WN_test: Testing for white noise hypothesis in high dimension

In HDTSA: High Dimensional Time Series Analysis Tools

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()
)

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.

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.

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. \Sexpr[results=rd]{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. \Sexpr[results=rd]{tools:::Rd_expr_doi("doi:10.1093/biomet/asw066")}.

See Also

PCA_TS

Examples

#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

HDTSA documentation built on April 3, 2025, 11:07 p.m.