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() is the test proposed in Chang, Yao and Zhou (2017) for the following hypothesis testing problems:

H_0:\{{\bf x}_t \}_{t=1}^n\mathrm{\ is\ white\ noise\ \ versus\ \ }H_1:\{{\bf x}_t \}_{t=1}^n\mathrm{\ is\ not\ white\ noise.}

Usage

WN_test(
  X,
  lag.k = 2,
  B = 2000,
  kernel.type = c("QS", "Par", "Bart"),
  pre = FALSE,
  alpha = 0.05,
  k0 = 5,
  thresh = FALSE,
  tuning.vec = NULL
)

Arguments

X	{\bf X} = \{{\bf x}_1, … , {\bf x}_n \}', an n\times p sample matrix, where n is the sample size and p is the dimension of {\bf x}_t.
lag.k	Time lag K, a positive integer, used to calculate the test statistic [See (4) in Chang, Yao and Zhou (2017)]. Default is lag.k =2.
B	Bootstrap times for generating multivariate normal distributed random vectors in calculating the critical value. Default is B =2000.
kernel.type	String, an option for choosing the symmetric kernel used in the estimation of long-run covariance matrix, for example, 'QS' (Quadratic spectral kernel), 'Par' (Parzen kernel) and 'Bart' (Bartlett kernel), see Andrews (1991) for more information. Default option iskernel.type = 'QS'.
pre	Logical value which determines whether to performs preprocessing procedure on data matrix X or not, see Remark 1 in Chang, Yao and Zhou (2017) for more information. If TRUE, then the segment procedure will be performed to data X first. The three additional options including thresh, tuning.vec and cv.num are the same as those in PCA4_TS.
alpha	The prescribed significance level. Default is 0.05.
k0	A positive integer specified to calculate \widehat{{\bf W}}_y. See parameter lag.k in PCA4_TS for more information.
thresh	Logical. It determines whether to perform the threshold method to estimate \widehat{{\bf W}}_y or not. See parameter thresh in PCA4_TS for more information.
tuning.vec	The value of thresholding tuning parameter λ. See parameter tuning.vec in PCA4_TS for more information.

Value

An object of class "WN_test" is a list containing the following components:

reject	Logical value. If TRUE, it means rejecting the null hypothesis, otherwise it means not rejecting the null hypothesis.
p.value	Numerical value which represents the p-value of the test based on the observed data \{{\bf x}_t\}_{t=1}^n.

References

Chang, J., Yao, Q. & Zhou, W. (2017). Testing for high-dimensional white noise using maximum cross-correlations, Biometrika, Vol. 104, pp. 111–127.

Chang, J., Guo, B. & Yao, Q. (2018). Principal component analysis for second-order stationary vector time series, The Annals of Statistics, Vol. 46, pp. 2094–2124.

Cai, T. and Liu, W. (2011). Adaptive thresholding for sparse covariance matrix estimation, Journal of the American Statistical Association, Vol. 106, pp. 672–684.

See Also

PCA4_TS

Examples

n <- 200
p <- 10
X <- matrix(rnorm(n*p),n,p)
res <- WN_test(X)
Pvalue <- res$p.value
rej <- res$reject

HDTSA documentation built on Jan. 7, 2023, 5:26 p.m.