tsboot {boot}  R Documentation 
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.
tsboot(tseries, statistic, R, l=NULL, sim="model", endcorr=TRUE, n.sim=NROW(tseries), orig.t=TRUE, ran.gen, ran.args=NULL, norm=TRUE, ...)
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 time statistic is
called it is passed a time series of length n.sim which is of the
same class as the original tseries . Any other arguments which
statistic takes must remain constant for each bootstrap replicate
and should be supplied through the ...{} argument to tsboot .

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 of
l ), "geom" (block resampling with block lengths
having a geometric distribution with mean l ) or
"scramble" (phase scrambling).

l 
If sim is "fixed" then l is the fixed block
length used in generating the replicate time series. If sim is
"geom" then l is the mean of the geometric distribution
used to generate the block lengths. l should be a positive
integer less than the length of tseries . This argument is not
required when sim 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" . When sim is
"geom" , endcorr is automatically set to TRUE ;
endcorr is not used when sim 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 if tseries 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 to tseries itself as well as the bootstrap replicate
series. If statistic is expecting a longer time series than
tseries or if applying statistic to tseries will
not yield any useful information then orig.t should be set to
FALSE .

ran.gen 
This is a function of three arguments. The first argument is a time
series. If sim is code{"model"} then it will always be
tseries that is passed. For other simulation types it is the
result of selecting n.sim observations from tseries by
some scheme and converting the result back into a time series of the
same form as tseries (although of length n.sim ). The
second argument to ran.gen is always the value n.sim , and
the third argument is ran.args , which is used to supply any other
objects needed by ran.gen . If sim is "model" then
the generation of the replicate time series will be done in
ran.gen (for example through use of arima.sim ).
For the other simulation types ran.gen is used for
“postblackening”. 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. If ran.gen needs
any extra arguments then they should be supplied as components of ran.args .
Multiple arguments may be passed by making ran.args a list. If ran.args
is NULL then it should not be used within ran.gen but note that ran.gen
must still have its third argument.

norm 
A logical argument indicating whether normal margins should be used for
phase scrambling. If norm is FALSE then margins corresponding to the exact
empirical margins are used.

... 
Any extra arguments to statistic may be supplied here.

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
endtoend 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
. Postblackening 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"
.
An object of class "boot"
with the following components.
t0 
If orig.t is TRUE then t0 is the result of statistic(tseries,...{})
otherwise it is NULL .

t 
The results of applying statistic to the replicate time series.

R 
The value of R as supplied to tsboot .

tseries 
The original time series. 
statistic 
The function statistic as supplied.

sim 
The simulation type used in generating the replicates. 
endcorr 
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" .

n.sim 
The value of n.sim used.

l 
The value of l used for block based resampling. This will be NULL if
block based resampling was not used.

ran.gen 
The ran.gen function used for generating the series or for "postblackening".

ran.args 
The extra arguments passed to ran.gen .

call 
The original call to tsboot .

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.
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$model mean(ts.orig)+ts(arima.sim(model=ts.mod, n=n.sim, rand.gen=rg1, res=as.vector(res))) } lynx.3 < tsboot(lynx.res, lynx.fun, R=99, sim="model", n.sim=114, orig.t=FALSE, ran.gen=lynx.sim, ran.args=list(ts=log(lynx), model=lynx.model)) # For "postblackening" we need to define another function lynx.black < function(res, n.sim, ran.args) { ts.orig < ran.args$ts ts.mod < ran.args$model mean(ts.orig) + ts(arima.sim(model=ts.mod,n=n.sim,innov=res)) } # Now we can run apply the two types of block resampling again but this # time applying postblackening. lynx.1b < tsboot(lynx.res, lynx.fun, R=99, l=20, sim="fixed", n.sim=114, orig.t=FALSE, ran.gen=lynx.black, ran.args=list(ts=log(lynx), model=lynx.model)) lynx.2b < tsboot(lynx.res, lynx.fun, R=99, l=20, sim="geom", n.sim=114, orig.t=FALSE, ran.gen=lynx.black, ran.args=list(ts=log(lynx), model=lynx.model)) # To compare the observed order of the bootstrap replicates we # proceed as follows. table(lynx.1$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 postblackened and modelbased bootstraps preserve # the true order of the model (11) in many more cases than the others.