ARCH.Quantile.Lags <- function(y, tau=.01, p=1, r=3)
{
################################################################################
#                                                                              #
#      ARCH.Quantile.Lags Function by Breno de Andrade Pinheiro Néri           #
#                                                                              #
#            brenoneri@gmail.com       www.fgv.br/aluno/bneri                  #
#                                                                              #
#                                                  Septembre, 2005 - Version 1 #
#                                                                              #
################################################################################
#                                                                              #
# This code tests the significance of the estimated coefficients in the ARCH   #
# Quantile specification.                                                      #
#                                                                              #
# You enter a time series (y), a quantile (tau), the number of lags (p) for    #
# the ols regression that estimates the conditional mean, and the maximum      #
# number of lags in the ARCH specification (r).                                #
#                                                                              #
# The code returns a vector of p-values of the significance test of the ARCH   #
# coefficients. For a joint teste, see Lima and Néri (2005).                   #
#                                                                              #
# Defaults: tau=.01, p=1 and r=3.                                              #
#                                                                              #
################################################################################
#                                                                              #
# You may use this code only if you accept the conditions:                     #
# (1) I am not liable for any problem caused by this code (i.e. you use it at  #
# your own risk);                                                              #
# (2) You must give me credit in your papers where this code has been used.    #
#                                                                              #
################################################################################

t <- length(y)
library(quantreg)
y.lag <- array(0, c(t-p, p))
for(i in 1:p) y.lag[,i] <- y[(p+1-i):(t-i)]
e <- residuals(lm(y[(p+1):t]~y.lag))
J <- 0
suppressWarnings(for(i in r:1)
{
    e.lag <- array(0, c(t-p-i, i))
    for(j in 1:i) e.lag[,j] <- e[(i+1-j):(t-p-j)]
    reg <- summary(rq(e[(i+1):(t-p)]~abs(e.lag), tau), se="nid")
    J[i] <- reg$coef[[i+1]]^2/reg$cov[i+1,i+1]
})
P <- array(1-pchisq(J, 1))
dimnames(P) <- list(paste("gamma", 1:r, sep=""))
return(P)
}