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