UR_test {HDTSA}

Testing for unit roots based on sample autocovariances

Description

The test proposed in Chang, Cheng and Yao (2021) for the following hypothesis testing problems:

H_0:Y_t \sim I(0)\ \ \mathrm{versus}\ \ H_1:Y_t \sim I(d)\ \mathrm{for\ some\ integer\ }d \geq 2.

Usage

UR_test(Y, lagk.vec = NULL, con_vec = NULL, alpha = 0.05)

Arguments

Y

Y = \{y_1, \dots , y_n \}, the observations of a univariate time series used for the test.

lagk.vec

Time lag K_0 used to calculate the test statistic, see Section 2.1 in Chang, Cheng and Yao (2021). It can be a vector containing more than one time lag. If it is a vector, the procedure will output all the test results based on the different K_0 in the vector lagk.vec. If lagk.vec is missing, the default value we choose lagk.vec=c(0,1,2,3,4).

con_vec

Constant c_\kappa, see (5) in Chang, Cheng and Yao (2021). It also can be a vector. If missing, the default value we use 0.55.

alpha

The prescribed significance level. Default is 0.05.

Value

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

statistic

A vector which represents the value of the test statistic, the length of this vector is the same as lag.vec

reject

A data matrix containing result with different arguments, each column represents the results of different c_\kappa calculations, and each column is a vector representing the results of different time lag K0 calculations.'1' means we reject the null hypothesis and '0' means we do not reject the null hypothesis

lag.vec

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 X.

References

Chang, J., Cheng, G. & Yao, Q. (2021). Testing for unit roots based on sample autocovariances. Available at https://arxiv.org/abs/2006.07551

Examples

N=100
Y=arima.sim(list(ar=c(0.9)), n = 2*N, sd=sqrt(1))
con_vec=c(0.45,0.55,0.65)
lagk.vec=c(0,1,2)
UR_test(Y,lagk.vec=lagk.vec, con_vec=con_vec,alpha=0.05)
UR_test(Y,alpha=0.05)