Spurious Regression and Trending Variables

Noriega, Antonio E. and Ventosa-Santaulària, Daniel (2007): Spurious Regression and Trending Variables. 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 different types of nonstationary behavior among the dependent and explanatory variables in a linear spurious regression model. We study cases when the nonstationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t−statistic in a linear regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases considered, when at least one of the variables behaves in a nonstationary way. Simulation experiments confirm our asymptotic results.

• Item Type: MPRA Paper
• Language: English
• Keywords: Spurious regression, trends, unit roots, trend stationarity, structural breaks
• Subjects: C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C12 - Hypothesis Testing: General; C - Mathematical and Quantitative Methods > C1 - Econometric and Statistical Methods and Methodology: General > C13 - Estimation: General; 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.

Coenen, G. and J.-L. Vega (2001), "The Demand for M3 in the Euro Area", Journal of Applied Econometrics, 16, 727-48.

D’Adda, C. and A. E. Scorcu (2003), "On the Time Stability of the Output-Capital Ratio", Economic Modelling, 20, 1175-1189.

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.

Haldrup, N. (1998), "An Econometric Analysis of I(2) Variables", Journal of Economic Surveys, 12(5), 595-650.

Hassler, U. (1996), "Spurious Regressions when Stationary Regressors are Included", Economics Letters, 50, 25-31.

______ (2000), "Simple Regressions with Linear Time Trends", Journal of Time Series Analysis, 21, 27-33.

______ (2003), "Nonsense Regressions Due to Neglected Time-Varying Means", Statistical Papers, 44, 169-182.

Juselius, K. (1996), "A Structured VAR under Changing Monetary Policy", Journal of Business and Economic Statistics, 16, 400-12.

Juselius, K. (1999), "Price Convergence in the Medium and Long Run: An I(2) Analysis of Six Price Indices", in Engle, R. F. and H. White (eds.): Cointegration, Causality and Forecasting. A Festschrift in Honour of Clive W. J. Granger, Oxford University Press.

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

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, F. (1996), "Nonsense Regressions Between Integrated Processes of Different Orders", Oxford Bulletin of Economics and Statistics, 58(3), 525-36.

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

MATHEMATICA 4.1 (2000), Wolfram Research Inc. Mehl, A. (2000), "Unit Root Tests with Double Trend Breaks and the 1990s Recession in Japan", Japan and the World Economy, 12, 363-379.

Muscatelli, V. A. and F. Spinelli (2000), "The Long-Run Stability of the Demand for Money: Italy 1861-1996", Journal of Monetary Economics, 45, 717-39.

Nielsen, H. B. (2002), "An I(2) Cointegration Analysis of Price and Quantity Formation in Danish Manufactured Exports", Oxford Bulletin of Economics and Statistics, 64(5), 449-72.

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. Forthcoming in Journal of Time Series Analysis.

Park, J. Y. and P. C. B. Phillips (1989), "Statistical Inference in Regressions with Integrated Processes: Part 2", Econometric Theory, 5, 95-131.

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 T. J. Vogelsang (1992), "Nonstationarity and Level Shifts with and Application to Purchasing Power Parity", Journal of Business and Economic Statistics, 10(3), 301-20.

Perron, P. and X. Zhu (2005), "Structural Breaks with Deterministic and Stochastic Trends", Journal of Econometrics, 129, 65-119.

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

Phillips, P.C.B. (1998), "New Tools for Understanding Spurious Regressions", Econometrica, 66(6), 1299-1325.

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

White, H. (1984), Asymptotic Theory for Econometricians, Academic Press.

Wu, J.-L. (2000), "Mean Reversion of the Current Account: Evidence from the Panel Data Unit-Root Test", Economics Letters, 66, 215-22.