Compute Optimal Block Length for Stationary and Circular Bootstrap

b.star is a function which computes the optimal block length for the continuous variable data using the method described in Patton, Politis and White (2009).

Usage

b.star(data,
       Kn = NULL,
       mmax= NULL,
       Bmax = NULL,
       c = NULL,
       round = FALSE)

Arguments

Data Input

Time-series data used for automatic block-length selection.

data: data, an n x k matrix, each column being a data series.

Block-Length Selection Controls

Tuning constants from Politis and White (2004) and Patton, Politis, and White (2009).

Kn: See footnote c, page 59, Politis and White (2004). Defaults to ceiling(log10(n)).
mmax: See Politis and White (2004). Defaults to ceiling(sqrt(n))+Kn.
Bmax: See Politis and White (2004). Defaults to ceiling(min(3*sqrt(n),n/3)).
c: See Politis and White (2004). Defaults to qnorm(0.975).

Output Rounding

Control for rounding the selected block lengths.

round: whether to round the result or not. Defaults to FALSE.

Value

A kx2 matrix of optimal bootstrap block lengths computed from data for the stationary bootstrap and circular bootstrap (column 1 is for the stationary bootstrap, column 2 the circular).

Details

b.star is a function which computes optimal block lengths for the stationary and circular bootstraps. This allows the use of tsboot from the boot package to be fully automatic by using the output from b.star as an input to the argument l = in tsboot. See below for an example.

References

Patton, A. and D.N. Politis and H. White (2009), “CORRECTION TO "Automatic block-length selection for the dependent bootstrap" by D. Politis and H. White”, Econometric Reviews 28(4), 372-375.

Politis, D.N. and J.P. Romano (1994), “Limit theorems for weakly dependent Hilbert space valued random variables with applications to the stationary bootstrap”, Statistica Sinica 4, 461-476.

Politis, D.N. and H. White (2004), “Automatic block-length selection for the dependent bootstrap”, Econometric Reviews 23(1), 53-70.

Author

Tristen Hayfield tristen.hayfield@gmail.com, Jeffrey S. Racine racinej@mcmaster.ca

Examples

set.seed(12345)

# Function to generate an AR(1) series

ar.series <- function(phi,epsilon) {
  n <- length(epsilon)
  series <- numeric(n)
  series[1] <- epsilon[1]/(1-phi)
  for(i in 2:n) {
    series[i] <- phi*series[i-1] + epsilon[i]
  }
  return(series)
}

yt <- ar.series(0.1,rnorm(10000))
b.star(yt,round=TRUE)
#>      BstarSB BstarCB
#> [1,]       7       8

yt <- ar.series(0.9,rnorm(10000))
b.star(yt,round=TRUE)
#>      BstarSB BstarCB
#> [1,]      78      89