Unit root testing with stationary covariates and a structural break in the trend function

Abstract

The issue of testing for a unit root allowing for a structural break in the trend function is considered. The focus is on the construction of more powerful tests using the information in relevant multi‐variate data sets. The proposed test adopts the generalized least squares detrending approach and uses correlated stationary covariates to improve power. As it is standard in the literature, the break date is treated as unknown. Asymptotic distributions are derived, and a set of asymptotic and finite sample critical values are tabulated. Asymptotic local power functions show that power gains can be large. Finite sample results show that the test exhibits small‐size distortions and power that can be far beyond what is achievable by univariate tests.

Covariate unit root tests with good size and power

“…In addition, this paper proposes a strategy to select the lead and lag orders for the CADF-GLS test that yields tests with better power. Finally, these results should also prove useful for the covariate unit root tests proposed in Fossati (2009) and Galvao (2009).…”

Predicting Ghana’s Daily Natural Gas Consumption Using Time Series Models

“…The ADF test is commonly used to check the stationarity of a time series by looking for the presence of a unit root in the data. If the ADF test rejects the null hypothesis of a unit root, then the time series is considered to be stationary [32]. In this study, the ADF test was used to find out whether the time series data used had unit root or were covariance stationary.…”

Synergy between an Improved Covariate Unit Root Test and Cross‐sectionally Dependent Panel Data Unit Root Tests

“…Juhl and Xiao () proposed modifying the POC test by introducing the standard of optimality proposed by Cox and Hinkley () to obtain the optimal point optimal covariate (OPOC) unit root test. More recently, Fossati () extended the covariate unit root tests to models with structural breaks, while Westerlund () allowed for conditional heteroskedasticity. These studies showed that the powers of the ADF and the ADF‐GLS tests could be much improved if we can find covariates that are highly correlated with the disturbance term.…”