AtiqurRehman, AtiqurRehman and Zaman, Asad (2008): Model specification, observational equivalence and performance of unit root tests.

PDF
MPRA_paper_13489.pdf Download (385kB)  Preview 
Abstract
In this paper we highlight the necessity of new criteria for evaluation of performance of unit root tests. We suggest focusing directly on the reasons that create ambiguity in unit root test’s results. Two reasons for unsatisfactory properties of unit root tests can be found in the literature (i) the model misspecification and (ii) observational equivalence. Regarding first reason, there is immense literature on several components of model specification covering specification techniques, consequence of misspecification and robust methods. However complete model specification involves multiple decisions and most of studies on performance of unit root tests do not address issue of multiple specification decisions simultaneously. The Monte Carlo studies are conditional on some of implicit specification and for Monte Carlo; these specifications are by construction valid. But for real data, the implicit decisions are often not true and specification decisions need to be endogenized. A closer match with real case is possible if multiple specification decisions are endogenized, thus providing more reliable measure of performance of unit root tests. Second problem in differentiating trend and difference stationary process is the observational equivalence between two processes. We suggest exploring data generating processes with different long run dynamics and small sample equivalence so that a researcher should have an idea about other plausible models for a data set for which he has estimated some model.
Item Type:  MPRA Paper 

Original Title:  Model specification, observational equivalence and performance of unit root tests 
Language:  English 
Keywords:  Observational equivalence, model specification, trend stationary, difference stationary 
Subjects:  C  Mathematical and Quantitative Methods > C1  Econometric and Statistical Methods and Methodology: General > C15  Statistical Simulation Methods: General C  Mathematical and Quantitative Methods > C2  Single Equation Models ; Single Variables > C22  TimeSeries Models ; Dynamic Quantile Regressions ; Dynamic Treatment Effect Models ; Diffusion Processes C  Mathematical and Quantitative Methods > C0  General > C01  Econometrics 
Item ID:  13489 
Depositing User:  Atiqur Rehman 
Date Deposited:  20. Feb 2009 08:41 
Last Modified:  17. Feb 2014 15:13 
References:  Andreou, E. and Spanos, A. (2003). Statistical Adequacy and the Testing of Trend Versus Difference Stationarity, Econometric Reviews, 22(3), 217 – 237. Banerjee, A., Lumsdaine, R. and Stock, J.H. (1992). Recursive and sequential tests of unitroot and the trend break hypotheses: theory and international evidence. Journal of Business Economics and Statistics, 10, 271287. Byrne J. P. and Roger Perman (2006). Unit Roots and Structural Breaks, A Survey of the Literature Campbell, J. Y., and Perron, P. (1991). Pitfalls and opportunities: what macroeconomists should know about unit roots? NBER Macroeconomics Annual. 6. 141–201. Cati, R. C., Garcia, M. G. P., Perron, P. (1999). Unit roots in the presence of abrupt governmental interventions with an application to Brazilian data. Journal of Applied Econometrics 14, 27–56. Cavaliere, G. (2005). Unit Root Tests under TimeVarying Variances. Econometric Reviews, 23, 3, 259 – 292. Christiano, L.J. (1992). Searching for a break in GNP. Journal of Business Economics and Statistics, 10, 237250. Cocharane., H. (1987)., "A Critique of the Application of Unit Root Tests," mimeo, University of Chicago. 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, 427431. Dickey, D.A. and Fuller, W.A. (1981). Likelihood Ratio Statistics for Autoregressive Time Series with a Unit Root, Econometrica, 49, 10571072. Diebold, F. X., and Senhadji, A. S. (1996). The Uncertain Root in Real GNP: Comment. American Economic Review, 86, 12911298. Elder J. and Kennedy P. E. (2001). Testing for Unit Roots: What Should Students Be Taught? Journal of Economic Education, 32(2), 13746. Enders, W. (2004). Applied Econometric Time Series, Second Edition. John Wiley & Sons, United States. Hamilton J. D. (1994). Time Series Analysis. Princeton University Press, Princeton, New Jersey. Kilian, L. and Ohanian, L. (2002), Unit Roots, Trend Breaks and Transitory Dynamics: A Macroeconomic Perspective. Macroeconomic Dynamics, 6, 614631. Kim, T. H., Leybourne, S., Newbold, P. (2002). Unit root tests with a break in innovation variance. Journal of Econometrics, 109, 365–387. Libanio, G. A. (2005). Unit roots in macroeconomic time series: theory, implications and evidence. nova Economia Belo Horizonte15 (3)145176 Loretan, M. and Phillips, P. C. B. (1994). Testing covariance stationarity under moment condition failure with an application to common stock returns. Journal of Empirical Finance 1, 211–248 Lumsdaine, R.L. and Papell, D.H. (1997). Multiple trend breaks and the unit root hypothesis. Review of Economics and Statistics, 79, 212218. McConnell, M. M. and Quiros, P. (2000). Output fluctuations in the United States, what has changed since the early 1980s? American Economic Review. 90, 1464–1476. Murray, C. J. and Nelson, C. R. (2000). The uncertain trend in U.S. GDP. Journal of Monetary Economics 46, 79–95. Nelson, C. R. and Plosser, C. I. (1982). Trend sand random walks in macroeconomics time series: some evidence and implications. Journal of Monetary Economics 10, 139–162. Ng, S. and Perron, P. (2001). Lag length selection and the construction of unit root tests with good size and power. Econometrica 69, 1519–1554. Nunes, L.C., CM. Kuan and P. Newbold (1997). Spurious regression. Econometric Theory, 11, 73649. Papell, D. H. and Prodan, R. (2003). Restricted Structural Change and the Unit Root Hypothesis. Working paper, University of Houston Perron P. (1988). Trends and Random Walks in Macroeconomic Time Series: Further Evidence from a New Approach. Journal of Economic Dynamics and Control, 12, 297332. Perron, P. (1989). The great crash, the oil price shock and the unit root hypothesis. Econometrica, 57, 13611401. Perron, P. (2003). Comment on "Statistical Adequacy and the Testing of Trend Versus Difference Stationarity" by Andreou and Spanos (Number 1)., Econometric Reviews, 22, 3, 239 – 245 Perron, P. (2005). Dealing with Structural Breaks. Mimeo forthcoming in the Handbook of Econometrics, Econometric Theory. Rudebusch, G. D. (1993), The Uncertain Unit Root in Real GNP. The American Economic Review, 83, 264272. Said, S.E. and Dickey, D.A. (1984). Testing for unit roots in autoregressive moving average models of unknown order. Biometrika, 71, 599607. Scott, H. R. and HatemiJ. A. (2006). The Properties of Procedures Dealing with Uncertainty about Intercept and Deterministic Trend in Unit Root Testing. Spanos A. and Anya McGuirk (2006). Revisiting the foundations of unit root testing: why the AR(1). model does not nest the unit root, Virginia Tech working paper series van Dijk, D., Osborn, D. R. and Sensier, M. (2002). Changes in variability of the business cycle in the G7 countries, Erasmus University Rotterdam, Econometric Institute Report EI 200228. Watson, M. W. (1999). Explaining the increased variability in longterm interest rates. Richmond Economic Quarterly, 85, 71–96. Zivot, E. and Andrews, D.W.K. (1992). Further evidence on the great crash, the oil price shock and the unit root hypothesis. Journal of Business and Economic Statistics, 10, 251270. 
URI:  https://mpra.ub.unimuenchen.de/id/eprint/13489 