UR_test: 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)

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.

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.

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

Run this code

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)

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