bootstrap(x, nb = 1, statistic = NULL, b = NULL,
type = c("stationary","block"), ...)
type
is "stationary"
, then b
is the
mean block length. If type
is "block"
, then b
is the fixed block length."stationary"
(stationary bootstrap with mean block length b
) and
"block"
(moving blocks bootstrap with block lenstatistic
which are
passed unchanged each time statistic
is called.statistic
is NULL
, then it returns a matrix or time
series with nb
columns and length(x)
rows containing the
bootstrap data. Each column contains one bootstrap sample. If statistic
is given, then a list of class
"resample.statistic"
with the following elements is returned:
statistic
to each of
the simulated time series.statistic
to the
original series.bootstrap
.type
is "stationary"
, then the stationary
bootstrap scheme with mean block length b
generates the
simulated series. If type
is "block"
, then the moving
blocks bootstrap with block length b
generates the
simulated series. For consistency, the (mean) block length b
should grow with
n
as const * n^(1/3)
, where n
is the number of
observations in x
. Note, that in general const
depends
on intricate properties of the process x
. The default value for
const
has been determined by a Monte Carlo simulation using a
Gaussian AR(1) (AR(1)-parameter of 0.5, 500 observations) process for
x
. It is chosen such that the mean square error for
the bootstrap estimate of the variance of the empirical mean is
minimized.
Missing values are not allowed.
There is a special print method for objects of class
"resample.statistic"
which by default uses
max(3, getOption("digits") - 3)
digits to format real numbers.
D. N. Politis and J. P. Romano (1994): The Stationary Bootstrap. Journal of the American Statistical Association 89, 1303--1313.
sample
,
surrogate
n <- 500 # Generate AR(1) process
e <- rnorm(n)
x <- double(n)
x[1] <- rnorm(1)
for(i in 2:n) {
x[i] <- 0.5 * x[i-1] + e[i]
}
x <- ts(x)
theta <- function(x) # Autocorrelations up to lag 10
return(acf(x, plot=FALSE)$acf[2:11])
bootstrap(x, nb=50, statistic=theta)
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