tsboot
Bootstrapping of Time Series
Generate R
bootstrap replicates of a statistic applied to a
time series. The replicate time series can be generated using fixed
or random block lengths or can be model based replicates.
- Keywords
- ts, nonparametric
Usage
tsboot(tseries, statistic, R, l = NULL, sim = "model",
endcorr = TRUE, n.sim = NROW(tseries), orig.t = TRUE,
ran.gen, ran.args = NULL, norm = TRUE, …,
parallel = c("no", "multicore", "snow"),
ncpus = getOption("boot.ncpus", 1L), cl = NULL)
Arguments
- tseries
A univariate or multivariate time series.
- statistic
A function which when applied to
tseries
returns a vector containing the statistic(s) of interest. Each timestatistic
is called it is passed a time series of lengthn.sim
which is of the same class as the originaltseries
. Any other arguments whichstatistic
takes must remain constant for each bootstrap replicate and should be supplied through the … argument totsboot
.- R
A positive integer giving the number of bootstrap replicates required.
- sim
The type of simulation required to generate the replicate time series. The possible input values are
"model"
(model based resampling),"fixed"
(block resampling with fixed block lengths ofl
),"geom"
(block resampling with block lengths having a geometric distribution with meanl
) or"scramble"
(phase scrambling).- l
If
sim
is"fixed"
thenl
is the fixed block length used in generating the replicate time series. Ifsim
is"geom"
thenl
is the mean of the geometric distribution used to generate the block lengths.l
should be a positive integer less than the length oftseries
. This argument is not required whensim
is"model"
but it is required for all other simulation types.- endcorr
A logical variable indicating whether end corrections are to be applied when
sim
is"fixed"
. Whensim
is"geom"
,endcorr
is automatically set toTRUE
;endcorr
is not used whensim
is"model"
or"scramble"
.- n.sim
The length of the simulated time series. Typically this will be equal to the length of the original time series but there are situations when it will be larger. One obvious situation is if prediction is required. Another situation in which
n.sim
is larger than the original length is iftseries
is a residual time series from fitting some model to the original time series. In this case,n.sim
would usually be the length of the original time series.- orig.t
A logical variable which indicates whether
statistic
should be applied totseries
itself as well as the bootstrap replicate series. Ifstatistic
is expecting a longer time series thantseries
or if applyingstatistic
totseries
will not yield any useful information thenorig.t
should be set toFALSE
.- ran.gen
This is a function of three arguments. The first argument is a time series. If
sim
is"model"
then it will always betseries
that is passed. For other simulation types it is the result of selectingn.sim
observations fromtseries
by some scheme and converting the result back into a time series of the same form astseries
(although of lengthn.sim
). The second argument toran.gen
is always the valuen.sim
, and the third argument isran.args
, which is used to supply any other objects needed byran.gen
. Ifsim
is"model"
then the generation of the replicate time series will be done inran.gen
(for example through use ofarima.sim
). For the other simulation typesran.gen
is used for ‘post-blackening’. The default is that the function simply returns the time series passed to it.- ran.args
This will be supplied to
ran.gen
each time it is called. Ifran.gen
needs any extra arguments then they should be supplied as components ofran.args
. Multiple arguments may be passed by makingran.args
a list. Ifran.args
isNULL
then it should not be used withinran.gen
but note thatran.gen
must still have its third argument.- norm
A logical argument indicating whether normal margins should be used for phase scrambling. If
norm
isFALSE
then margins corresponding to the exact empirical margins are used.- ...
Extra named arguments to
statistic
may be supplied here. Beware of partial matching to the arguments oftsboot
listed above.- parallel, ncpus, cl
See the help for
boot
.
Details
If sim
is "fixed"
then each replicate time series is
found by taking blocks of length l
, from the original time
series and putting them end-to-end until a new series of length
n.sim
is created. When sim
is "geom"
a similar
approach is taken except that now the block lengths are generated from
a geometric distribution with mean l
. Post-blackening can be
carried out on these replicate time series by including the function
ran.gen
in the call to tsboot
and having tseries
as a time series of residuals.
Model based resampling is very similar to the parametric bootstrap and all simulation must be in one of the user specified functions. This avoids the complicated problem of choosing the block length but relies on an accurate model choice being made.
Phase scrambling is described in Section 8.2.4 of Davison and Hinkley
(1997). The types of statistic for which this method produces
reasonable results is very limited and the other methods seem to do
better in most situations. Other types of resampling in the frequency
domain can be accomplished using the function boot
with the
argument sim = "parametric"
.
Value
An object of class "boot"
with the following components.
If orig.t
is TRUE
then t0
is the result of
statistic(tseries,…{})
otherwise it is NULL
.
The results of applying statistic
to the replicate time series.
The value of R
as supplied to tsboot
.
The original time series.
The function statistic
as supplied.
The simulation type used in generating the replicates.
The value of endcorr
used. The value is meaningful only when
sim
is "fixed"
; it is ignored for model based simulation
or phase scrambling and is always set to TRUE
if sim
is
"geom"
.
The value of n.sim
used.
The value of l
used for block based resampling. This will be
NULL
if block based resampling was not used.
The ran.gen
function used for generating the series or for
‘post-blackening’.
The extra arguments passed to ran.gen
.
The original call to tsboot
.
References
Davison, A.C. and Hinkley, D.V. (1997) Bootstrap Methods and Their Application. Cambridge University Press.
Kunsch, H.R. (1989) The jackknife and the bootstrap for general stationary observations. Annals of Statistics, 17, 1217--1241.
Politis, D.N. and Romano, J.P. (1994) The stationary bootstrap. Journal of the American Statistical Association, 89, 1303--1313.
See Also
Examples
# NOT RUN {
lynx.fun <- function(tsb) {
ar.fit <- ar(tsb, order.max = 25)
c(ar.fit$order, mean(tsb), tsb)
}
# the stationary bootstrap with mean block length 20
lynx.1 <- tsboot(log(lynx), lynx.fun, R = 99, l = 20, sim = "geom")
# the fixed block bootstrap with length 20
lynx.2 <- tsboot(log(lynx), lynx.fun, R = 99, l = 20, sim = "fixed")
# Now for model based resampling we need the original model
# Note that for all of the bootstraps which use the residuals as their
# data, we set orig.t to FALSE since the function applied to the residual
# time series will be meaningless.
lynx.ar <- ar(log(lynx))
lynx.model <- list(order = c(lynx.ar$order, 0, 0), ar = lynx.ar$ar)
lynx.res <- lynx.ar$resid[!is.na(lynx.ar$resid)]
lynx.res <- lynx.res - mean(lynx.res)
lynx.sim <- function(res,n.sim, ran.args) {
# random generation of replicate series using arima.sim
rg1 <- function(n, res) sample(res, n, replace = TRUE)
ts.orig <- ran.args$ts
ts.mod <- ran.args$model
mean(ts.orig)+ts(arima.sim(model = ts.mod, n = n.sim,
rand.gen = rg1, res = as.vector(res)))
}
lynx.3 <- tsboot(lynx.res, lynx.fun, R = 99, sim = "model", n.sim = 114,
orig.t = FALSE, ran.gen = lynx.sim,
ran.args = list(ts = log(lynx), model = lynx.model))
# For "post-blackening" we need to define another function
lynx.black <- function(res, n.sim, ran.args) {
ts.orig <- ran.args$ts
ts.mod <- ran.args$model
mean(ts.orig) + ts(arima.sim(model = ts.mod,n = n.sim,innov = res))
}
# Now we can run apply the two types of block resampling again but this
# time applying post-blackening.
lynx.1b <- tsboot(lynx.res, lynx.fun, R = 99, l = 20, sim = "fixed",
n.sim = 114, orig.t = FALSE, ran.gen = lynx.black,
ran.args = list(ts = log(lynx), model = lynx.model))
lynx.2b <- tsboot(lynx.res, lynx.fun, R = 99, l = 20, sim = "geom",
n.sim = 114, orig.t = FALSE, ran.gen = lynx.black,
ran.args = list(ts = log(lynx), model = lynx.model))
# To compare the observed order of the bootstrap replicates we
# proceed as follows.
table(lynx.1$t[, 1])
table(lynx.1b$t[, 1])
table(lynx.2$t[, 1])
table(lynx.2b$t[, 1])
table(lynx.3$t[, 1])
# Notice that the post-blackened and model-based bootstraps preserve
# the true order of the model (11) in many more cases than the others.
# }