| Title: | Panel Cointegration Tests |
|---|---|
| Description: | Computation of the Pedroni (1999) panel cointegration test statistics. Reported are the empirical and the standardized values. |
| Authors: | Georgi Marinov |
| Maintainer: | Georgi Marinov <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.1 |
| Built: | 2024-11-01 11:22:09 UTC |
| Source: | CRAN |
Computation of the Pedroni (1999) panel cointegration test statistics. Reported are the empirical values and the standardized values (as suggested in Pedroni, 1999).
| Package: | pco |
| Type: | Package |
| Version: | 1.0.1 |
| Date: | 2015-07-26 |
| License: | GPL-2 |
Computation of the Pedroni (1999) panel cointegration test statistics. Reported are the empirical and the standardized values (as suggested in Pedroni, 1999).
The package includes two functions: 'pedroni99' is for the bivariate case (one Y, one X, no NA values), data must be in matrices (easier for use); 'pedroni99m' is for the multivariate case (one Y, multiple X, no NA values), data must be in an array of all variables.
Georgi Marinov Maintainer: Georgi Marinov <[email protected]>
Newey, Whitney K.; West, Kenneth D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies 61 (4): 631-654.
Pedroni, Peter, 1999. "Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-70, Special I.
data(gdi) data(gds) pedroni99(gdi, gds) xx<-array(cumsum(rnorm(10000)),dim=c(100,20,5)) pedroni99m(xx)data(gdi) data(gds) pedroni99(gdi, gds) xx<-array(cumsum(rnorm(10000)),dim=c(100,20,5)) pedroni99m(xx)
Gross domestic investment as a share of GDP (in percent) for 25 high income OECD countries, 1973-2013. Retrieved from the World Development Indicators Worldbank Database.
data(gdi)data(gdi)
The format is: num [1:41, 1:25] 29.1 28.6 25.9 26.3 25.9 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:41] "X1973..YR1973." "X1974..YR1974." "X1975..YR1975." "X1976..YR1976." ... ..$ : chr [1:25] "AUS" "AUT" "BEL" "CAN" ...
Gross fixed capital formation (percent of GDP), "Gross fixed capital formation (NE.GDI.FTOT.ZS, formerly gross domestic fixed investment).", "World Bank national accounts data, and OECD National Accounts data files."
http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators
The World Bank: Dataset name: Gross fixed capital formation (percent of GDP).
data(gdi) plot(gdi) ## maybe str(gdi) ; plot(gdi) ...data(gdi) plot(gdi) ## maybe str(gdi) ; plot(gdi) ...
Gross domestic savings as a share of GDP (in percent) for 25 high income OECD countries, 1973-2013. Retrieved from the World Development Indicators Worldbank Database.
data(gds)data(gds)
The format is: num [1:41, 1:25] 31.5 30.5 26.4 26.6 26.4 ... - attr(*, "dimnames")=List of 2 ..$ : chr [1:41] "X1973..YR1973." "X1974..YR1974." "X1975..YR1975." "X1976..YR1976." ... ..$ : chr [1:25] "AUS" "AUT" "BEL" "CAN" ...
Gross domestic savings (percent of GDP), Gross domestic savings (NY.GDS.TOTL.ZS) are calculated as GDP less final consumption expenditure (total consumption)., "World Bank national accounts data, and OECD National Accounts data files."
http://databank.worldbank.org/data/reports.aspx?source=world-development-indicators
The World Bank: Dataset name: Gross domestic savings (percent of GDP).
data(gds) plot(gds) ## maybe str(gds) ; plot(gds) ...data(gds) plot(gds) ## maybe str(gds) ; plot(gds) ...
Computation of the Pedroni (1999) panel cointegration test statistics. All statistics are asymptotically normal. Reported are their empirical values and their standardized values (as suggested in Pedroni, 1999).
pedroni99(Y, X, kk = 0, type.stat = 1, ka = 2)pedroni99(Y, X, kk = 0, type.stat = 1, ka = 2)
Y |
The 'dependent' variable in the cointegration regression. Must be a matrix (TxN), 'time' in rows, 'individuals' in columns. No missing values are allowed. |
X |
The 'independent' variable in the cointegration regression. Must be a matrix (TxN), 'time' in rows, 'individuals' in columns. No missing values are allowed. |
kk |
Parameter for the Newey-West (1994) long term variance estimation (number of lags). Can be a vector, with a different value for each individual series, or a scalar. By default it is set to 'round(4 * (T/100)^(2/9))'. |
type.stat |
Type of the main regresion: 1 - 'none', 2 - 'intercept', 3 - 'intercept and time trend'. |
ka |
Number of lags for the ADF type regression on residuals, for the parametric statistics. |
The function closely follows the instructions in Pedroni (1999). Calculated and reported are the 7 statistics on page 660 in Pedroni (1999) for the bivariate case. Also reported are their standardized values, as described on page 665 and by use of the adjustment terms in Table 2, page 666, op.cit. H0 is 'no cointegration'.
CALL |
The result of 'match.call()'. |
METHOD |
Title of the test. |
STATISTIC |
The 7 test statistics in Pedroni (1999), in two columns - for the empirical and the standardized values. |
Under H0 ('no cointegration') the autoregressive coefficients, gamma_i = 1 for all i, versus H1: gamma_i < 1 for all i.
The standardized values of the test statistics are asymptotically normal (0,1) under H0.
Georgi Marinov
Newey, Whitney K.; West, Kenneth D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies 61 (4): 631-654.
Pedroni, Peter, 1999. "Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-70, Special I.
data(gdi) data(gds) # An illustration for the (non-existent) Feldstein-Horioka paradox. pedroni99(gdi,gds) ## The function is currently defined as function (Y, X, kk = 0, type.stat = 1, ka = 2) { ff <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] - 1)$residuals }) } ff1 <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l])$residuals }) } ff2 <- function(Y1, X1) { NN = ncol(X1) trend = 1:nrow(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] + trend)$residuals }) } nw <- function(xx, ki) { tt = length(xx) (1/tt) * sum(sapply(1:ki, function(s) { (1 - s/(ki + 1)) * sum(xx[(s + 1):tt] * xx[1:(tt - s)]) })) } adfl<-function (ee, lags) { nn<-length(ee) z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] zd<-matrix(cbind(rep(z,lags)),ncol=lags) ii<-embed(1:nn,lags) ii<-ii[-(nrow(ii)),] zd<-zd-ee[ii] zd<-zd[,-1] z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] return(lm(z ~ zl + zd -1)$residuals) } Y <- as.matrix(Y) X <- as.matrix(X) if (any((dim(Y) != dim(X)))) { stop("Y and X are not compatible.") } na.fail(Y) na.fail(X) TD = nrow(X) N = ncol(X) if (is.vector(kk) && length(kk) == N) { k = kk } else if (kk > 0) { k = rep(round(kk), N) } else { i = round(4 * (TD/100)^(2/9)) k = rep(i, N) } if (ka < 2) { ka = 2 warning("Parameter 'ka' was changed to 2.") } ka <- as.vector(ka) if (length(ka) != N) { ka <- rep(ka[1], N) } stats <- matrix(nrow = 7, ncol = 2) rownames(stats) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stats) <- c("empirical", "standardized") statsm <- cbind(c(6.982, -6.388, -1.662, -1.662, -9.889, -1.992, -1.992), c(11.754, -9.495, -2.177, -2.177, -12.938, -2.453, -2.453), c(21.162, -14.011, -2.648, -2.648, -17.359, -2.872, -2.872)) rownames(statsm) <- c("nipanel", "rhopanel", "tpanel", "tpanelp", "rhogroup", "tgroup", "tgroupp") colnames(statsm) <- c("none", "intercept", "trend") statsv <- cbind(c(81.145, 64.288, 1.559, 1.559, 41.943, 0.649, 0.649), c(104.546, 57.61, 0.964, 0.964, 51.49, 0.618, 0.618), c(160.249, 64.219, 0.69, 0.69, 66.387, 0.555, 0.555)) rownames(statsv) <- c("nipanel", "rhopanel", "tpanel", "tpanelp", "rhogroup", "tgroup", "tgroupp") colnames(statsv) <- c("none", "intercept", "trend") e <- matrix(ncol = N, nrow = TD) if (type.stat == 2) { e <- ff1(Y, X) } else if (type.stat == 3) { e <- ff2(Y, X) } else { e <- ff(Y, X) type.stat = 1 } De <- diff(e) estar <- e Destar <- diff(estar) DX <- diff(X) DY <- diff(Y) eta <- matrix(ncol = ncol(DX), nrow = nrow(DX)) eta <- ff(DY, DX) L11hat2 <- sapply(1:N, function(i) { (1/nrow(eta)) * sum(eta[, i]^2) + 2 * nw(eta[, i], k[i]) }) mu <- matrix(ncol = ncol(DX), nrow = nrow(DX)) mu <- ff(e[2:TD, ], e[1:(TD - 1), ]) lambdahat <- sapply(1:N, function(i) { nw(mu[, i], k[i]) }) mustar <- matrix(ncol = ncol(DX), nrow = nrow(DX)) mustar <- sapply(1:N, function(i) { adfl(e[, i], ka[i]) }) shatstar2 <- sapply(1:N, function(i) { (1/nrow(mustar)) * sum(mustar[, i]^2) }) stildestar2 <- (1/N) * sum(shatstar2) shat2 <- sapply(1:N, function(i) { (1/nrow(mu)) * sum(mu[, i]^2) }) sigmahat2 <- shat2 + 2 * lambdahat sigmatilde2 <- (1/N) * sum(L11hat2^(-2) * sigmahat2) nipa <- sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * (e[1:(TD - 1), i]^2)) })) lel <- sum(sapply(1:N, function(i) { (L11hat2[i]^(-2)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[(ttt), i] * De[ttt, i] - lambdahat[i]) })) })) nipanel <- (TD^2) * (N^(3/2)) * nipa^(-1) stats[1, 1] <- nipanel rhopanel <- TD * (N^(1/2)) * (nipa^(-1)) * lel stats[2, 1] <- rhopanel tpanelnonpar <- ((sigmatilde2 * nipa)^(-1/2)) * lel stats[3, 1] <- tpanelnonpar tpanelpar <- ((stildestar2 * sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * estar[1:(nrow(estar) - 1), i]^2) })))^(-1/2)) * sum(sapply(1:N, function(i) { sum(sapply(1:(nrow(Destar)), function(ttt) { (L11hat2[i]^(-2)) * (estar[ttt, i] * Destar[ttt, i]) })) })) stats[4, 1] <- tpanelpar rhogroup <- TD * (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sum(e[1:(nrow(e) - 1), i]^2))^(-1)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[ttt, i] * De[ttt, i] - lambdahat[i]) })) })) stats[5, 1] <- rhogroup tgroupnonpar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sigmahat2[i] * sum(e[1:(nrow(e) - 1), i]^2))^(-1/2)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[(ttt), i] * De[ttt, i] - lambdahat[i]) })) })) stats[6, 1] <- tgroupnonpar tgrouppar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { (sum(shat2[i] * estar[1:(nrow(estar) - 1), i]^2))^(-1/2) * sum(estar[1:(nrow(estar) - 1), i] * Destar[1:(nrow(estar) - 1), i]) })) stats[7, 1] <- tgrouppar stats[, 2] <- sapply(1:7, function(i) { (stats[i, 1] - statsm[i, type.stat] * sqrt(N))/sqrt(statsv[i, type.stat]) }) list(CALL = match.call(), METHOD = "Pedroni(1999) panel tests for cointegration", STATISTIC = stats) }data(gdi) data(gds) # An illustration for the (non-existent) Feldstein-Horioka paradox. pedroni99(gdi,gds) ## The function is currently defined as function (Y, X, kk = 0, type.stat = 1, ka = 2) { ff <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] - 1)$residuals }) } ff1 <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l])$residuals }) } ff2 <- function(Y1, X1) { NN = ncol(X1) trend = 1:nrow(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] + trend)$residuals }) } nw <- function(xx, ki) { tt = length(xx) (1/tt) * sum(sapply(1:ki, function(s) { (1 - s/(ki + 1)) * sum(xx[(s + 1):tt] * xx[1:(tt - s)]) })) } adfl<-function (ee, lags) { nn<-length(ee) z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] zd<-matrix(cbind(rep(z,lags)),ncol=lags) ii<-embed(1:nn,lags) ii<-ii[-(nrow(ii)),] zd<-zd-ee[ii] zd<-zd[,-1] z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] return(lm(z ~ zl + zd -1)$residuals) } Y <- as.matrix(Y) X <- as.matrix(X) if (any((dim(Y) != dim(X)))) { stop("Y and X are not compatible.") } na.fail(Y) na.fail(X) TD = nrow(X) N = ncol(X) if (is.vector(kk) && length(kk) == N) { k = kk } else if (kk > 0) { k = rep(round(kk), N) } else { i = round(4 * (TD/100)^(2/9)) k = rep(i, N) } if (ka < 2) { ka = 2 warning("Parameter 'ka' was changed to 2.") } ka <- as.vector(ka) if (length(ka) != N) { ka <- rep(ka[1], N) } stats <- matrix(nrow = 7, ncol = 2) rownames(stats) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stats) <- c("empirical", "standardized") statsm <- cbind(c(6.982, -6.388, -1.662, -1.662, -9.889, -1.992, -1.992), c(11.754, -9.495, -2.177, -2.177, -12.938, -2.453, -2.453), c(21.162, -14.011, -2.648, -2.648, -17.359, -2.872, -2.872)) rownames(statsm) <- c("nipanel", "rhopanel", "tpanel", "tpanelp", "rhogroup", "tgroup", "tgroupp") colnames(statsm) <- c("none", "intercept", "trend") statsv <- cbind(c(81.145, 64.288, 1.559, 1.559, 41.943, 0.649, 0.649), c(104.546, 57.61, 0.964, 0.964, 51.49, 0.618, 0.618), c(160.249, 64.219, 0.69, 0.69, 66.387, 0.555, 0.555)) rownames(statsv) <- c("nipanel", "rhopanel", "tpanel", "tpanelp", "rhogroup", "tgroup", "tgroupp") colnames(statsv) <- c("none", "intercept", "trend") e <- matrix(ncol = N, nrow = TD) if (type.stat == 2) { e <- ff1(Y, X) } else if (type.stat == 3) { e <- ff2(Y, X) } else { e <- ff(Y, X) type.stat = 1 } De <- diff(e) estar <- e Destar <- diff(estar) DX <- diff(X) DY <- diff(Y) eta <- matrix(ncol = ncol(DX), nrow = nrow(DX)) eta <- ff(DY, DX) L11hat2 <- sapply(1:N, function(i) { (1/nrow(eta)) * sum(eta[, i]^2) + 2 * nw(eta[, i], k[i]) }) mu <- matrix(ncol = ncol(DX), nrow = nrow(DX)) mu <- ff(e[2:TD, ], e[1:(TD - 1), ]) lambdahat <- sapply(1:N, function(i) { nw(mu[, i], k[i]) }) mustar <- matrix(ncol = ncol(DX), nrow = nrow(DX)) mustar <- sapply(1:N, function(i) { adfl(e[, i], ka[i]) }) shatstar2 <- sapply(1:N, function(i) { (1/nrow(mustar)) * sum(mustar[, i]^2) }) stildestar2 <- (1/N) * sum(shatstar2) shat2 <- sapply(1:N, function(i) { (1/nrow(mu)) * sum(mu[, i]^2) }) sigmahat2 <- shat2 + 2 * lambdahat sigmatilde2 <- (1/N) * sum(L11hat2^(-2) * sigmahat2) nipa <- sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * (e[1:(TD - 1), i]^2)) })) lel <- sum(sapply(1:N, function(i) { (L11hat2[i]^(-2)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[(ttt), i] * De[ttt, i] - lambdahat[i]) })) })) nipanel <- (TD^2) * (N^(3/2)) * nipa^(-1) stats[1, 1] <- nipanel rhopanel <- TD * (N^(1/2)) * (nipa^(-1)) * lel stats[2, 1] <- rhopanel tpanelnonpar <- ((sigmatilde2 * nipa)^(-1/2)) * lel stats[3, 1] <- tpanelnonpar tpanelpar <- ((stildestar2 * sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * estar[1:(nrow(estar) - 1), i]^2) })))^(-1/2)) * sum(sapply(1:N, function(i) { sum(sapply(1:(nrow(Destar)), function(ttt) { (L11hat2[i]^(-2)) * (estar[ttt, i] * Destar[ttt, i]) })) })) stats[4, 1] <- tpanelpar rhogroup <- TD * (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sum(e[1:(nrow(e) - 1), i]^2))^(-1)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[ttt, i] * De[ttt, i] - lambdahat[i]) })) })) stats[5, 1] <- rhogroup tgroupnonpar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sigmahat2[i] * sum(e[1:(nrow(e) - 1), i]^2))^(-1/2)) * sum(sapply(1:(nrow(De)), function(ttt) { (e[(ttt), i] * De[ttt, i] - lambdahat[i]) })) })) stats[6, 1] <- tgroupnonpar tgrouppar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { (sum(shat2[i] * estar[1:(nrow(estar) - 1), i]^2))^(-1/2) * sum(estar[1:(nrow(estar) - 1), i] * Destar[1:(nrow(estar) - 1), i]) })) stats[7, 1] <- tgrouppar stats[, 2] <- sapply(1:7, function(i) { (stats[i, 1] - statsm[i, type.stat] * sqrt(N))/sqrt(statsv[i, type.stat]) }) list(CALL = match.call(), METHOD = "Pedroni(1999) panel tests for cointegration", STATISTIC = stats) }
Computation of the Pedroni (1999) panel cointegration test statistics. All statistics are asymptotically normal. Reported are their empirical values and their standardized values (as suggested in Pedroni, 1999).
pedroni99m(X, kk = 0, type.stat = 1, ka = 2)pedroni99m(X, kk = 0, type.stat = 1, ka = 2)
X |
The data to be tested for cointegration. Must be a 'cube', an array (TxNxM) with multiple 'sheets', the first 'sheet' is the 'dependent' variable, 'independent' variables are the rest. The first dimension is 'time', the second is 'individuals' and the third is 'variables'. No missing values are allowed. |
kk |
Parameter for the Newey-West (1994) long term variance estimation (number of lags). Can be a vector, with a different value for each individual series, or a scalar. By default it is set to 'round(4 * (T/100)^(2/9))'. |
type.stat |
Type of the main regresion: 1 - 'none', 2 - 'intercept', 3 - 'intercept and time trend'. |
ka |
Number of lags for the ADF type regression on residuals, for the parametric statistics. |
The function closely follows the instructions in Pedroni (1999). Calculated and reported are the 7 statistics on page 660 in Pedroni (1999) for the multivariate case. Also reported are their standardized values, as described on page 665 and by use of the adjustment terms in Table 2, page 666, op.cit. H0 is 'no cointegration'.
CALL |
The result of 'match.call()'. |
METHOD |
Title of the test. |
STATISTIC |
The 7 test statistics in Pedroni (1999), in two columns - for the empirical and the standardized values. |
Under H0 ('no cointegration') the autoregressive coefficients, gamma_i = 1 for all i, versus H1: gamma_i < 1 for all i.
The standardized values of the test statistics are asymptotically normal (0,1) under H0.
Georgi Marinov
Newey, Whitney K.; West, Kenneth D. (1994). "Automatic lag selection in covariance matrix estimation". Review of Economic Studies 61 (4): 631-654.
Pedroni, Peter, 1999. "Critical Values for Cointegration Tests in Heterogeneous Panels with Multiple Regressors," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 61(0), pages 653-70, Special I.
xx<-array(cumsum(rnorm(10000)),dim=c(100,20,5)) pedroni99m(xx) ## The function is currently defined as function (X, kk = 0, type.stat = 1, ka = 2) { ffm <- function(Y2, X2) { NN = ncol(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ] - 1)$residuals }) } ff1m <- function(Y2, X2) { NN = ncol(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ])$residuals }) } ff2m <- function(Y2, X2) { NN = ncol(X2) trend = 1:nrow(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ] + trend)$residuals }) } ffmm <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] - 1)$residuals }) } nwm <- function(xx, ki) { tt = length(xx) (1/tt) * sum(sapply(1:ki, function(s) { (1 - s/(ki + 1)) * sum(xx[(s + 1):tt] * xx[1:(tt - s)]) })) } adflm<-function (ee, lags) { nn<-length(ee) z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] zd<-matrix(cbind(rep(z,lags)),ncol=lags) ii<-embed(1:nn,lags) ii<-ii[-(nrow(ii)),] zd<-zd-ee[ii] zd<-zd[,-1] z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] return(lm(z ~ zl + zd -1)$residuals) } na.fail(X) Y <- as.matrix(X[, , 1]) XX <- X[, , (2:dim(X)[3])] TD <- dim(X)[1] N <- dim(X)[2] M <- dim(X)[3] if (is.vector(kk) && length(kk) == N) { k = kk } else if (kk > 0) { k = rep(round(kk), N) } else { i = round(4 * (TD/100)^(2/9)) k = rep(i, N) } if (ka < 2) { ka = 2 warning("Parameter 'ka' was changed to 2.") } ka <- as.vector(ka) if (length(ka) != N) { ka <- rep(ka[1], N) } stamm <- array(dim = c(7, 3, 6)) stamm[, , 1] <- cbind(c(6.982, -6.388, -1.662, -1.662, -9.889, -1.992, -1.992), c(11.754, -9.495, -2.177, -2.177, -12.938, -2.453, -2.453), c(21.162, -14.011, -2.648, -2.648, -17.359, -2.872, -2.872)) stamm[, , 2] <- cbind(c(10.402, -10.191, -2.156, -2.156, -13.865, -2.44, -2.44), c(15.197, -13.256, -2.567, -2.567, -16.888, -2.827, -2.827), c(24.556, -17.6, -2.967, -2.967, -21.116, -3.179, -3.179)) stamm[, , 3] <- cbind(c(14.254, -14.136, -2.571, -2.571, -17.834, -2.819, -2.819), c(18.91, -17.163, -2.93, -2.93, -20.841, -3.157, -3.157), c(28.046, -21.287, -3.262, -3.262, -24.93, -3.464, -3.464)) stamm[, , 4] <- cbind(c(18.198, -18.042, -2.926, -2.926, -21.805, -3.151, -3.151), c(22.715, -21.013, -3.241, -3.241, -24.775, -3.452, -3.452), c(31.738, -25.13, -3.545, -3.545, -28.849, -3.737, -3.737)) stamm[, , 5] <- cbind(c(22.169, -21.985, -3.244, -3.244, -25.75, -3.45, -3.45), c(26.603, -24.944, -3.531, -3.531, -28.72, -3.726, -3.726), c(35.537, -28.981, -3.806, -3.806, -32.716, -3.986, -3.986)) stamm[, , 6] <- cbind(c(26.12, -25.889, -3.533, -3.533, -29.627, -3.723, -3.723), c(30.457, -28.795, -3.795, -3.795, -32.538, -3.976, -3.976), c(39.231, -32.756, -4.047, -4.047, -36.494, -4.217, -4.217)) rownames(stamm) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stamm) <- c("none", "intercept", "trend") stavv <- array(dim = c(7, 3, 6)) stavv[, , 1] <- cbind(c(81.145, 64.288, 1.559, 1.559, 41.943, 0.649, 0.649), c(104.546, 57.61, 0.964, 0.964, 51.49, 0.618, 0.618), c(160.249, 64.219, 0.69, 0.69, 66.387, 0.555, 0.555)) stavv[, , 2] <- cbind(c(140.804, 89.962, 1.286, 1.286, 57.801, 0.6, 0.6), c(151.094, 81.772, 0.923, 0.923, 67.123, 0.585, 0.585), c(198.167, 83.815, 0.686, 0.686, 81.832, 0.548, 0.548)) stavv[, , 3] <- cbind(c(182.45, 103.176, 1.028, 1.028, 72.097, 0.567, 0.567), c(190.661, 99.331, 0.843, 0.843, 81.835, 0.56, 0.56), c(239.425, 103.905, 0.688, 0.688, 97.362, 0.543, 0.543)) stavv[, , 4] <- cbind(c(217.784, 120.787, 0.928, 0.928, 88.611, 0.559, 0.559), c(231.864, 119.546, 0.8, 0.8, 98.278, 0.553, 0.553), c(276.997, 124.613, 0.686, 0.686, 113.145, 0.538, 0.538)) stavv[, , 5] <- cbind(c(256.53, 132.499, 0.82, 0.82, 103.371, 0.544, 0.544), c(270.451, 134.341, 0.75, 0.75, 113.131, 0.542, 0.542), c(310.982, 138.227, 0.654, 0.654, 127.989, 0.53, 0.53)) stavv[, , 6] <- cbind(c(277.429, 143.561, 0.75, 0.75, 117.059, 0.53, 0.53), c(293.431, 144.615, 0.685, 0.685, 126.059, 0.525, 0.525), c(348.217, 154.378, 0.638, 0.638, 140.756, 0.518, 0.518)) rownames(stavv) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stavv) <- c("none", "intercept", "trend") statsm <- matrix(nrow = 7, ncol = 2) rownames(statsm) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(statsm) <- c("empirical", "standardized") e <- matrix(ncol = N, nrow = TD) if (type.stat == 2) { e <- ff1m(Y, XX) } else if (type.stat == 3) { e <- ff2m(Y, XX) } else { e <- ffm(Y, XX) type.stat = 1 } De <- diff(e) estar <- e Destar <- diff(estar) DXX <- array(dim = c((dim(XX)[1] - 1), dim(XX)[2], dim(XX)[3])) DXX[, , 1:dim(XX)[3]] <- sapply(1:dim(XX)[3], function(i) { DXX[, , i] <- diff(XX[, , i]) }) DY <- diff(Y) eta <- ffm(DY, DXX) L11hat2 <- sapply(1:N, function(i) { (1/nrow(eta)) * sum(eta[, i]^2) + 2 * nwm(eta[, i], k[i]) }) mu <- matrix(ncol = ncol(DY), nrow = nrow(DY)) mu <- ffmm(e[2:TD, ], e[1:(TD - 1), ]) lambdahat <- sapply(1:N, function(i) { nwm(mu[, i], k[i]) }) mustar <- matrix(ncol = ncol(DY), nrow = nrow(DY)) mustar <- sapply(1:N, function(i) { adflm(e[, i], ka[i]) }) shatstar2 <- sapply(1:N, function(i) { (1/nrow(mustar)) * sum(mustar[, i]^2) }) stildestar2 <- (1/N) * sum(shatstar2) shat2 <- sapply(1:N, function(i) { (1/nrow(mu)) * sum(mu[, i]^2) }) sigmahat2 <- shat2 + 2 * lambdahat sigmatilde2 <- (1/N) * sum(L11hat2^(-2) * sigmahat2) nipa <- sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * (e[1:(TD - 1), i]^2)) })) lel <- sum(sapply(1:N, function(i) { (L11hat2[i]^(-2)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) nipanel <- (TD^2) * (N^(3/2)) * nipa^(-1) statsm[1, 1] <- nipanel rhopanel <- TD * (N^(1/2)) * (nipa^(-1)) * lel statsm[2, 1] <- rhopanel tpanelnonpar <- ((sigmatilde2 * nipa)^(-1/2)) * lel statsm[3, 1] <- tpanelnonpar tpanelpar <- ((stildestar2 * sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * estar[1:(nrow(estar) - 1), i]^2) })))^(-1/2)) * sum(sapply(1:N, function(i) { sum(sapply(2:(nrow(Destar)), function(ttt) { (L11hat2[i]^(-2)) * (estar[(ttt - 1), i] * Destar[ttt, i]) })) })) statsm[4, 1] <- tpanelpar rhogroup <- TD * (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sum(e[1:(nrow(e) - 1), i]^2))^(-1)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) statsm[5, 1] <- rhogroup tgroupnonpar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sigmahat2[i] * sum(e[1:(nrow(e) - 1), i]^2))^(-1/2)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) statsm[6, 1] <- tgroupnonpar tgrouppar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { (sum(shat2[i] * estar[1:(nrow(estar) - 1), i]^2))^(-1/2) * sum(sapply(2:nrow(Destar), function(tt1) { estar[(tt1 - 1), i] * Destar[tt1, i] })) })) statsm[7, 1] <- tgrouppar statsm[, 2] <- sapply(1:7, function(i) { (statsm[i, 1] - stamm[i, type.stat, M] * sqrt(N))/sqrt(stavv[i, type.stat, M]) }) list(CALL = match.call(), METHOD = "Pedroni(1999) panel tests for cointegration", STATISTIC = statsm) }xx<-array(cumsum(rnorm(10000)),dim=c(100,20,5)) pedroni99m(xx) ## The function is currently defined as function (X, kk = 0, type.stat = 1, ka = 2) { ffm <- function(Y2, X2) { NN = ncol(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ] - 1)$residuals }) } ff1m <- function(Y2, X2) { NN = ncol(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ])$residuals }) } ff2m <- function(Y2, X2) { NN = ncol(X2) trend = 1:nrow(X2) sapply(1:NN, function(l) { lm(Y2[, l] ~ X2[, l, ] + trend)$residuals }) } ffmm <- function(Y1, X1) { NN = ncol(X1) sapply(1:NN, function(l) { lm(Y1[, l] ~ X1[, l] - 1)$residuals }) } nwm <- function(xx, ki) { tt = length(xx) (1/tt) * sum(sapply(1:ki, function(s) { (1 - s/(ki + 1)) * sum(xx[(s + 1):tt] * xx[1:(tt - s)]) })) } adflm<-function (ee, lags) { nn<-length(ee) z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] zd<-matrix(cbind(rep(z,lags)),ncol=lags) ii<-embed(1:nn,lags) ii<-ii[-(nrow(ii)),] zd<-zd-ee[ii] zd<-zd[,-1] z<-ee[(lags+1):nn] zl<-ee[lags:(nn-1)] return(lm(z ~ zl + zd -1)$residuals) } na.fail(X) Y <- as.matrix(X[, , 1]) XX <- X[, , (2:dim(X)[3])] TD <- dim(X)[1] N <- dim(X)[2] M <- dim(X)[3] if (is.vector(kk) && length(kk) == N) { k = kk } else if (kk > 0) { k = rep(round(kk), N) } else { i = round(4 * (TD/100)^(2/9)) k = rep(i, N) } if (ka < 2) { ka = 2 warning("Parameter 'ka' was changed to 2.") } ka <- as.vector(ka) if (length(ka) != N) { ka <- rep(ka[1], N) } stamm <- array(dim = c(7, 3, 6)) stamm[, , 1] <- cbind(c(6.982, -6.388, -1.662, -1.662, -9.889, -1.992, -1.992), c(11.754, -9.495, -2.177, -2.177, -12.938, -2.453, -2.453), c(21.162, -14.011, -2.648, -2.648, -17.359, -2.872, -2.872)) stamm[, , 2] <- cbind(c(10.402, -10.191, -2.156, -2.156, -13.865, -2.44, -2.44), c(15.197, -13.256, -2.567, -2.567, -16.888, -2.827, -2.827), c(24.556, -17.6, -2.967, -2.967, -21.116, -3.179, -3.179)) stamm[, , 3] <- cbind(c(14.254, -14.136, -2.571, -2.571, -17.834, -2.819, -2.819), c(18.91, -17.163, -2.93, -2.93, -20.841, -3.157, -3.157), c(28.046, -21.287, -3.262, -3.262, -24.93, -3.464, -3.464)) stamm[, , 4] <- cbind(c(18.198, -18.042, -2.926, -2.926, -21.805, -3.151, -3.151), c(22.715, -21.013, -3.241, -3.241, -24.775, -3.452, -3.452), c(31.738, -25.13, -3.545, -3.545, -28.849, -3.737, -3.737)) stamm[, , 5] <- cbind(c(22.169, -21.985, -3.244, -3.244, -25.75, -3.45, -3.45), c(26.603, -24.944, -3.531, -3.531, -28.72, -3.726, -3.726), c(35.537, -28.981, -3.806, -3.806, -32.716, -3.986, -3.986)) stamm[, , 6] <- cbind(c(26.12, -25.889, -3.533, -3.533, -29.627, -3.723, -3.723), c(30.457, -28.795, -3.795, -3.795, -32.538, -3.976, -3.976), c(39.231, -32.756, -4.047, -4.047, -36.494, -4.217, -4.217)) rownames(stamm) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stamm) <- c("none", "intercept", "trend") stavv <- array(dim = c(7, 3, 6)) stavv[, , 1] <- cbind(c(81.145, 64.288, 1.559, 1.559, 41.943, 0.649, 0.649), c(104.546, 57.61, 0.964, 0.964, 51.49, 0.618, 0.618), c(160.249, 64.219, 0.69, 0.69, 66.387, 0.555, 0.555)) stavv[, , 2] <- cbind(c(140.804, 89.962, 1.286, 1.286, 57.801, 0.6, 0.6), c(151.094, 81.772, 0.923, 0.923, 67.123, 0.585, 0.585), c(198.167, 83.815, 0.686, 0.686, 81.832, 0.548, 0.548)) stavv[, , 3] <- cbind(c(182.45, 103.176, 1.028, 1.028, 72.097, 0.567, 0.567), c(190.661, 99.331, 0.843, 0.843, 81.835, 0.56, 0.56), c(239.425, 103.905, 0.688, 0.688, 97.362, 0.543, 0.543)) stavv[, , 4] <- cbind(c(217.784, 120.787, 0.928, 0.928, 88.611, 0.559, 0.559), c(231.864, 119.546, 0.8, 0.8, 98.278, 0.553, 0.553), c(276.997, 124.613, 0.686, 0.686, 113.145, 0.538, 0.538)) stavv[, , 5] <- cbind(c(256.53, 132.499, 0.82, 0.82, 103.371, 0.544, 0.544), c(270.451, 134.341, 0.75, 0.75, 113.131, 0.542, 0.542), c(310.982, 138.227, 0.654, 0.654, 127.989, 0.53, 0.53)) stavv[, , 6] <- cbind(c(277.429, 143.561, 0.75, 0.75, 117.059, 0.53, 0.53), c(293.431, 144.615, 0.685, 0.685, 126.059, 0.525, 0.525), c(348.217, 154.378, 0.638, 0.638, 140.756, 0.518, 0.518)) rownames(stavv) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(stavv) <- c("none", "intercept", "trend") statsm <- matrix(nrow = 7, ncol = 2) rownames(statsm) <- c("nipanel", "rhopanel", "tpanelnonpar", "tpanelpar", "rhogroup", "tgroupnonpar", "tgrouppar") colnames(statsm) <- c("empirical", "standardized") e <- matrix(ncol = N, nrow = TD) if (type.stat == 2) { e <- ff1m(Y, XX) } else if (type.stat == 3) { e <- ff2m(Y, XX) } else { e <- ffm(Y, XX) type.stat = 1 } De <- diff(e) estar <- e Destar <- diff(estar) DXX <- array(dim = c((dim(XX)[1] - 1), dim(XX)[2], dim(XX)[3])) DXX[, , 1:dim(XX)[3]] <- sapply(1:dim(XX)[3], function(i) { DXX[, , i] <- diff(XX[, , i]) }) DY <- diff(Y) eta <- ffm(DY, DXX) L11hat2 <- sapply(1:N, function(i) { (1/nrow(eta)) * sum(eta[, i]^2) + 2 * nwm(eta[, i], k[i]) }) mu <- matrix(ncol = ncol(DY), nrow = nrow(DY)) mu <- ffmm(e[2:TD, ], e[1:(TD - 1), ]) lambdahat <- sapply(1:N, function(i) { nwm(mu[, i], k[i]) }) mustar <- matrix(ncol = ncol(DY), nrow = nrow(DY)) mustar <- sapply(1:N, function(i) { adflm(e[, i], ka[i]) }) shatstar2 <- sapply(1:N, function(i) { (1/nrow(mustar)) * sum(mustar[, i]^2) }) stildestar2 <- (1/N) * sum(shatstar2) shat2 <- sapply(1:N, function(i) { (1/nrow(mu)) * sum(mu[, i]^2) }) sigmahat2 <- shat2 + 2 * lambdahat sigmatilde2 <- (1/N) * sum(L11hat2^(-2) * sigmahat2) nipa <- sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * (e[1:(TD - 1), i]^2)) })) lel <- sum(sapply(1:N, function(i) { (L11hat2[i]^(-2)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) nipanel <- (TD^2) * (N^(3/2)) * nipa^(-1) statsm[1, 1] <- nipanel rhopanel <- TD * (N^(1/2)) * (nipa^(-1)) * lel statsm[2, 1] <- rhopanel tpanelnonpar <- ((sigmatilde2 * nipa)^(-1/2)) * lel statsm[3, 1] <- tpanelnonpar tpanelpar <- ((stildestar2 * sum(sapply(1:N, function(i) { sum((L11hat2[i]^(-2)) * estar[1:(nrow(estar) - 1), i]^2) })))^(-1/2)) * sum(sapply(1:N, function(i) { sum(sapply(2:(nrow(Destar)), function(ttt) { (L11hat2[i]^(-2)) * (estar[(ttt - 1), i] * Destar[ttt, i]) })) })) statsm[4, 1] <- tpanelpar rhogroup <- TD * (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sum(e[1:(nrow(e) - 1), i]^2))^(-1)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) statsm[5, 1] <- rhogroup tgroupnonpar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { ((sigmahat2[i] * sum(e[1:(nrow(e) - 1), i]^2))^(-1/2)) * sum(sapply(2:(nrow(De)), function(ttt) { (e[(ttt - 1), i] * De[ttt, i] - lambdahat[i]) })) })) statsm[6, 1] <- tgroupnonpar tgrouppar <- (N^(-1/2)) * sum(sapply(1:N, function(i) { (sum(shat2[i] * estar[1:(nrow(estar) - 1), i]^2))^(-1/2) * sum(sapply(2:nrow(Destar), function(tt1) { estar[(tt1 - 1), i] * Destar[tt1, i] })) })) statsm[7, 1] <- tgrouppar statsm[, 2] <- sapply(1:7, function(i) { (statsm[i, 1] - stamm[i, type.stat, M] * sqrt(N))/sqrt(stavv[i, type.stat, M]) }) list(CALL = match.call(), METHOD = "Pedroni(1999) panel tests for cointegration", STATISTIC = statsm) }