# pwsd: Politis and White (2004) Spectral Density "PWSD" Automatic... In blocklength: Select an Optimal Block-Length to Bootstrap Dependent Data (Block Bootstrap)

 pwsd R Documentation

## Politis and White (2004) Spectral Density "PWSD" Automatic Block-Length Selection

### Description

Run the Automatic Block-Length selection method proposed by Politis and White (2004) and corrected in Patton, Politis, and White (2009). The method is based on spectral density estimation via flat-top lag windows of Politis and Romano (1995). This code was adapted from `b.star` to add functionality and include correlogram support including an S3 method, see Hayfield and Racine (2008).

### Usage

```pwsd(
data,
K_N = NULL,
M_max = NULL,
m_hat = NULL,
b_max = NULL,
c = NULL,
round = FALSE,
correlogram = TRUE
)
```

### Arguments

 `data` an n x k data.frame, matrix, or vector (if k = 1) where the optimal block-length will be computed for each of the k columns. `K_N` an integer value, the maximum lags for the auto-correlation, rho_k, which to apply the implied hypothesis test. Defaults to `max(5, log(N))`. See Politis and White (2004) footnote c. `M_max` an integer value, the upper-bound for the optimal number of lags, M, to compute the auto-covariance for. See Theorem 3.3 (ii) of Politis and White (2004). `m_hat` an integer value, if set to `NULL` (the default), then `m_hat` is estimated as the smallest integer after which the correlogram appears negligible for `K_N` lags. In problematic cases, setting `m_hat` to an integer value can be used to override the estimation procedure. `b_max` a numeric value, the upper-bound for the optimal block-length. Defaults to `ceiling(min(3 * sqrt(n), n / 3))` per Politis and White (2004). `c` a numeric value, the constant which acts as the significance level for the implied hypothesis test. Defaults to `qnorm(0.975)` for a two-tailed 95% confidence level. Politis and White (2004) suggest `c = 2`. `round` a logical value, if set to `FALSE` then the final block-length output will not be rounded, the default. If set to `TRUE` the final estimates for the optimal block-length will be rounded to whole numbers. `correlogram` a logical value, if set to `TRUE` a plot of the correlogram (i.e. a plot of R(k) vs. k) will be output to the console. If set to `FALSE`, no interim plots will be output to the console, but may be plotted later using the corresponding S3 method, plot.pwsd.

### Value

an object of class 'pwsd'

### References

Andrew Patton, Dimitris N. Politis & Halbert White (2009) Correction to "Automatic Block-Length Selection for the Dependent Bootstrap" by D. Politis and H. White, Econometric Review, 28:4, 372-375, DOI: doi: 10.1080/07474930802459016

Dimitris N. Politis & Halbert White (2004) Automatic Block-Length Selection for the Dependent Bootstrap, Econometric Reviews, 23:1, 53-70, DOI: doi: 10.1081/ETC-120028836

Politis, D.N. and Romano, J.P. (1995), Bias-Corrected Nonparametric Spectral Estimation. Journal of Time Series Analysis, 16: 67-103, DOI: doi: 10.1111/j.1467-9892.1995.tb00223.x

Tristen Hayfield and Jeffrey S. Racine (2008). Nonparametric Econometrics: The np Package. Journal of Statistical Software 27(5). DOI: doi: 10.18637/jss.v027.i05

### Examples

```# Generate AR(1) time series
sim <- stats::arima.sim(list(order = c(1, 0, 0), ar = 0.5),
n = 500, innov = rnorm(500))

# Calculate optimal block length for series
pwsd(sim, round = TRUE)

# Use S3 Method
b <- pwsd(sim, round = TRUE, correlogram = FALSE)
plot(b)

```

blocklength documentation built on March 18, 2022, 7:12 p.m.