| 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)