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