bootstrap {tseries} | R Documentation |
Generates 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), ...)
x |
a numeric vector or time series. |
nb |
the number of bootstrap series to compute. |
statistic |
a function which when applied to a time series returns a vector containing the statistic(s) of interest. |
b |
if type is "stationary" , then b is the
mean block length. If type is "block" , then b
is the fixed block length. |
type |
the type of bootstrap to generate the simulated time
series. The possible input values are "stationary"
(stationary bootstrap with mean block length b ) and
"block" (moving blocks bootstrap with block length
b ). |
object |
a list with class "resample.statistic" . |
digits |
the number of digits to format real numbers. |
... |
either additional arguments for statistic which are
passed unchanged each time statistic is called
(bootstrap ), or additional arguments for print
(print.resample.statistic ). |
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.
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.
If 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 |
the results of applying statistic to each of
the simulated time series. |
orig.statistic |
the results of applying statistic to the
original series. |
bias |
the bias of the statistics computed as in a bootstrap setup. |
se |
the standard error of the statistics computed as in a bootstrap setup. |
call |
the original call of bootstrap . |
A. Trapletti
H. R. Kuensch (1989): The Jackknife and the Bootstrap for General Stationary Observations. The Annals of Statistics 17, 1217-1241.
D. N. Politis and J. P. Romano (1994): The Stationary Bootstrap. J. Amer. Statist. Assoc. 89, 1303-1313.
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)