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An Exact Test For A Stochastic Coefficient In A Time Series Regression Model

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  • Thomas S. Shively

Abstract

An exact small‐sample test is developed for testing the hypothesis that a regression coefficient is constant against the alternative that it is generated by a random walk process. The test is mean‐ and scale‐invariant and approximates the most powerful invariant test against any specific alternative. It thus outperforms tests previously given in the literature. Computationally efficient algorithms are given to compute the test statistic and its distribution using a modified version of the Kalman filter.

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  • Thomas S. Shively, 1988. "An Exact Test For A Stochastic Coefficient In A Time Series Regression Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 9(1), pages 81-88, January.
    • Handle: RePEc:bla:jtsera:v:9:y:1988:i:1:p:81-88
    DOI: 10.1111/j.1467-9892.1988.tb00455.x
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    Cited by:

    1. Perron, Pierre & Wada, Tatsuma, 2009. "Let's take a break: Trends and cycles in US real GDP," Journal of Monetary Economics, Elsevier, vol. 56(6), pages 749-765, September.
    2. Li, Hong, 2008. "Estimation and testing of Euler equation models with time-varying reduced-form coefficients," Journal of Econometrics, Elsevier, vol. 142(1), pages 425-448, January.
    3. Pierre Perron & Yohei Yamamoto, 2016. "On the Usefulness or Lack Thereof of Optimality Criteria for Structural Change Tests," Econometric Reviews, Taylor & Francis Journals, vol. 35(5), pages 782-844, May.
    4. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    5. Narayan, Seema & Smyth, Russell, 2015. "The financial econometrics of price discovery and predictability," International Review of Financial Analysis, Elsevier, vol. 42(C), pages 380-393.
    6. Ai Deng & Pierre Perron, 2006. "A comparison of alternative asymptotic frameworks to analyse a structural change in a linear time trend," Econometrics Journal, Royal Economic Society, vol. 9(3), pages 423-447, November.
    7. Tatsuma Wada & Pierre Perron, 2005. "Trend and Cycles: A New Approach and Explanations of Some Old Puzzles," Computing in Economics and Finance 2005 252, Society for Computational Economics.
    8. Piotr Eliasz & James H. Stock & Mark W. Watson, 2003. "Optimal Tests for Reduced Rank Time Variation in Regression Coefficients and Level Variation in the Multivariate Local Level Model," Working Papers 2003-1, Princeton University. Economics Department..
    9. repec:wut:journl:v:3-4:y:2011:id:1015 is not listed on IDEAS
    10. Fabio Busetti, 2012. "On detecting end-of-sample instabilities," Temi di discussione (Economic working papers) 881, Bank of Italy, Economic Research and International Relations Area.
    11. Ben Omrane, Walid & Savaser, Tanseli & Welch, Robert & Zhou, Xinyao, 2019. "Time-varying effects of macroeconomic news on euro-dollar returns," The North American Journal of Economics and Finance, Elsevier, vol. 50(C).
    12. 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.
    13. Manohar B. Rajarshi & Thekke V. Ramanathan & Chanchala A. Ghadge, 2011. "Rank based tests for testing the constancy of the regression coefficients against random walk alternatives," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 21(3-4), pages 35-55.
    14. El-Bassiouni, M. Y. & Charif, H. A., 2004. "Testing a null variance ratio in mixed models with zero degrees of freedom for error," Computational Statistics & Data Analysis, Elsevier, vol. 46(4), pages 707-719, July.
    15. Shively, Thomas S. & Kohn, Robert, 1997. "A Bayesian approach to model selection in stochastic coefficient regression models and structural time series models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 39-52.

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