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Testing for trend

Author

Listed:
  • Fabio Busetti

    () (Bank of Italy)

  • Andrew Harvey

    () (Cambridge University)

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.

Suggested Citation

  • Fabio Busetti & Andrew Harvey, 2007. "Testing for trend," Temi di discussione (Economic working papers) 614, Bank of Italy, Economic Research and International Relations Area.
  • Handle: RePEc:bdi:wptemi:td_614_07
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    File URL: http://www.bancaditalia.it/pubblicazioni/temi-discussione/2007/2007-0614/en_tema_614.pdf
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    References listed on IDEAS

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    14. 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.
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    Cited by:

    1. Stefan Reitz & Jan C. Rülke & Mark P. Taylor, 2011. "On the Nonlinear Influence of Reserve Bank of Australia Interventions on Exchange Rates," The Economic Record, The Economic Society of Australia, vol. 87(278), pages 465-479, September.
    2. Cavaliere, Giuseppe & Harvey, David I. & Leybourne, Stephen J. & Taylor, A.M. Robert, 2011. "Testing For Unit Roots In The Presence Of A Possible Break In Trend And Nonstationary Volatility," Econometric Theory, Cambridge University Press, vol. 27(05), pages 957-991, October.
    3. Xu, Ke-Li, 2016. "Multivariate trend function testing with mixed stationary and integrated disturbances," Journal of Multivariate Analysis, Elsevier, vol. 147(C), pages 38-57.
    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. Gomez Zaldivar, M. & Ventosa-Santaularia, D., 2009. "Bilateral Relationship between Consumption and GDP in Mexico and the USA: A Comment," Applied Econometrics and International Development, Euro-American Association of Economic Development, vol. 9(1).
    6. 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.
    7. 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.
    8. Shelley, Gary L. & Wallace, Frederick H., 2011. "Further evidence regarding nonlinear trend reversion of real GDP and the CPI," Economics Letters, Elsevier, vol. 112(1), pages 56-59, July.
    9. Josep Carrion-i-Silvestre & Andreu Sansó, 2007. "The KPSS test with two structural breaks," Spanish Economic Review, Springer;Spanish Economic Association, vol. 9(2), pages 105-127, June.
    10. Cavaliere, Giuseppe & Taylor, A.M. Robert, 2008. "Testing for a change in persistence in the presence of non-stationary volatility," Journal of Econometrics, Elsevier, vol. 147(1), pages 84-98, November.
    11. Chevillon, Guillaume, 2007. "Inference in the Presence of Stochastic and Deterministic Trends," ESSEC Working Papers DR 07021, ESSEC Research Center, ESSEC Business School.
    12. Nikolaos Giannellis & Minoas Koukouritakis, 2011. "Behavioural equilibrium exchange rate and total misalignment: evidence from the euro exchange rate," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 38(4), pages 555-578, November.
    13. Jushan Bai & Serena Ng, 2001. "A New Look at Panel Testing of Stationarity and the PPP Hypothesis," Boston College Working Papers in Economics 518, Boston College Department of Economics.
    14. Jushan Bai & Josep Lluís Carrion-I-Silvestre, 2009. "Structural Changes, Common Stochastic Trends, and Unit Roots in Panel Data," Review of Economic Studies, Oxford University Press, vol. 76(2), pages 471-501.
    15. 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.
    16. Joakim Westerlund & David L. Edgerton, 2007. "New Improved Tests for Cointegration with Structural Breaks," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(2), pages 188-224, March.
    17. James Morley & Tara M. Sinclair, 2005. "Testing for Stationarity and Cointegration in an Unobserved Components Framework," Computing in Economics and Finance 2005 451, Society for Computational Economics.
    18. Chevillon, Guillaume, 2012. "Local-Explosive Approximations to Null Distributions of the Johansen Cointegration Test, with an Application to Cyclical Concordance in the Euro Area," ESSEC Working Papers WP1210, ESSEC Research Center, ESSEC Business School.
    19. Josep Lluís Carrion-i-Silvestre & Tomás del Barrio-Castro & Enrique López-Bazo, 2005. "Breaking the panels: An application to the GDP per capita," Econometrics Journal, Royal Economic Society, vol. 8(2), pages 159-175, July.
    20. Riccardo Corradini, 2005. "An Empirical Analysis of Permanent Income Hypothesis Applied to Italy using State Space Models with non zero correlation between trend and cycle," Computing in Economics and Finance 2005 28, Society for Computational Economics.
    21. Sauro Mocetti, 2012. "Educational choices and the selection process: before and after compulsory schooling," Education Economics, Taylor & Francis Journals, vol. 20(2), pages 189-209, February.
    22. 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;Sociedad de Estadística e Investigación Operativa, vol. 12(1), pages 195-213, June.

    More about this item

    Keywords

    Cram�r-von Mises distribution; stationarity test; stochastic trend; unit root; unobserved component.;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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