UR_test function

Testing for unit roots based on sample autocovariances

This function implements the test proposed in Chang, Cheng and Yao (2022) for the following hypothesis testing problem: [REMOVE_ME]$H_0:Y_t \sim I(0)\ \ \mathrm{versus}\ \ H_1:Y_t \simI(d)\ \mathrm{for\ some\ integer\ }d \geq 1\,, [REMOVE_ME_2]$ where $Y_t$ is a univariate time series.

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

Arguments

• Y: A vector ${\bf Y} = (Y_1, \dots , Y_n )'$, where $n$ is the number of the observations.
• lagk.vec: The time lag $K_0$ used to calculate the test statistic [See Section 2.1 of Chang, Cheng and Yao (2022)]. It can be a vector specifying multiple time lags. If provided as a $s \times 1$ vector, the function will output the test results corresponding to each of the $s$ values in lagk.vec. The default is c(0, 1, 2, 3, 4).
• con_vec: The constant $c_\kappa$ specified in (5) of Chang, Cheng and Yao (2022). The default is 0.55. Alternatively, it can be an $m \times 1$ vector specified by users, representing $m$ candidate values of $c_\kappa$.
• alpha: The significance level of the test. The default is 0.05.

Returns

An object of class "urtest", which contains the following components:

• statistic: A $s \times 1$ vector with each element representing the test statistic value associated with each of the $s$ time lags specified in lagk.vec.

• reject: An $m \times s$ data matrix ${\bf R}=(R_{i,j})$ where $R_{i,j}$ represents whether the null hypothesis $H_0$ should be rejected for $c_\kappa$ specified by the $i$-th component of con_vec, and $K_0$ specified by the $j$-th component of lagk.vec. $R_{i,j}=1$ indicates rejection of the null hypothesis, while $R_{i,j}=0$ indicates non-rejection.

• lag.vec: The time lags used in function.

Description

This function implements the test proposed in Chang, Cheng and Yao (2022) for the following hypothesis testing problem:

where $Y_t$ is a univariate time series.

Examples

# Example 1
## Generate yt
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)

References

Chang, J., Cheng, G., & Yao, Q. (2022). Testing for unit roots based on sample autocovariances. Biometrika, 109 , 543--550. tools:::Rd_expr_doi("doi:10.1093/biomet/asab034") .