MartG_test  R Documentation 
MartG_test()
implements a new test proposed in
Chang, Jiang and Shao (2021) for the following hypothesis testing problem:
H_0:\{{\bf x}_t\}_{t=1}^n\mathrm{\ is\ a\ MDS\ \ versus\ \ }H_1:
\{{\bf x}_t\}_{t=1}^n\mathrm{\ is\ not\ a\ MDS,}
where MDS is the abbreviation of "martingale difference sequence".
MartG_test(
X,
lag.k = 2,
B = 1000,
type = c("Linear", "Quad"),
alpha = 0.05,
kernel.type = c("QS", "Par", "Bart")
)
X 

lag.k 
Time lag 
B 
Bootstrap times for generating multivariate normal distributed
random vectors in calculating the critical value.
Default is 
type 
String, a map is chosen by the R users, such as the
default option is 
alpha 
The prescribed significance level. Default is 0.05. 
kernel.type 
String, an option for choosing the symmetric kernel
used in the estimation of longrun covariance matrix,
for example, 
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. 
lag.k 
The time lag used in function. 
method 
A character string indicating what method was performed. 
type 
A character string which map used on data matrix 
kernel.type 
A character string indicating what kenel method was performed. 
Chang, J., Jiang, Q. & Shao, X. (2022). Testing the martingale difference hypothesis in high dimension. Journal of Econometrics, in press
n < 200
p < 10
X < matrix(rnorm(n*p),n,p)
res < MartG_test(X, type="Linear")
res < MartG_test(X, type=cbind(X, X^2)) #the same as Linear type
res < MartG_test(X, type=quote(cbind(X, X^2))) # expr using quote
res < MartG_test(X, type=substitute(cbind(X, X^2))) # expr using substitute
res < MartG_test(X, type=expression(cbind(X, X^2))) # expr using expression
res < MartG_test(X, type=parse(text="cbind(X, X^2)")) # expr using parse
map_fun < function(X) {X < cbind(X,X^2); X}
res < MartG_test(X, type=map_fun)
Pvalue < res$p.value
rej < res$reject
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