HDTSA (version 1.0.5)

UR_test: Testing for unit roots based on sample autocovariances

Description

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

Usage

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

Value

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.

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.

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").

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)