UR_test: Testing for unit roots based on sample autocovariances

In HDTSA: High Dimensional Time Series Analysis Tools

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)

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.

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.

References

Chang, J., Cheng, G., & Yao, Q. (2022). Testing for unit roots based on sample autocovariances. Biometrika, 109, 543–550. \Sexpr[results=rd]{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)

HDTSA documentation built on April 3, 2025, 11:07 p.m.