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Block Bootstrap for Time Series (Rcpp Implementation)

blockBootstrap.Rd

Generates bootstrap replicates of a multivariate time series using either the Moving Block Bootstrap (MBB) or Stationary Bootstrap (SB) methods. Not intended to be called directly by user, only to be called internally by tsbs().

Usage

blockBootstrap(
  x,
  n_boot = NULL,
  block_length = NULL,
  bs_type = "moving",
  block_type = "overlapping",
  taper_type = "cosine",
  tukey_alpha = 0.5,
  num_blocks = NULL,
  num_boots = 20L,
  p = 0.1,
  stationary_max_percentile = 0.99,
  stationary_max_fraction_of_n = 0.1
)

Arguments

x

A numeric matrix with rows representing time points and columns representing variables.

n_boot

Integer or NULL. Desired number of time points in the bootstrap sample. If NULL, the original series length is used.

block_length

Integer or NULL. Length of each block. If NULL, a heuristic is used based on the average lag-1 autocorrelation across variables.

bs_type

Bootstrap type. Character string: One of "moving" or "stationary". Default "moving".

block_type

Character. Block type. Either "non-overlapping", "overlapping" or "tapered". Default "overlapping".

taper_type

Tapering window function. Character. One of "cosine", "bartlett", or "tukey". Default "cosine".

tukey_alpha

alpha when block_type = "tapered" and taper_type = "tukey". Default 0.5.

num_blocks

Integer or NULL. Number of blocks to use. If NULL, this is inferred from n_boot.

num_boots

Number of bootstrap replicates to generate.

p

numeric \(p \in (0, 1)\). Probability parameter for the geometric block length (used in Stationary Bootstrap). Default is 0.1.

stationary_max_percentile

Stationary max percentile. Default is 0.99.

stationary_max_fraction_of_n

Stationary max fraction of n. Default is 0.10.

Value

A list of matrices, each one a bootstrap replicate with dimensions approximately n_length × ncol(x).

Details

The Moving Block Bootstrap (MBB) resamples fixed-length overlapping blocks from the original time series. The Stationary Bootstrap (SB) samples blocks with geometrically distributed lengths and can optionally enforce non-overlap constraints.

If n_boot is set, the last block will be trimmed when necessary. If n_boot is not set, and num_blocks is set, the length of each bootstrap series will be determined by the number of blocks and the lengths of the individual blocks for that particular series. If neither n_boot nor num_blocks is set, n_boot will default to the number of rows in x and the last block will be trimmed when necessary.

References

Politis, D., & Romano, J. (1994). The Stationary Bootstrap. Journal of the American Statistical Association, 89, 1303-1313. http://dx.doi.org/10.1080/01621459.1994.10476870

Examples

set.seed(123)
x <- matrix(rnorm(100), ncol = 1)
boots <- blockBootstrap(x, bs_type = "stationary", num_boots = 5L)
dim(boots[[1]])
#> [1] 100   1