WN_test: Testing for white noise hypothesis in high dimension

Description

WN_test() implements the test proposed in Chang, Yao and Zhou (2017) for the following hypothesis testing problem: $$H_0:\{{\bf y}_t \}_{t=1}^n\mathrm{\ is\ white\ noise\ \ versus\ \ }H_1:\{{\bf y}_t \}_{t=1}^n\mathrm{\ is\ not\ white\ noise.} $$

Usage

WN_test(
  Y,
  lag.k = 2,
  B = 1000,
  kernel.type = c("QS", "Par", "Bart"),
  pre = FALSE,
  alpha = 0.05,
  control.PCA = list()
)

Value

An object of class "hdtstest", which contains the following components:

statistic: The test statistic of the test.
p.value: The p-value of the test.
lag.k: The time lag used in function.
kernel.type: The kernel used in function.

Arguments

Y: An $n \times p$ data matrix ${\bf Y} = ({\bf y}_1, \dots , {\bf y}_n )'$, where $n$ is the number of the observations of the $p \times 1$ time series $\{{\bf y}_t\}_{t=1}^n$.
lag.k: The time lag $K$ used to calculate the test statistic [See (4) of Chang, Yao and Zhou (2017)]. The default is 2.
B: The number of bootstrap replications for generating multivariate normally distributed random vectors when calculating the critical value. The default is 1000.
kernel.type: The option for choosing the symmetric kernel used in the estimation of long-run covariance matrix. Available options include: "QS" (the default) for the Quadratic spectral kernel, "Par" for the Parzen kernel, and "Bart" for the Bartlett kernel. See Chang, Yao and Zhou (2017) for more information.
pre: Logical. If TRUE (the default), the time series PCA proposed in Chang, Guo and Yao (2018) should be performed on $\{{\bf y}_t\}_{t=1}^n$ before implementing the white noise test [See Remark 1 of Chang, Yao and Zhou (2017)]. The time series PCA is implemented by using the function PCA_TS with the arguments passed by control.PCA.
alpha: The significance level of the test. The default is 0.05.
control.PCA: A list of control arguments passed to the function PCA_TS(), including lag.k, opt, thresh, delta, and the associated arguments passed to the clime function (when opt = 2). See 'Details’ in PCA_TS.

References

Chang, J., Guo, B., & Yao, Q. (2018). Principal component analysis for second-order stationary vector time series. The Annals of Statistics, 46, 2094--2124. tools:::Rd_expr_doi("doi:10.1214/17-AOS1613").

Chang, J., Yao, Q., & Zhou, W. (2017). Testing for high-dimensional white noise using maximum cross-correlations. Biometrika, 104, 111--127. tools:::Rd_expr_doi("doi:10.1093/biomet/asw066").

Examples

Run this code

#Example 1
## Generate xt
n <- 200
p <- 10
Y <- matrix(rnorm(n * p), n, p)

res <- WN_test(Y)
Pvalue <- res$p.value
rej <- res$reject