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### Original file:
### copyright 1991 Department of Statistics, Univeristy of Washington
### Patched by Friedrich.Leisch, for use with R, 22.1.1997
### fixed & changed by Martin Maechler, since Dec 2003
if(getRversion() < "2.15")
paste0 <- function(...) paste(..., sep="")
.fdcov <- function(x, d, h, nar, nma, hess, fdf.work)
{
npq <- as.integer(nar + nma)
npq1 <- npq + 1L # integer, too
stopifnot(length(di <- dim(hess)) == 2, di == c(npq1, npq1))
fdc <- .C(fdcov, ## --> ../src/fdhess.c
x,
d,
h = as.double(if(missing(h)) -1 else h),
hd = double(npq1),
cov = hess, npq1,
cor = hess, npq1,
se = double(npq1),
fdf.work,
info = integer(1))[c("h","hd", "cov","cor", "se", "info")]
f.msg <-
if(fdc$info) {
msg <-
switch(fdc$info,
"fdcov problem in gamma function", # 1
"singular Hessian", # 2
## FIXME improve: different reasons for info = 3 :
"unable to compute correlation matrix; maybe change 'h'",
# 3
stop("error in gamma function")) # 4
warning(msg, call. = FALSE)
msg
} else "ok"
se.ok <- fdc$info %in% 0:2
nam <- "d"
if(nar) nam <- c(nam, paste0("ar", 1:nar))
if(nma) nam <- c(nam, paste0("ma", 1:nma))
dimnames(fdc$cov) <- dn <- list(nam, nam)
if(se.ok) dimnames(fdc$cor) <- dn
list(msg = f.msg, d = d, nam = nam,
h = fdc$h, hd = fdc$hd, se.ok = se.ok,
covariance.dpq = fdc$cov,
stderror.dpq = if(se.ok) fdc$se, # else NULL
correlation.dpq= if(se.ok) fdc$cor)
}## end{.fdcov}
fracdiff <- function(x, nar = 0, nma = 0,
ar = rep(NA, max(nar, 1)), ma = rep(NA, max(nma, 1)),
dtol = NULL, drange = c(0, 0.5), h, M = 100, trace = 0)
{
## #########################################################################
##
## x - time series for the ARIMA model
## nar - number of autoregressive parameters
## nma - number of moving average parameters
## ar - initial autoregressive parameters
## ma - initial moving average parameters
## dtol - desired accurcay for d
## by default (and if negative), (4th root of machine precision)
## is used. dtol will be changed internally if necessary
## drange - interval over which the likelihood function is to be maximized
## as a function of d
## h - finite difference interval
## M - number of terms in the likelihood approximation
##
## (see Haslett and Raftery 1989)
##
## ########################################################################
cl <- match.call()
if(any(is.na(x)))
stop("missing values not allowed in time series")
if(is.matrix(x) && ncol(x) > 2)
stop("multivariate time series not allowed")
n <- length(x)
if(round(nar) != nar || nar < 0 || round(nma) != nma || nma < 0)
stop("'nar' and 'nma' must be non-negative integer numbers")
npq <- as.integer(nar + nma)
npq1 <- npq + 1L # integer, too
lenw <- max(npq + 2*(n + M),
3*n + (n+6)*npq + npq %/% 2 + 1,
31 * 12, ## << added because checked in ../src/fdcore.f
(3 + 2*npq1) * npq1 + 1)## << this is *not* checked (there)
lenw <- as.integer(lenw)
ar[is.na(ar)] <- 0
ma[is.na(ma)] <- 0
if(is.null(dtol))
dtol <- .Machine$double.eps^0.25 # ~ 1.22e-4
## if dtol < 0: the fortran code will choose defaults
tspx <- tsp(x) # Added by RJH. 9 Dec 2019
x <- as.double(x)
## this also initializes "common blocks" that are used in .C(.) calls :
fdf <- .C(fracdf,
x,
n,
as.integer(M),
as.integer(nar),
as.integer(nma),
dtol = as.double(dtol),
drange = as.double(drange),
hood.etc = double(3),
d = double(1),
ar = as.double(ar),
ma = as.double(ma),
w = double(lenw),
lenw = lenw,
iw = integer(npq), ## <<< new int-work array
info = as.integer(trace > 0),## <- "verbose" [input]
.Machine$double.xmin,
.Machine$double.xmax,
.Machine$double.neg.eps,
.Machine$double.eps)[c("dtol","drange","hood.etc",
"d", "ar", "ma", "w", "lenw", "info")]
fd.msg <-
if(fdf$info) {
msg <-
switch(fdf$info,
stop("insufficient workspace; need ", fdf$lenw,
" instead of just ", lenw), # 1
stop("error in gamma function"), # 2
stop("invalid MINPACK input"), # 3
"warning in gamma function", # 4
"C fracdf() optimization failure", # 5
"C fracdf() optimization limit reached") # 6
## otherwise
## stop("unknown .C(fracdf, *) info -- should not happen")
warning(msg, call. = FALSE, immediate. = TRUE)
msg
} else "ok"
if(nar == 0) fdf$ar <- numeric(0)
if(nma == 0) fdf$ma <- numeric(0)
hess <- .C(fdhpq,
hess = matrix(double(1), npq1, npq1),
npq1,
fdf$w)$hess
## NOTA BENE: The above hess[.,.] is further "transformed",
## well, added to and inverted in fdcov :
## Cov == (-H)^{-1} == solve(-H)
## Note that the following can be "redone" using fracdiff.var() :
fdc <- .fdcov(x, fdf$d, h,
nar=nar, nma=nma, hess=hess, fdf.work = fdf$w)
dimnames(hess) <- dimnames(fdc$covariance.dpq)
hess[1, ] <- fdc$hd
hess[row(hess) > col(hess)] <- hess[row(hess) < col(hess)]
hstat <- fdf[["hood.etc"]]
var.WN <- hstat[3]
## Following lines added by RJH. 9 Dec 2019
diffx <- diffseries(x, d = fdf$d)
armafit <- arima(diffx, order = c(length(fdf$ar), 0L, length(fdf$ma)),
include.mean = FALSE, fixed = c(fdf$ar, -fdf$ma))
res <- armafit$residuals
tsp(res) <- tspx
structure(list(log.likelihood = hstat[1],
n = n,
msg = c(fracdf = fd.msg, fdcov = fdc$msg),
d = fdf$d, ar = fdf$ar, ma = fdf$ma,
covariance.dpq = fdc$covariance.dpq,
fnormMin = hstat[2], sigma = sqrt(var.WN),
stderror.dpq = if(fdc$se.ok) fdc$stderror.dpq, # else NULL
correlation.dpq= if(fdc$se.ok) fdc$correlation.dpq,
h = fdc$h, d.tol = fdf$dtol, M = M, hessian.dpq = hess,
length.w = lenw,
residuals = res, fitted = x - res, ## by RJH
call = cl),
class = "fracdiff")
}
### FIXME [modularity]: a lot of this is "cut & paste" also in fracdiff() itself
### ----- NOTABLY, now use .fdcov() !
fracdiff.var <- function(x, fracdiff.out, h)
{
if(!is.numeric(h))
stop("h must be numeric")
if(!is.list(fracdiff.out) || !is.numeric(M <- fracdiff.out$M))
stop("invalid ", sQuote("fracdiff.out"))
p <- length(fracdiff.out$ar)
q <- length(fracdiff.out$ma)
n <- length(x)
npq <- p + q
npq1 <- npq + 1
lwork <- max(npq + 2 * (n + M),
3 * n + (n + 6) * npq + npq %/% 2 + 1,
(3 + 2 * npq1) * npq1 + 1)
## Initialize
.C(fdcom,
n,
as.integer(M),
(p),
(q),
as.double(fracdiff.out$log.likelihood),
.Machine$double.xmin,
.Machine$double.xmax,
.Machine$double.neg.eps,
.Machine$double.eps)
## Re compute Covariance Matrix:
fdc <- .C(fdcov,
as.double(x),
as.double(fracdiff.out$d),
h = as.double(h),
hd = double(npq1),
cov = as.double(fracdiff.out$hessian.dpq),
as.integer(npq1),
cor = as.double(fracdiff.out$hessian.dpq),
as.integer(npq1),
se = double(npq1),
as.double(c(fracdiff.out$ma,
fracdiff.out$ar,
rep(0, lwork))),
info = integer(1))
## FIXME: should be *automatically* same messages as inside fracdiff() above!
fracdiff.out$msg <-
if(fdc$info) {
msg <-
switch(fdc$info,
"warning in gamma function",
"singular Hessian",
"unable to compute correlation matrix",
stop("error in gamma function"))
warning(msg)
} else "ok"
se.ok <- fdc$info != 0 || fdc$info < 3 ## << FIXME -- illogical!!
nam <- "d"
if(p) nam <- c(nam, paste0("ar", 1:p))
if(q) nam <- c(nam, paste0("ma", 1:q))
fracdiff.out$h <- fdc$h
fracdiff.out$covariance.dpq <- array(fdc$cov, c(npq1,npq1), list(nam,nam))
fracdiff.out$stderror.dpq <- if(se.ok) fdc$se # else NULL
fracdiff.out$correlation.dpq <- if(se.ok) array(fdc$cor, c(npq1, npq1))
fracdiff.out$hessian.dpq[1, ] <- fdc$hd
fracdiff.out$hessian.dpq[, 1] <- fdc$hd
fracdiff.out
}## end{ fracdiff.var() }
## MM: Added things for more arima.sim() compatibility.
## really, 'mu' is nonsense since can be done separately (or via 'innov').
fracdiff.sim <- function(n, ar = NULL, ma = NULL, d, rand.gen = rnorm,
innov = rand.gen(n+q, ...), n.start = NA,
backComp = TRUE, allow.0.nstart = FALSE, # <- for back-compatibility
start.innov = rand.gen(n.start, ...), ..., mu = 0)
{
p <- length(ar)
q <- length(ma)
if(p) {
minroots <- min(Mod(polyroot(c(1, -ar))))
if(minroots <= 1) {
warning("'ar' part of fracdiff model is not stationary!!")
minroots <- 1.01 # -> n.start= 603 by default
}
}
if(is.na(n.start))
n.start <- p + q + ifelse(p > 0, ceiling(6/log(minroots)), 0)
if(n.start < p + q && !allow.0.nstart)
stop("burn-in 'n.start' must be as long as 'ar + ma'")
if(missing(start.innov)) {
if(!backComp) force(start.innov)
} else if(length(start.innov) < n.start)
stop(gettextf("'start.innov' is too short: need %d points",
n.start), domain = NA)
if(length(innov) < n+q) stop("'innov' must have length >= n + q")
y <- c(start.innov[seq_len(n.start)], innov[1:(n+q)])
stopifnot(is.double(y), length(y) == n + q + n.start)
if(d < -1/2 || d > 1/2)
stop("'d' must be in [-1/2, 1/2]. Consider using cumsum(.) or diff(.)
for additional integration or differentiation")
ii <- n.start - (if(backComp) 0L else q) + 1:n
y <- .C(fdsim,
as.integer(n + n.start),
(p),
(q),
as.double(ar),
as.double(ma),
as.double(d),
as.double(mu),
y = y,
s = double(length(y)),
.Machine$double.xmin,
.Machine$double.xmax,
.Machine$double.neg.eps,
.Machine$double.eps)[["s"]][ii]
list(series = y, ar = ar, ma = ma, d = d, mu = mu, n.start = n.start)
}
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