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Testing for trend

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Author Info
Fabio Busetti () (Bank of Italy)
Andrew Harvey () (Cambridge University)

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Abstract

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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File URL: http://www.bancaditalia.it/pubblicazioni/econo/temidi/td07/td614_07/td614/en_tema_614.pdf
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Paper provided by Bank of Italy, Economic Research Department in its series Temi di discussione (Economic working papers) with number 614.

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Date of creation: Feb 2007
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Handle: RePEc:bdi:wptemi:td_614_07

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Related research
Keywords: Cramér-von Mises distribution; stationarity test; stochastic trend; unit root; unobserved component.;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

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References listed on IDEAS
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.:
  1. 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.
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  2. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2006. "Inflation convergence and divergence within the European Monetary Union," Working Paper Series 574, European Central Bank. [Downloadable!]
    Other versions:
  3. 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. [Downloadable!]
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  4. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-58, May. [Downloadable!] (restricted)
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  5. 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, Blackwell Publishing, vol. 24(5), pages 539-551, 09. [Downloadable!] (restricted)
  6. Angelini, Paolo, 2000. "Are Banks Risk Averse? Intraday Timing of Operations in the Interbank Market," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 32(1), pages 54-73, February.
  7. Leonardo Gambacorta, 2001. "Bank-specific characteristics and monetary policy transmission: the case of Italy," Working Paper Series 103, European Central Bank. [Downloadable!]
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  8. 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. [Downloadable!] (restricted)
  9. 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.
  10. Busettti, F. & Harvey, A., 2002. "Testing for Drift in a Time Series," Cambridge Working Papers in Economics 0237, Faculty of Economics, University of Cambridge. [Downloadable!]
  11. 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. [Downloadable!] (restricted)
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  12. Timothy J. Vogelsang, 1998. "Trend Function Hypothesis Testing in the Presence of Serial Correlation," Econometrica, Econometric Society, vol. 66(1), pages 123-148, January.
  13. 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.
  14. Sun, Hongguang & Pantula, Sastry G., 1999. "Testing for trends in correlated data," Statistics & Probability Letters, Elsevier, vol. 41(1), pages 87-95, January. [Downloadable!] (restricted)
  15. Herman J. Bierens, 2000. "Complex Unit Roots and Business Cycles: Are They Real?," Econometric Society World Congress 2000 Contributed Papers 0197, Econometric Society. [Downloadable!]
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  16. 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. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, 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.)

  1. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School. [Downloadable!]
  2. Fabio Busetti & Lorenzo Forni & Andrew Harvey & Fabrizio Venditti, 2006. "Inflation convergence and divergence within the European Monetary Union," Working Paper Series 574, European Central Bank. [Downloadable!]
    Other versions:
  3. James H. Stock & Mark W. Watson, 1996. "Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model," NBER Technical Working Papers 0201, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  4. Josep Carrion-i-Silvestre & Andreu Sansó, 2006. "A guide to the computation of stationarity tests," Empirical Economics, Springer, vol. 31(2), pages 433-448, June. [Downloadable!] (restricted)
  5. 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, Yale University. [Downloadable!]
    Other versions:
  6. Josep Carrion-i-Silvestre & Andreu Sansó, 2007. "The KPSS test with two structural breaks," Spanish Economic Review, Springer, vol. 9(2), pages 105-127, June. [Downloadable!] (restricted)
    Other versions:
  7. María Presno & Anna López, 2003. "Testing for stationarity in series with a shift in the mean. A fredholm approach," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer, vol. 12(1), pages 195-213, June. [Downloadable!] (restricted)
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