Generate Bootstrap Data and Statistics

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), ...)
a numeric vector or time series.
the number of bootstrap series to compute.
a function which when applied to a time series returns a vector containing the statistic(s) of interest.
if type is "stationary", then b is the mean block length. If type is "block", then b is the fixed block length.
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 leng
a list with class "resample.statistic".
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:

  • statisticthe results of applying statistic to each of the simulated time series.
  • orig.statisticthe results of applying statistic to the original series.
  • biasthe bias of the statistics computed as in a bootstrap setup.
  • sethe standard error of the statistics computed as in a bootstrap setup.
  • callthe original call of bootstrap.


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.

See Also

sample, surrogate

  • bootstrap
  • print.resample.statistic
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)
Documentation reproduced from package tseries, version 0.7-4, License: GPL (see file COPYING), except for ./src/muin2ser.f and ./misc which are free for non-commercial purposes. See file README for details.

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