Nonlinearly testing for a unit root in the presence of a break in the mean

Gluschenko, Konstantin (2004): Nonlinearly testing for a unit root in the presence of a break in the mean.

Abstract

This paper deals with testing a time series with a structural break in its mean for a unit root when the break date is known. A nonlinear (with respect to coefficients) test equation is used, providing asymptotically efficient estimates. Finite-sample and quasi-asymptotic empirical distributions of the unit root test statistics are estimated, comparing them with those associated with the Perron-type equations. Asymptotic distributions of the nonlinear test statistics are found to be the Dickey-Fuller distributions. The nonlinear test proves to have more power than the test based on the linear model.

• Item Type: MPRA Paper
• Language: English
• Keywords: structural break; nonlinear regression; nonstandard distribution
• Subjects: C - Mathematical and Quantitative Methods > C2 - Single Equation Models ; Single Variables > C22 - Time-Series Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes; ; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C15 - Statistical Simulation Methods: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General

References

Bartley, W.A., Lee, J., and Strazicich, M.C. (2001), “Testing the null of cointegration in the presence of a structural break,” Economics Letters, 73, 315–323. Dickey, D.A., and Fuller, W.A. (1979), “Distribution of the estimators for autoregressive time series with a unit root,” Journal of the American Statistical Association. 74, 427-431. Evans, G.B.A., and Savin, N.E. (1981), “Testing for Unit Roots: 1,” Econometrica, 49, 753-779. Evans, G.B.A., and Savin, N.E. (1984), “Testing for Unit Roots: 2,” Econometrica, 52, 1241-1270. Gluschenko, K. (2004), “Integration of the Russian Market: Empirical Analysis,” EERC Working paper No. 04/06. Hansen, B.E. (1997), “Approximate Asymptotic P Values for Structural-Change Tests,” Journal of Business and Economic Statistics, 15, 60-67. Hansen, B.E. (2001), “The New Econometrics of Structural Change: Dating Breaks in U.S. labor productivity,” Journal of Economic Perspectives, 15, 117-128. Lanne, M., Lütkepohl, H., and Saikkonen, P. (2002), “Comparison of Unit Root Tests for Time Series With Level Shifts,” Journal of Time Series Analysis, 23 (6), 667-685. MacKinnon, J. G. (1996), “Numerical Distribution Functions for Unit Root and Cointegration Tests,” Journal of Applied Econometrics, 11, 601-618. Müller, U.K., and Elliott, G. (2003), “Tests for Unit Roots and the Initial Condition,” Econometrica, 71, 1269-1286. Newey, W. K., and West, K. D. (1994), “Automatic Lag Selection in Covariance Matrix Estimation,” Review of Economic Studies, 61, 631-653. Perron, P. (1989), “The Great Crash, the Oil Price Shock, and The Unit Root Hypothesis,” Econometrica, 57, 1361-1401. Perron, P. (1990), “Testing for a Unit Root in a Time Series with a Changing Mean,” Journal of Business and Economics Statistics, 8, 153-162. Perron, P., and Vogelsang, T.J. (1992), “Nonstationarity and Level Shifts with an Application to Purchasing Power Parity,” Journal of Business and Economics Statistics, 10, 301-320. Phillips, P.C.B. (1987), “Time Series Regression with a Unit Root,” Econometrica, 55, 277-301. Rappoport, P., and Reichlin, L. (1989), “Segmented Trends and Non-Stationary Time Series,” Economic Journal, 99 (395), 168-177. Quantitative Micro Software, LLC (2004), EViews 5 User’s Guide.