Spurious regression under broken trend stationarity

Noriega, Antonio E. and Ventosa Santaulària, Daniel (2005): Spurious regression under broken trend stationarity. Published in: Journal of time series analysis , Vol. 27, No. 5 (2006): pp. 671-684.

Abstract

We study the phenomenon of spurious regression between two random variables,when the generating mechanism of individual series is assumed to follow a stationary process around a trend with (possibly) multiple breaks in the level and slope of trend. We develop the relevant asymptotic theory and show that the phenomenon of spurious regression occurs independently of the structure assumed for the errors. In contrast to previous findings, the presence of a spurious relationship will be less severe when breaks are present in the generating mechanism of individual series. This is true whether the regression model includes a linear trend or not. Simulations confirm our asymptotic results, and reveal that in finite samples, the phenomenon of spurious regression is sensitive to the presence of a linear trend in the regression model, and to the relative location of breaks within the sample.

• Item Type: MPRA Paper
• Language: English
• Keywords: 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

Acemoglu, D. and A. Scott (1997), "Asymmetric Business Cycles: Theory and Time Series Evidence", Journal of Monetary Economics, 40(3), 501-533.

Bai, J. (1997a), ”Estimating Multiple Breaks One at a Time”, Econometric Theory, 13(3), 315-352.

--- (1997b), ”Estimation of a Change Point in Multiple Regression Models”, The Review of Economics and Statistics, 79(4), 551-563.

Bai, J, and P. Perron (1998a), ”Estimating and Testing Linear Models with Multiple Structural Changes”, Econometrica, 66(1), 47-78.

Bai, J, and P. Perron (1998b), ”Computation and Analysis of Multiple Structural Change Models”, Mimeo.

Ben-David, D. and D.H. Papell (1995), ”The Great Wars, the Great Crash, and Steady State Growth: Some New Evidence About an Old Stylized Fact”, Journal of Monetary Economics, 36, 453-475.

––— (1998), ”Slowdowns and Meltdowns: Postwar Growth Evidence from 74 Countries”, Review of Economics and Statistics, 80, 561-571.

Clemente, J., A. Montañéz and M. Reyes (1998), ”Testing for a Unit Root in Variables with a Double Change in the Mean”, Economics Letters, 59, 175-182.

Cooper, R. (1994), "Equilibrium Selection in Imperfectly Competitive Economies with Multiple Equilibria", Economic Journal, 104 (426), 1106-1122.

Duck, N.W. (1992), ”UK Evidence on Breaking Trend Functions”, Oxford Economic Papers, 44, 426-439.

Durlauf, S. (1993), "Nonergodic Economic Growth", Review of Economic Studies, 60, 349-366.

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

Granger, C.W.J. and P. Newbold (1974), "Spurious Regression in Econometrics", Journal of Econometrics, 2, 111-120.

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

Hansen, B. (2001), "The New Econometrics of Structural Change: Dating Breaks in U.S. Labour Productivity", Journal of Economic Perspectives, 15(4), 117-128.

Kejak, M. (2003), "Stages of Growth in Economic Development", Journal of Economic Dynamics and Control, 27 (5), 771-800.

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.

Lau, S.-H. P. (1997), "Using Stochastic Growth Models to Understand Unit Roots and Breaking Trends", Journal of Economic Dynamics and Control, 21, 1645-1667.

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.

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

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

Perron, P. (1989), ”The Great Crash, The Oil Price Shock, and The Unit Root Hypothesis”, Econometrica, 57, 1361-1401.

––- (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.

-–- (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.

Raj, B. (1992), "International Evidence on Persistence in Output in the Presence of an Episodic Change", Journal of Applied Econometrics, 7, 281-293.

Startz, R. (1998), "Growth States and Shocks", Journal of Economic Growth, 3, 203-215.

Stock, J.H. (1994), ”Unit Roots, Structural Breaks and Trends”, Handbook of Econometrics, IV, 2740-2841.

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

Zelhorst, D. and Haan, Jakob de (1995), ”Testing for a Break in Output: New International Evidence”, Oxford Economic Papers, 47, 357-362.

Zivot, E. and D.W.K. Andrews (1992), ”Further Evidence on the Great Crash, the Oil Price Shock, and the Unit Root Hypothesis”, Journal of Business and Economic Statistics, 10, 251-270.