A New Approach to Unit Root Testing
A novel simulation based approach to unit root testing is proposed in this paper. The test is constructed from the distinct orders in probability of the OLS parameter estimates obtained from a spurious and an unbalanced regression, respectively. While the parameter estimate from a regression of two integrated and uncorrelated time series is of order O p (1), the estimate is of order O p (T −1) if the dependent variable is stationary. The test statistic is constructed as an interquantile range from the empirical distribution obtained from regressing the standardized data sufficiently often on controlled random walks. GLS detrending (Elliott et al., Econometrica 64(4):813–836, 1996) and spectral density variance estimators (Perron and Ng, Econom Theory 14(5):560–603, 1998) are applied to account for deterministic terms and residual autocorrelation in the data. A Monte Carlo study confirms that the proposed test has favorable empirical size properties and is powerful in local-to-unity neighborhoods. As an empirical illustration, we test the purchasing power parity hypothesis for a sample of G7 economies.
KeywordsUnit root tests Simulation based test Simulation study PPP hypothesis
JEL ClassificationC22 C12
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