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 white noise tests proposed in Chang, Yao and Zhou (2017) and Chang et al. (2026+) 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,
  method = c("L_inf", "L_2"),
  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) and (6) of Chang et al. (2026+).]. The default is 2.
B	The number of bootstrap replications for calculating the critical value. The default is 1000.
method	The option for method used in the white noise test. Available options include: "L_inf" (the default) for the method proposed by Chang, Yao and Zhou (2017), and "L_2" for the method proposed by Chang et al. (2026+).
kernel.type	The option for choosing the symmetric kernel used in the estimation of long-run covariance matrix, which is used when method = "L_inf". 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. This parameter is used when method = "L_inf". 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 when method = "L_inf" and pre = TRUE, 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., He, J., Li, W., & Lin, C. (2026+). An adaptive L_2-type test for high-dimensional white noise. Preprint.

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 data
n <- 200
p <- 10
Y <- matrix(rnorm(n * p), n, p)

## L_inf
res1 <- WN_test(Y, method ="L_inf")
Pvalue1 <- res1$p.value
statistic1 <- res1$statistic

## L_2
res2 <- WN_test(Y, method = "L_2")
Pvalue2 <- res2$p.value
statistic2 <- res2$statistic

HDTSA documentation built on April 3, 2026, 9:07 a.m.