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ch.test <- function(x, type = c("dummy", "trigonometric"),
lag1 = FALSE, NW.order = NULL, sid = NULL, xreg = NULL,
pvalue = c("RS", "raw"), rs.nobsreg = 13)
{
ch.test0 <- function(id)
{
# robust covariance matrix estimator
# scaled by the seasonal components
# based on function "sandwich::NeweyWest"
# (other options used in package "sandwich" could be considered here)
# OmegafHat <- crossprod(SD * ehat) / n
SDe <- SD[,id,drop=FALSE] * ehat
if (NW.order > 0)
{
weights <- 1 - seq_len(NW.order) / (NW.order + 1)
OmegafHat <- 0.5 * crossprod(SDe)
for (i in seq_along(weights))
OmegafHat <- OmegafHat +
weights[i] * crossprod(SDe[seq_len(n-i),,drop=FALSE], SDe[-seq_len(i),,drop=FALSE])
OmegafHat <- OmegafHat + t(OmegafHat)
} else
OmegafHat <- crossprod(SDe)
OmegafHat <- OmegafHat / n
# auxiliary elements
# cumulative sum by columns in "SDe" ("SD" multiplied by "ehat" by columns)
Fhat <- apply(SDe, MARGIN = 2, FUN = cumsum)
# summation of crossproducts of "Fhat"
Fhat.cp <- matrix(0, nrow = nrow(OmegafHat), ncol = ncol(OmegafHat))
for (i in seq_len(n))
Fhat.cp <- Fhat.cp + tcrossprod(Fhat[i,])
# test statistic
sum(diag(chol2inv(chol(OmegafHat)) %*% Fhat.cp)) / n^2
}
data.name <- deparse(substitute(x))
type <- match.arg(type)
pvalue <- match.arg(pvalue)
isNullxreg <- is.null(xreg)
n <- length(x)
if (!isNullxreg && NROW(xreg) != n)
stop("wrong dimension of argument ", sQuote("xreg"))
S <- frequency(x)
if (S < 2)
stop("the time series is not seasonal")
if (is.null(NW.order))
NW.order <- round(S * (n/100)^0.25)
# indicator variable for the target seasonal dummies or cycles
if (is.null(sid)) {
sid <- "all"
} else {
#if (!identical(sid, "all"))
if (is.numeric(sid))
{
if (type == "trigonometric")
{
if (length(sid) != floor(S/2))
stop("wrong length of argument ", sQuote("sid"))
tmp <- head(sid, -1)
id <- which(c(rbind(tmp, tmp)) == 1)
if (tail(sid, 1) == 1)
id <- c(id, S-1)
} else {
if (any(!(sid %in% seq_len(S)))) # assumed that no duplicates are defined
stop("wrong definition of argument ", sQuote("sid"))
id <- sid
}
} else
if (!(sid %in% c("all", "joint")))
stop("wrong definition of argument ", sQuote("sid"))
}
# create target regressor variables (seasonal dummies or seasonal cycles)
switch(type,
"dummy" = { # seasonal dummies
#SD <- seasonal.dummies(x)
SD <- do.call("rbind", replicate(ceiling(n/S), diag(S), simplify = FALSE))
SD <- ts(SD, frequency = S, start = c(start(x)[1], 1))
# ignore warning "'end' value not changed"
SD <- suppressWarnings(window(SD, start = start(x), end = end(x)))
},
"trigonometric" = { # seasonal cycles
Sh <- floor(S/2)
isSeven <- as.numeric(S %% 2 == 0)
if (S %in% c(4, 12) && n/S <= 50) {
SD <- .SDtrig[[as.character(S)]][seq_len(n),]
} else {
#SD <- seasonal.cycles(x)
tmp <- matrix(seq_len(n), nrow = Sh-isSeven, ncol = n, byrow = TRUE)
seqsm1 <- seq_len(nrow(tmp))
tmp <- (2 * seqsm1 * pi / S) * tmp
SD <- rbind(cos(tmp), sin(tmp))
SD <- t(SD[c(rbind(seqsm1, seqsm1 + nrow(tmp))),])
if ((S %% 2) == 0)
SD <- cbind(SD, rep(c(-1, 1), len = n))
#SD <- ts(SD, frequency = S, start = c(start(x)[1], 1))
}
}
) # switch
colnames(SD) <- paste0("SD", seq_len(ncol(SD)))
# arrange other possible exogenous variables
if (lag1) {
SD <- SD[-1,] # updating SD is required as well as it will be used by "ch.test0"
xreg <- cbind(lag1 = x[-n], SD, xreg[-1,])
x <- x[-1]
n <- n - 1
} else
xreg <- cbind(SD, xreg)
##NOTE
# in principle it is not a good idea to define the intercept in "xreg" and
# use lm(x ~ 0 + xreg) because stats::summary.lm uses attr(z$terms, "intercept")
# to compute the R-squared, but here the R-squared is not used
if (type == "trigonometric")
xreg <- cbind(c = 1, xreg)
# fit regression model and get residuals
fit <- lm(x ~ 0 + xreg)
ehat <- residuals(fit)
# used with pvalue = "RS"
Nc <- n - ncol(xreg)
# test statistics
if (identical(sid, "all"))
{
if (type == "dummy")
{
stat <- matrix(nrow = S+1, ncol = 2)
id <- 0
for (i in seq_len(S))
{
id <- id + 1
stat[i,1] <- ch.test0(id)
stat[i,2] <- switch(pvalue,
#"raw" = 1 - .CH.cvals[[1]](stat[i,1]),
"raw" = uroot.raw.pvalue(stat[i,1], "CH", 1),
"RS" = ch.rs.pvalue(stat[i,1], "dummy", lag1, S, Nc, rs.nobsreg, 1))
}
stat[S+1,1] <- ch.test0(seq_len(S))
##NOTE to mention in documentation
#"RS" p-value is not available for the joint test with dummies
stat[S+1,2] <- uroot.raw.pvalue(stat[S+1,1], "CH", S)
colnames(stat) <- c("statistic", "p-value")
rownames(stat) <- c(switch(as.character(S),
"4" = paste0("Quarter", seq_len(S)), "12" = month.abb,
paste0("Season", seq_len(S))), "joint")
} else { #type == "trigonometric"
Shp1 <- Sh + 1
stat <- matrix(nrow = Shp1, ncol = 2)
id <- c(-1, 0)
for (i in seq_len(Sh-isSeven))
{
id <- id + 2
stat[i,1] <- ch.test0(id)
stat[i,2] <- switch(pvalue,
"raw" = uroot.raw.pvalue(stat[i,1], "CH", 2),
"RS" = ch.rs.pvalue(stat[i,1], "trigonometric", lag1, S, Nc, rs.nobsreg, 2))
}
if (isSeven)
{
stat[Sh,1] <- ch.test0(S-1)
stat[Sh,2] <- switch(pvalue,
"raw" = uroot.raw.pvalue(stat[Sh,1], "CH", 1),
"RS" = ch.rs.pvalue(stat[Sh,1], "trigonometric", lag1, S, Nc, rs.nobsreg, 1))
}
stat[Shp1,1] <- ch.test0(seq_len(S-1))
stat[Shp1,2] <- switch(pvalue,
"raw" = uroot.raw.pvalue(stat[Shp1,1], "CH", S-1),
"RS" = ch.rs.pvalue(stat[Shp1,1], "trigonometric", lag1, S, Nc, rs.nobsreg, S-1))
colnames(stat) <- c("statistic", "p-value")
if (isSeven) {
rownames(stat) <- c(paste0("pi/", Sh),
if(Sh > 2) paste0(seq.int(2, Sh-1), "pi/", Sh), "pi", "joint")
} else
rownames(stat) <- c(paste0(seq.int(2, S, 2), "pi/", S), "joint")
}
} else # sid != "all"
if (identical(sid, "joint")) {
if (type == "dummy")
{
stat <- ch.test0(seq_len(S))
stat <- cbind("joint" = stat, "p-value" = uroot.raw.pvalue(stat, "CH", S))
} else { # type trigonometric
stat <- ch.test0(seq_len(S-1))
pval <- switch(pvalue,
"raw" = uroot.raw.pvalue(stat, "CH", S-1),
"RS" = ch.rs.pvalue(stat, type, lag1, S, Nc, rs.nobsreg, S-1))
stat <- cbind("joint" = stat, "p-value" = pval)
}
} else {
# "sid" is a numeric vector indicating the index of the
# seasonal dummy(s) or cycle(s) to be tested
if (pvalue == "RS")
{
#it could be checked if a case for which "RS" p-values are available
#is requested through "sid", but for that end, simply use default "sid" value
pvalue <- "raw"
warning("argument ", sQuote("pvalue"), " was changed to ", sQuote("raw"))
}
#if length(id) > 1, a joint test for those seasons or cycles is obtained
stat <- ch.test0(id)
pval <- uroot.raw.pvalue(stat, "CH", length(id))
stat <- rbind(c(stat, pval))
colnames(stat) <- c("statistic", "p-value")
if (type == "dummy")
{
rownames(stat) <- switch(as.character(S),
"4" = paste("Quarter(s)", paste0(id, collapse = ",")),
"12" = paste(month.abb[id], collapse = ","),
paste("Season(s)", paste0(id, collapse = ",")))
} else { # type trigonometric
##TODO S odd (see how this is arranged above)
}
}
# output
res <- list(statistics = stat[,1], pvalues = stat[,2],
method = "Canova and Hansen test for seasonal stability", data.name = data.name,
type = type, fitted.model = fit,
NW.order = NW.order, lag1 = lag1, isNullxreg = isNullxreg, type.pvalue = pvalue,
pvlabels = symnum(stat[,"p-value"], corr = FALSE, na = FALSE,
cutpoints = c(0, 0.001, 0.01, 0.05, 0.1, 1),
symbols = c("***","**","*","."," ")))
class(res) <- "CHtest"
res
}
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