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 long-run 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 p-value 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 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.
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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