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 = lagk.vec, con_vec = con_vec, alpha = alpha)

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

A dataframe containing the following components:

result

'1' means we reject the null hypothesis and '0' means we do not reject the null hypothesis.

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)