Spurious regression under deterministic and stochastic trends

Noriega, Antonio E. and Ventosa-Santaulària, Daniel (2005): Spurious regression under deterministic and stochastic trends. Published in: Oxford Bulletin of Economics and Statistics , Vol. 69, No. 3 (2007): pp. 439-444.

Abstract

This paper analyses the asymptotic and finite sample implications of a mixed nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study the cases when the nonstationarity in the dependent variable is deterministic (stochastic), while the nonstationarity in the explanatory variable is stochastic (deterministic). In particular, we derive the asymptotic distribution of statistics in a spurious regression equation when one variable follows a difference stationary process (a random walk with and without drift), while the other is characterized by deterministic nonstationarity (a linear trend model with and without structural breaks in the trend function). We find that the divergence rate is sensitive to the assumed mixture of nonstationarity in the data generating process, and the phenomenon of spurious regression itself, contrary to previous findings, depends on the presence of a linear trend in the regression equation. Simulation experiments and real data confirm our asymptotic results.

• Item Type: MPRA Paper
• Language: English
• Keywords: Unit roots, Trend stationarity, Structural breaks, Spurious regression
• 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

References

Cappuccio, N. and D. Lubian (1997), ”Spurious Regressions Between I(1) Processes with Long Memory Errors”, Journal of Time Series Analysis, 18, 341-354.

Entorf, H. (1997), "Random Walks with Drifts: Nonsense Regression and Spurious Fixed-Effect Estimation", Journal of Econometrics, 80, 287-296.

Granger, C.W.J., N. Hyung, and Y. Jeon (1998), "Spurious Regressions with Stationary Series", Mimeo.

Kim, T.-H., Y.-S. Lee and P. Newbold (2003), "Spurious Regressions with Processes Around Linear Trends of Drifts", Discussion Paper in Economics, No. 03-07, University of Nottingham.

Kim, T.-H., Y.-S. Lee and P. Newbold (2004), "Spurious Regressions with Stationary Processes Around Linear Trends", Economics Letters, 83, 257-262.

Kormendi, R. C. and P. Meguire (1990), ”A Multicountry Characterization of the Nonstationarity of Aggregate Output”, Journal of Money, Credit and Banking, 22, 77-93.

Lumsdaine, R.L. and D.H. Papell (1997), ” Multiple Trend Breaks and the Unit Root Hypothesis”, The Review of Economics and Statistics, 79, 212-218.

Marmol (1995), "Spurious Regressions for I(d) Processes", Journal of Time Series Analysis, 16, 313-321.

Marmol (1996), "Correlation Theory for Spuriously Related Higher Order Integrated Processes", Economics Letters, 50, 163-73.

Marmol (1998), "Spurious Regression Theory with Nonstationary Fractionally Integrated Processes", Journal of Econometrics, 84, 233-50.

Mehl, A. (2000), ”Unit Root Tests with Double Trend Breaks and the 1990s Recession in Japan”, Japan and the World Economy, 12, 363-379.

Nelson, C.R. and C. Plosser (1982), ”Trends and Random Walks in Macroeconomic Time Series: Some Evidence and Implications”, Journal of Monetary Economics, 10, 139-162.

Noriega, A. and E. de Alba (2001), ”Stationarity and Structural Breaks: Evidence from Classical and Bayesian Approaches”, Economic Modelling, 18, 503-524.

Noriega, A. and D. Ventosa-Santaulària (2005), "Spurious Regression Under Broken Trend Stationarity", Working Paper EM-0501, School of Economics, University of Guanajuato.

Perron, P. (1992), ”Trend, Unit Root and Structural Change: A Multi-Country Study with Historical Data”, in Proceedings of the Business and Economic Statistics Section, American Statistical Association, 144-149.

Perron, P. (1997), ”Further Evidence on Breaking Trend Functions in Macroeconomic Variables”, Journal of Econometrics, 80, 355-385.

Perron, P. and X. Zhu (2002), "Structural Breaks with Deterministic and Stochastic Trends", Mimeo.

Phillips, P.C.B. (1986), ”Understanding Spurious Regressions in Econometrics”, Journal of Econometrics, 33, 311-340.

Tsay, W.-J. and C.-F. Chung (1999), "The Spurious Regression of Fractionally Integrated Processes", Mimeo.