blockboot {boodd}R Documentation

Block Bootstrap

Description

The function applies block bootstrap methods to a time series.

This function allows the following block bootstrap methods to be used: the Moving Block Bootstrap (Kunsch (1989), Liu and Singh (1992)), the Nonoverlapping Block Bootstrap (Carlstein (1986)), the Circular Block Bootstrap (Politis and Romano (1992)), and the Stationary Bootstrap (Politis and Romano (1994)).

Usage

blockboot(
  x,
  func,
  B,
  length.block = NULL,
  method = c("movingblock", "nonoverlapping", "circular", "stationary"),
  moon = NULL,
  replace = "TRUE",
  ...
)

Arguments

x

A vector or a time series.

func

The function to apply to each sample.

B

A positive integer; the number of bootstrap replications.

length.block

A positive integer; the length of the blocks.

method

The block bootstrap method. The possible values of the method argument are: "movingblock", "nonoverlapping", "circular" or "stationary". If it is not specified, the default method is "movingblock". Method names may be abbreviated.

moon

Integer or NULL. When moon = NULL (default), blockboot performs a regular block bootstrap without subsampling. If moon is equal to some integer value, the function creates block bootstrap samples of size moon, drawing blocks of length length.block. Ensure that moon is less than n - 5, where n is the size of the data.

replace

Logical. If replace = TRUE (default), the function performs block bootstrap with replacement. If replace = FALSE, it performs Block Bootstrap Subsampling without replacement. In this case moon should be specified.

...

Optional additional arguments for the func function.

Details

Nonoverlapping Block Bootstrap (NBB) consists in cutting the original time series into nonoverlapping blocks of fixed length length.block and in resampling these blocks to reconstruct a bootstrap time series. Moving Block Bootstrap (MBB) consists in drawing independently overlapping blocks of fixed size length.block to reconstruct a bootstrap time series of length of the original process. Circular Block Bootstrap (CBB) consists in wrapping the data on a circle and to create the corresponding overlapping blocks, so that each value of the time series appears globally the same number of times in all the blocks. This generally reduce the bias of the bootstrap distribution. Stationary Bootstrap (SB) is based on blocks with random length, which ensure that the bootstrap sample is stationary.

Value

An object of class boodd.

References

Bertail, P. and Dudek, A. (2025). Bootstrap for Dependent Data, with an R package (by Bernard Desgraupes and Karolina Marek) - submitted.

Carlstein E. (1986). The use of subseries methods for estimating the variance of a general statistic from a stationary time series. Annals of Statist., 14, 1171-1179.

Künsch, H. (1989). The jackknife and the bootstrap for general stationary observations. Ann. Statist., 17, 1217-1241.

Liu, R. and Singh, K. (1992). Moving block jackknife and bootstrap capture weak dependence. Exploring the Limits of Bootstrap., Series in Probab. Math. Statist. Wiley, New York, pp 225-248.

Politis, D.N. and Romano, J.P. (1994). The stationary bootstrap. J. Amer. Statist. Assoc., 89, 1303–1313.

Politis, D.N. and Romano, J.P. (1992). A circular block-resampling procedure for stationary data. Exploring the Limits of Bootstrap., Series in Probab. Math. Statist. Wiley, New York, pp 263-270.

See Also

boots, bootsemi, plot.boodd, confint.boodd, fieldboot, jackVarBlock.

Examples

B <- 999
data(airquality)
x <- airquality$Wind
n <- length(x)
b <- floor(sqrt(n))
boo1 <- blockboot(x,mean,B,b,method="moving")
plot(boo1,main="MBB", nclass=30)
confint(boo1, method="all")

[Package boodd version 0.1 Index]