WN_test  R Documentation 
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.}
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
)
X 

lag.k 
Time lag 
B 
Bootstrap times for generating multivariate normal distributed
random vectors in calculating the critical value. Default is 
kernel.type 
String, an option for choosing the symmetric kernel used
in the estimation of longrun covariance matrix, for example, 
pre 
Logical value which determines whether to performs preprocessing
procedure on data matrix 
alpha 
The prescribed significance level. Default is 0.05. 
k0 
A positive integer specified to calculate 
thresh 
Logical. It determines whether to perform the threshold method
to estimate 
tuning.vec 
The value of thresholding tuning parameter 
An object of class "hdtstest" is a list containing the following components:
statistic 
The value of the test statistic. 
p.value 
Numerical value which represents the pvalue of the test
based on the observed data 
lag.k 
The time lag used in function. 
method 
A character string indicating what method was performed. 
kernel.type 
A character string indicating what kenel method was performed. 
Chang, J., Yao, Q. & Zhou, W. (2017). Testing for highdimensional white noise using maximum crosscorrelations, Biometrika, Vol. 104, pp. 111–127.
Chang, J., Guo, B. & Yao, Q. (2018). Principal component analysis for secondorder 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.
PCA_TS
n < 200
p < 10
X < matrix(rnorm(n*p),n,p)
res < WN_test(X)
Pvalue < res$p.value
rej < res$reject
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