| bootstrap {tseries} | R Documentation |
bootstrap generates bootstrap samples for general stationary
data and computes the bootstrap estimate of standard error and bias
if a statistic is given.
bootstrap(x, nb = 1, statistic = NULL, b = NULL,
type = c("stationary","block"), ...)
x |
a numeric vector or time series giving the original data. |
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" (blockwise bootstrap with block length
b). Default to "stationary". |
... |
additional arguments for statistic which are
passed unchanged each time statistic is called. |
If type is "stationary", then the stationary
bootstrap scheme with mean block length b according to Politis
and Romano (1994) is used to generate the simulated series. For
type equals "block", the blockwise bootstrap with block
length b according to Kuensch (1989) is used.
Note, that this bootstrap procedure does not implement the block of
blocks bootstrap. Hence, it may only be used for symmetric statistics,
i.e., for statistics which are invariant under permutations of
x.
For consistency, the (mean) block length b should grow with
n at an appropriate rate. If b is not given, then a
default growth rate of const * n^(1/3) is used (n is the
number of observations in x). This rate is "optimal" under
certain conditions (see the references for more details). However, in
general the growth rate depends on the specific properties of the
process which has generated x. Therefore, a default value for
const has been determined by a Monte Carlo simulation using a
Gaussian AR(1) process (AR(1)-parameter of 0.5, 500
observations). const has been 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.
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 bootstrap estimate of the bias of statistic. |
se |
the bootstrap estimate of the standard error of statistic. |
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. Journal of the American Statistical Association 89, 1303–1313.
n <- 500 # Generate AR(1) process
a <- 0.6
e <- rnorm(n+100)
x <- double(n+100)
x[1] <- rnorm(1)
for(i in 2:(n+100)) {
x[i] <- a * x[i-1] + e[i]
}
x <- ts(x[-(1:100)])
bootstrap(x, nb=500, statistic=mean) # ok
bootstrap(x, nb=500, statistic=mean, type="block", b=1) # wrong here
# std. error for mean should approximately be
sqrt(1/(n*(1-a)^2))