Testing for trend
AbstractThe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Bank of Italy, Economic Research and International Relations Area in its series Temi di discussione (Economic working papers) with number 614.
Date of creation: Feb 2007
Date of revision:
CramÃ©r-von Mises distribution; stationarity test; stochastic trend; unit root; unobserved component.;
Other versions of this item:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
This paper has been announced in the following NEP Reports:
- NEP-ALL-2007-03-10 (All new papers)
- NEP-CBA-2007-03-10 (Central Banking)
- NEP-ECM-2007-03-10 (Econometrics)
- NEP-ETS-2007-03-10 (Econometric Time Series)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Bunzel, Helle & Vogelsang, Timothy J., 2005. "Powerful Trend Function Tests That Are Robust to Strong Serial Correlation, With an Application to the Prebisch-Singer Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 23, pages 381-394, October.
- Helle Bunzel & Timothy Vogelsang, 2003. "Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis," Econometrics 0304002, EconWPA.
- Denis Kwiatkowski & Peter C.B. Phillips & Peter Schmidt, 1991.
"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?,"
Cowles Foundation Discussion Papers
979, Cowles Foundation for Research in Economics, Yale University.
- 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.
- Kwiatkowski, D. & Phillips, P.C.B. & Schmidt, P., 1990. "Testing the Null Hypothesis of Stationarity Against the Alternative of Unit Root : How Sure are we that Economic Time Series have a Unit Root?," Papers 8905, Michigan State - Econometrics and Economic Theory.
- Tom Doan, . "KPSS: RATS procedure to perform KPSS (Kwiatowski, Phillips, Schmidt, and Shin) stationarity test," Statistical Software Components RTS00100, Boston College Department of Economics.
- Eugene Canjels & Mark W. Watson, 1994.
"Estimating deterministic trends in the presence of serially correlated errors,"
Working Paper Series, Macroeconomic Issues
94-19, Federal Reserve Bank of Chicago.
- Eugene Canjels & Mark W. Watson, 1997. "Estimating Deterministic Trends In The Presence Of Serially Correlated Errors," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 184-200, May.
- 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.
- Bierens, Herman J., 2001.
"Complex Unit Roots And Business Cycles: Are They Real?,"
Cambridge University Press, vol. 17(05), pages 962-983, October.
- Herman J. Bierens, 2000. "Complex Unit Roots and Business Cycles: Are They Real?," Econometric Society World Congress 2000 Contributed Papers 0197, Econometric Society.
- Donald W.K. Andrews, 1988.
"Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation,"
Cowles Foundation Discussion Papers
877R, Cowles Foundation for Research in Economics, Yale University, revised Jul 1989.
- Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May.
- 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.
- 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.
- Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January.
- Bailey, R.W. & Taylor, A.M.R., 2000.
"An Optimal Test against a Random Walk Component in a Non-Orthogonal Unobserved Components Model,"
00-09, Department of Economics, University of Birmingham.
- 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.
- Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
- Busettti, F. & Harvey, A., 2002. "Testing for Drift in a Time Series," Cambridge Working Papers in Economics 0237, Faculty of Economics, University of Cambridge.
- 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.
- 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.
- Busetti, Fabio & Forni, Lorenzo & Harvey, Andrew & Venditti, Fabrizio, 2006. "Inflation convergence and divergence within the European Monetary Union," Working Paper Series 0574, European Central Bank.
- 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.
- Phillips, P.C.B., 1986. "Testing for a Unit Root in Time Series Regression," Cahiers de recherche 8633, Universite de Montreal, Departement de sciences economiques.
- Tom Doan, . "PPUNIT: RATS procedure to perform Phillips-Perron Unit Root test," Statistical Software Components RTS00160, Boston College Department of Economics.
This item has more than 25 citations. To prevent cluttering this page, these citations are listed on a separate page. reading list or among the top items on IDEAS.Access and download statisticsgeneral information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.