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Testing For Trend

  • Busetti, Fabio
  • Harvey, Andrew

The paper examines various tests for assessing whether a time series model requires a slope component. We first consider the simple t-test on the mean of first differences and show that it achieves high power against the alternative hypothesis of a stochastic nonstationary slope as well as against a purely deterministic slope. The test may be modified, parametrically or nonparametrically to deal with serial correlation. Using both local limiting power arguments and finite sample Monte Carlo results, we compare the t-test with the nonparametric tests of Vogelsang (1998) and with a modified stationarity test. Overall the t-test seems a good choice, particularly if it is implemented by fitting a parametric model to the data. When standardized by the square root of the sample size, the simple t-statistic, with no correction for serial correlation, has a limiting distribution if the slope is stochastic. We investigate whether it is a viable test for the null hypothesis of a stochastic slope and conclude that its value may be limited by an inability to reject a small deterministic slope. Empirical illustrations are provided using series of relative prices in the euro-area and data on global temperature.

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Article provided by Cambridge University Press in its journal Econometric Theory.

Volume (Year): 24 (2008)
Issue (Month): 01 (February)
Pages: 72-87

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Handle: RePEc:cup:etheor:v:24:y:2008:i:01:p:72-87_08
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  1. Kwiatkowski, Denis & Phillips, Peter C. B. & Schmidt, Peter & Shin, Yongcheol, 1992. "Testing the null hypothesis of stationarity against the alternative of a unit root : How sure are we that economic time series have a unit root?," Journal of Econometrics, Elsevier, vol. 54(1-3), pages 159-178.
  2. Eugene Canjels & Mark W. Watson, 1994. "Estimating Deterministic Trends in the Presence of Serially Correlated Errors," NBER Technical Working Papers 0165, National Bureau of Economic Research, Inc.
  3. Bunzel, Helle & Vogelsang, Timothy J., 2003. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation with an Application to the Prebisch-Singer Hypothesis," Staff General Research Papers 10353, Iowa State University, Department of Economics.
  4. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2007. "Inflation Convergence and Divergence within the European Monetary Union," International Journal of Central Banking, International Journal of Central Banking, vol. 3(2), pages 95-121, June.
  5. Busettti, F. & Harvey, A., 2002. "Testing for Drift in a Time Series," Cambridge Working Papers in Economics 0237, Faculty of Economics, University of Cambridge.
  6. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
  7. Ralph W. Bailey & A. M. Robert Taylor, 2002. "An optimal test against a random walk component in a non-orthogonal unobserved components model," Econometrics Journal, Royal Economic Society, vol. 5(2), pages 520-532, 06.
  8. Leybourne, S J & McCabe, B P M, 1994. "A Consistent Test for a Unit Root," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(2), pages 157-66, April.
  9. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  10. Peter C.B. Phillips & Pierre Perron, 1986. "Testing for a Unit Root in Time Series Regression," Cowles Foundation Discussion Papers 795R, Cowles Foundation for Research in Economics, Yale University, revised Sep 1987.
  11. Herman J. Bierens, 2000. "Complex Unit Roots and Business Cycles: Are They Real?," Econometric Society World Congress 2000 Contributed Papers 0197, Econometric Society.
  12. Eduardo Zambrano & Timothy J. Vogelsang, 2000. "A Simple Test of the Law of Demand for the United States," Econometrica, Econometric Society, vol. 68(4), pages 1013-1022, July.
  13. Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
  14. Tae-Hwan Kim & Stephan Pfaffenzeller & Tony Rayner & Paul Newbold, 2003. "Testing for Linear Trend with Application to Relative Primary Commodity Prices," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 539-551, 09.
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