the coefficient for the positive term was reported as -0.251 (-2.130) but # it should be -0.106 (-0.764), as cacluated from below codes. # The main conclusion about the research issue is still qualitatively the same. vv <- 3 (f1 <- ciTarFit(y=prVi, x=prCh, model="tar", lag=vv, thresh=0 )) (f2 <- ciTarFit(y=prVi, x=prCh, model="tar", lag=vv, thresh=t.tar )) (f3 <- ciTarFit(y=prVi, x=prCh, model="mtar", lag=vv, thresh=0 )) (f4 <- ciTarFit(y=prVi, x=prCh, model="mtar", lag=vv, thresh=t.mtar)) r0 <- cbind(summary(f1)$dia, summary(f2)$dia, summary(f3)$dia, summary(f4)$dia) diag <- r0[c(1:4, 6:7, 12:14, 8, 9, 11), c(1,2,4,6,8)] rownames(diag) <- 1:nrow(diag); diag e1 <- summary(f1)$out; e2 <- summary(f2)$out e3 <- summary(f3)$out; e4 <- summary(f4)$out; rbind(e1, e2, e3, e4) ee <- list(e1, e2, e3, e4); vect <- NULL for (i in 1:4) { ef <- data.frame(ee[i]) vect2 <- c(paste(ef[3, "estimate"], ef[3, "sign"], sep=""), paste("(", ef[3, "t.value"], ")", sep=""), paste(ef[4, "estimate"], ef[4, "sign"], sep=""), paste("(", ef[4, "t.value"], ")", sep="")) vect <- cbind(vect, vect2) } item <- c("pos.coeff","pos.t.value", "neg.coeff","neg.t.value") ve <- data.frame(cbind(item, vect)); colnames(ve) <- colnames(diag) ( res.CI <- rbind(diag, ve)[c(1:2, 13:16, 3:12), ] ) rownames(res.CI) <- 1:nrow(res.CI) # 4. APT + ECM _______________________________________________________________ (sem <- ecmSymFit(y=prVi, x=prCh, lag=4)); names(sem) aem <- ecmAsyFit(y=prVi, x=prCh,lag=4, model="mtar", split=TRUE, thresh=t.mtar) aem (ccc <- summary(aem)) coe <- cbind(as.character(ccc[1:19, 2]), paste(ccc[1:19, "estimate"], ccc$signif[1:19], sep=""), ccc[1:19, "t.value"], paste(ccc[20:38,"estimate"], ccc$signif[20:38],sep=""), ccc[20:38,"t.value"]) colnames(coe) <- c("item", "China.est", "China.t", "Vietnam.est","Vietnam.t") (edia <- ecmDiag(aem, 3)) (ed <- edia[c(1,6,7,8,9), ]) ed2 <- cbind(ed[,1:2], "_", ed[,3], "_") colnames(ed2) <- colnames(coe) (tes <- ecmAsyTest(aem)$out) (tes2 <- tes[c(2,3,5,11,12,13,1), -1]) tes3 <- cbind(as.character(tes2[,1]), paste(tes2[,2], tes2[,6], sep=''), paste("[", round(tes2[,4],2), "]", sep=''), paste(tes2[,3], tes2[,7], sep=''), paste("[", round(tes2[,5],2), "]", sep='')) colnames(tes3) <- colnames(coe) (coe <- data.frame(apply(coe, 2, as.character), stringsAsFactors=FALSE)) (ed2 <- data.frame(apply(ed2, 2, as.character), stringsAsFactors=FALSE)) (tes3 <- data.frame(apply(tes3,2, as.character), stringsAsFactors=FALSE)) table.4 <- data.frame(rbind(coe, ed2, tes3)) table.4# The following codes reproduce the main results in Sun (2011 FPE). # All the codes have been tested and should work. # 1. Data preparation __________________________________________________________ library(urca); data(daVich) head(daVich); tail(daVich); str(daVich) prVi <- y <- daVich[, 1] prCh <- x <- daVich[, 2] # 2. EG cointegration _________________________________________________________ LR <- lm(y ~ x); summary(LR) (LR.coef <- round(summary(LR)$coefficients, 3)) (ry <- ts(residuals(LR), start=start(prCh), end=end(prCh), frequency =12)) summary(eg <- ur.df(ry, type=c("none"), lags=1)); plot(eg) (eg4 <- Box.test(eg@res, lag = 4, type="Ljung") ) (eg8 <- Box.test(eg@res, lag = 8, type="Ljung") ) (eg12 <- Box.test(eg@res, lag = 12, type="Ljung")) # 3. TAR + Cointegration ______________________________________________________ # best threshold t3 <- ciTarThd(y=prVi, x=prCh, model="tar", lag=0) (th.tar <- t3$basic); plot(t3) for (i in 1:12) { # 20 seconds t3a <- ciTarThd(y=prVi, x=prCh, model="tar", lag=i) th.tar[i+2] <- t3a$basic[,2] } th.tar t4 <- ciTarThd(y=prVi, x=prCh, model="mtar", lag=0); (th.mtar <- t4$basic) plot(t4) for (i in 1:12) { t4a <- ciTarThd(y=prVi, x=prCh, model="mtar", lag=i) th.mtar[i+2] <- t4a$basic[,2] } th.mtar # The following threshold values are specific to this data. They HAVE TO be # revised for another data set. Otherwise, various errors will occur. t.tar <- -8.041; t.mtar <- -0.451 # lag = 0 to 4 # t.tar <- -8.701 ; t.mtar <- -0.451 # lag = 5 to 12 # lag selection mx <- 12 (g1 <-ciTarLag(y=prVi, x=prCh, model="tar", maxlag=mx, thresh= 0)); plot(g1) (g2 <-ciTarLag(y=prVi, x=prCh, model="mtar",maxlag=mx, thresh= 0)); plot(g2) (g3 <-ciTarLag(y=prVi, x=prCh, model="tar", maxlag=mx, thresh=t.tar)); plot(g3) (g4 <-ciTarLag(y=prVi, x=prCh, model="mtar",maxlag=mx, thresh=t.mtar)); plot(g4) # Table 3 Results of EG and threshold cointegration tests # Note: Some results in Table 3 in the published paper were incorrect because # of a mistake made when the paper was done in 2009. I found the mistake when # the package was build in later 2010. For example, for the consistent MTAR, # the coefficient for the positive term was reported as -0.251 (-2.130) but # it should be -0.106 (-0.764), as cacluated from below codes. # The main conclusion about the research issue is still qualitatively the same. vv <- 3 (f1 <- ciTarFit(y=prVi, x=prCh, model="tar", lag=vv, thresh=0 )) (f2 <- ciTarFit(y=prVi, x=prCh, model="tar", lag=vv, thresh=t.tar )) (f3 <- ciTarFit(y=prVi, x=prCh, model="mtar", lag=vv, thresh=0 )) (f4 <- ciTarFit(y=prVi, x=prCh, model="mtar", lag=vv, thresh=t.mtar)) r0 <- cbind(summary(f1)$dia, summary(f2)$dia, summary(f3)$dia, summary(f4)$dia) diag <- r0[c(1:4, 6:7, 12:14, 8, 9, 11), c(1,2,4,6,8)] rownames(diag) <- 1:nrow(diag); diag e1 <- summary(f1)$out; e2 <- summary(f2)$out e3 <- summary(f3)$out; e4 <- summary(f4)$out; rbind(e1, e2, e3, e4) ee <- list(e1, e2, e3, e4); vect <- NULL for (i in 1:4) { ef <- data.frame(ee[i]) vect2 <- c(paste(ef[3, "estimate"], ef[3, "sign"], sep=""), paste("(", ef[3, "t.value"], ")", sep=""), paste(ef[4, "estimate"], ef[4, "sign"], sep=""), paste("(", ef[4, "t.value"], ")", sep="")) vect <- cbind(vect, vect2) } item <- c("pos.coeff","pos.t.value", "neg.coeff","neg.t.value") ve <- data.frame(cbind(item, vect)); colnames(ve) <- colnames(diag) ( res.CI <- rbind(diag, ve)[c(1:2, 13:16, 3:12), ] ) rownames(res.CI) <- 1:nrow(res.CI) # 4. APT + ECM _______________________________________________________________ (sem <- ecmSymFit(y=prVi, x=prCh, lag=4)); names(sem) aem <- ecmAsyFit(y=prVi, x=prCh,lag=4, model="mtar", split=TRUE, thresh=t.mtar) aem (ccc <- summary(aem)) coe <- cbind(as.character(ccc[1:19, 2]), paste(ccc[1:19, "estimate"], ccc$signif[1:19], sep=""), ccc[1:19, "t.value"], paste(ccc[20:38,"estimate"], ccc$signif[20:38],sep=""), ccc[20:38,"t.value"]) colnames(coe) <- c("item", "China.est", "China.t", "Vietnam.est","Vietnam.t") (edia <- ecmDiag(aem, 3)) (ed <- edia[c(1,6,7,8,9), ]) ed2 <- cbind(ed[,1:2], "_", ed[,3], "_") colnames(ed2) <- colnames(coe) (tes <- ecmAsyTest(aem)$out) (tes2 <- tes[c(2,3,5,11,12,13,1), -1]) tes3 <- cbind(as.character(tes2[,1]), paste(tes2[,2], tes2[,6], sep=''), paste("[", round(tes2[,4],2), "]", sep=''), paste(tes2[,3], tes2[,7], sep=''), paste("[", round(tes2[,5],2), "]", sep='')) colnames(tes3) <- colnames(coe) (coe <- data.frame(apply(coe, 2, as.character), stringsAsFactors=FALSE)) (ed2 <- data.frame(apply(ed2, 2, as.character), stringsAsFactors=FALSE)) (tes3 <- data.frame(apply(tes3,2, as.character), stringsAsFactors=FALSE)) table.4 <- data.frame(rbind(coe, ed2, tes3)) table.4
Estimate an asymmetric error correction model (ECM) for two time series.
ecmAsyFit(y, x, lag = 1, split = TRUE, model = c("linear", "tar", "mtar"), thresh = 0)ecmAsyFit(y, x, lag = 1, split = TRUE, model = c("linear", "tar", "mtar"), thresh = 0)
y |
dependent or left-side variable for the long-run regression. |
x |
independent or right-side variable for the long-run regression. |
lag |
number of lags for variables on the right side. |
split |
a logical value (default of TRUE) of whether the right-hand variables should be split into positive and negative parts. |
model |
a choice of three models: linear, tar , or mtar cointegration. |
thresh |
a threshold value; this is only required when the model is specified as 'tar' or 'mtar.' |
There are two specficiations of an asymmetric ECM. The first one is how to calculate the error correction terms. One way is through linear two-step Engle Granger approach, as specificied by model="linear". The other two ways are threshold cointegration by either 'tar' or 'mtar' with a threshold value. The second specification is related to the possible asymmetric price transmission in the lagged price variables, as specified in split = TRUE. Note that the linear cointegration specification is a special case of the threshold cointegration. A model with model="linear" is the same as a model with model="tar", thresh = 0.
Return a list object of class "ecm" and "ecmAsyFit" with the following components:
y |
dependend variable |
x |
independent variable |
lag |
number of lags |
split |
logical value of whether the right-hand variables are split |
model |
model choice |
IndVar |
data frame of the right-hand variables used in the ECM |
name.x |
name of the independent variable |
name.y |
name of the dependent variable |
ecm.y |
ECM regression for the dependent variable |
ecm.x |
ECM regression for the independent variable |
data |
all the data combined for the ECM |
thresh |
thresh value for TAR and MTAR model |
Two methods are defined as follows:
print:showing the key outputs.
summary:summarizing thekey outputs.
Changyou Sun ([email protected])
Enders, W., and C.W.J. Granger. 1998. Unit-root tests and asymmetric adjustment with an example using the term structure of interest rates. Journal of Business & Economic Statistics 16(3):304-311.
print.ecm; summary.ecm; ecmDiag; and ecmAsyTest.
# see example at daVich# see example at daVich
Conduct several F-tests on the coefficients from asymmetric ECM.
ecmAsyTest(w, digits = 3)ecmAsyTest(w, digits = 3)
w |
an object of 'ecmAsyFit' class. |
digits |
number of digits used in rounding outputs. |
There are two ECM equations for the two price series. In each equation, four types of hypotheses are tested; equilibrium adjustment path symmetry on the error correction terms (H1), Granger causality test (H2), distributed lag symmetry at each lag (H3), and cumulative asymmetry of all lags (H4). The latter two tests are only feasible and availabe for models with split variables. The number of H3 tests is equal to the number of lags.
Return a list object with the following components:
H1ex |
H01 in equation x: equilibrium adjustment path symmetry |
H1ey |
H01 in equation y: equilibrium adjustment path symmetry |
H2xx |
H02 in equation x: x does not Granger cause x |
H2yx |
H02 in equation y: x does not Granger cause y |
H2xy |
H02 in equation x: y does not Granger cause x |
H2yy |
H02 in equation y: y does not Granger cause y |
H3xx |
H03 in equation x: distributed lag symmetry of x at each lag |
H3yx |
H03 in equation y: distributed lag symmetry of x at each lag |
H3xy |
H03 in equation x: distributed lag symmetry of y at each lag |
H3yy |
H03 in equation y: distributed lag symmetry of y at each lag |
H4xx |
H04 in equation x: cumulative asymmetry of x for all lags |
H4yx |
H04 in equation y: cumulative asymmetry of x for all lags |
H4xy |
H04 in equation x: cumulative asymmetry of y for all lags |
H4yy |
H04 in equation y: cumulative asymmetry of y for all lags |
out |
summary of the four types of hypothesis tests |
One method is are defined as follows:
print: This shows the out component in the returned list object.
Changyou Sun ([email protected])
Frey, G., and M. Manera. 2007. Econometric models of asymmetric price transmission. Journal of Economic Surveys 21(2):349-415.
# see example at daVich# see example at daVich
Report a set of diagnostic statistics for symmetric or asymmetric error correction models
ecmDiag(m, digits = 2)ecmDiag(m, digits = 2)
m |
an object of class |
digits |
number of digits used in rounding outputs. |
Compute several diagnostic statistics for each ECM equation. This is mainly used to assess the serial correlation in the residuals and model adequacy.
Return a data frame object with the following components by equation: R-squared, Adjusted R-squared, F-statistic, Durbin Watson statistic, p-value for DW statistic, AIC, BIC, and p-value of Ljung_Box Q statistics with 4, 8, 12 autocorrelation coefficients.
Changyou Sun ([email protected])
Enders, W. 2004. Applied Econometric Time Series. John Wiley & Sons, Inc., New York. 480 P.
ecmAsyFit; ecmSymFit; and ecmDiag.
# see example at daVich# see example at daVich
Estimate a symmetric error correction model (ECM) for two time series.
ecmSymFit(y, x, lag = 1)ecmSymFit(y, x, lag = 1)
y |
dependent or left-side variable for the long-run regression. |
x |
independent or right-side variable for the long-run regression. |
lag |
number of lags for variables on the right side. |
The package apt focuses on price transmission between two series. This function estimates a standard error correction model for two time series. While it can be extended for more than two series, it is beyond the objective of the package now.
Return a list object of class "ecm" and "ecmSymFit" with the following components:
y |
dependend variable |
x |
independent variable |
lag |
number of lags |
data |
all the data combined for the ECM |
IndVar |
data frame of the right-hand variables used in the ECM |
name.x |
name of the independent variable |
name.y |
name of the dependent variable |
ecm.y |
ECM regression for the dependent variable |
ecm.x |
ECM regression for the independent variable |
Changyou Sun ([email protected])
Enders, W. 2004. Applied Econometric Time Series. John Wiley & Sons, Inc., New York. 480 P.
print.ecm; summary.ecm; ecmDiag; and ecmAsyFit.
# see example at daVich# see example at daVich
Show main outputs from symmetric ecmSymFit or asymmetric ecmAsyFit error correction models.
## S3 method for class 'ecm' print(x, ...)## S3 method for class 'ecm' print(x, ...)
x |
an object of class |
... |
additional arguments to be passed. |
This is the print method for ecmAsyFit or ecmSymFit to show main model outputs.
Summary results of the two ECM equations are shown for the two focal price series.
Changyou Sun ([email protected])
# see example at daVich# see example at daVich
This summarizes the main results from threshold cointegration regression.
## S3 method for class 'ciTarFit' summary(object, digits=3, ...)## S3 method for class 'ciTarFit' summary(object, digits=3, ...)
object |
an object of class 'ciTarFit'. |
digits |
number of digits for rounding outputs. |
... |
additional arguments to be passed. |
This wraps up the outputs from threshold cointegration regression in two data frames, one for diagnostic statistics and the other for coeffients.
A list with two data frames. dia contains the main model specifications and hypothesis test results. out contains the regression results for both the long run (LR) and threshold cointegration (CI).
Changyou Sun ([email protected])
# see example at daVich# see example at daVich
This summarizes the main results from error correction models.
## S3 method for class 'ecm' summary(object, digits=3, ...)## S3 method for class 'ecm' summary(object, digits=3, ...)
object |
an object of class |
digits |
number of digits for rounding outputs |
... |
additional arguments to be passed. |
This wraps up the coefficents and statistics from ECM by equation.
A data frame object with coefficients and related statistics by equation.
Changyou Sun ([email protected])
# see example at daVich# see example at daVich