New Unit Root Tests to Decrease Spurious Results with Applications in Finance and Temperature Anomalies

Abstract

Simulation studies show that when testing for cointegration with pairs of independent explosive($\gls{phi1} >1$) AR(1) time series almost invariably lead to spurious cointegrating relationships. A new unit root test, the lagged-series test, is proposed with similar power to the ADF test for non-explosive AR(1) series but higher power in the explosive case. The lagged-series unit root test can be combined with other unit root tests such as the Elliot-Rothenberg-Stock tests and the Zivot-Andrews test, as well as the ADF test to improve the statistical power in the explosive case. A new unit root test, the Hybrid Bai-Perron Zivot-Andrews test, is proposed which allows for structural breaks in intercept and linear trend under the null hypothesis and compares favorably in some cases to the Lee-Stratizich unit root test. A new testing procedure to check for stationary to nonstationary shifts in a time series, referred to as the Hybrid Bai-Perron ADF procedure, is proposed and tested. It is shown that different unit root test related statistics can be combined using deep learning neural networks and results in techniques that outperform individual unit root tests in various simulation studies. Simulation based studies of the ADF, ERS-Ptest, ERS-DFGLS, the Zivot-Andrews, and the new lagged-series unit root tests, under various model configurations were made and compared.