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 and also 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, Econometrica 66, 123 148) 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.The second author thanks the Economic and Social Research Council (ESRC) for support as part of a project on Dynamic Common Factor Models for Regional Time Series, grant L138 25 1008. Support from the Bank of Italy is also gratefully acknowledged. Earlier versions of this paper were presented at the meeting on Frontiers in Time Series held in Olbia, Italy, in June 2005 and at the NSF NBER Time Series conference in Heidelberg, Germany, in September 2005; we are grateful to several participants for helpful comments. We also thank Peter Phillips, Robert Taylor, Jesus Gonzalo, and a number of other participants at the Unit Root and Co-integration Testing meeting in Faro, Portugal, for helpful comments. We are grateful to Paulo Rodrigues and two referees for their comments.
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 InfoArticle provided by Cambridge University Press in its journal Econometric Theory.
Volume (Year): 24 (2008)
Issue (Month): 01 (February)
Contact details of provider:
Postal: The Edinburgh Building, Shaftesbury Road, Cambridge CB2 2RU UK
Fax: +44 (0)1223 325150
Web page: http://journals.cambridge.org/jid_ECTProvider-Email:firstname.lastname@example.org
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
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.:
- 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.
- 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.
- 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.
- 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.
- Helle Bunzel & Timothy Vogelsang, 2003.
"Powerful Trend Function Tests That are Robust to Strong Serial Correlation with an Application to the Prebisch Singer Hypothesis,"
- 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.
- 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.
- 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.
- 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," Working Paper Series, Macroeconomic Issues 94-19, Federal Reserve Bank of Chicago.
- 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.
- 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.
- 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.
- Herman J. Bierens, 2000.
"Complex Unit Roots and Business Cycles: Are They Real?,"
Econometric Society World Congress 2000 Contributed Papers
0197, Econometric Society.
- Bierens, Herman J., 2001. "Complex Unit Roots And Business Cycles: Are They Real?," Econometric Theory, Cambridge University Press, vol. 17(05), pages 962-983, October.
- 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.
- Busettti, F. & Harvey, A., 2002. "Testing for Drift in a Time Series," Cambridge Working Papers in Economics 0237, Faculty of Economics, University of Cambridge.
- 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.
- Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
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: (Keith Waters).
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.