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Testing for randomness in a random coefficient autoregression model

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  • Lajos Horvath
  • Lorenzo Trapani

Abstract

We propose a test to discern between an ordinary autoregressive model, and a random coefficient one. To this end, we develop a full-edged estimation theory for the variances of the idiosyncratic innovation and of the random coefficient, based on a two-stage WLS approach. Our results hold irrespective of whether the series is stationary or nonstationary, and, as an immediate result, they afford the construction of a test for "relevant" randomness. Further, building on these results, we develop a randomised test statistic for the null that the coefficient is non-random, as opposed to the alternative of a standard RCA(1) model. Monte Carlo evidence shows that the test has the correct size and very good power for all cases considered.

Suggested Citation

  • Lajos Horvath & Lorenzo Trapani, 2018. "Testing for randomness in a random coefficient autoregression model," Discussion Papers 18/03, University of Nottingham, Granger Centre for Time Series Econometrics.
  • Handle: RePEc:not:notgts:18/03
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    References listed on IDEAS

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    1. Chang, Yoosoon, 2012. "Taking a new contour: A novel approach to panel unit root tests," Journal of Econometrics, Elsevier, vol. 169(1), pages 15-28.
    2. Peter C. B. Phillips & Yangru Wu & Jun Yu, 2011. "EXPLOSIVE BEHAVIOR IN THE 1990s NASDAQ: WHEN DID EXUBERANCE ESCALATE ASSET VALUES?," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 52(1), pages 201-226, February.
    3. Anurag Narayan Banerjee & Guillaume Chevillon & Marie Kratz, 2013. "Detecting and Forecasting Large Deviations and Bubbles in a Near-Explosive Random Coefficient Model," Working Papers hal-00870795, HAL.
    4. Wang, Xiaohu & Yu, Jun, 2015. "Limit theory for an explosive autoregressive process," Economics Letters, Elsevier, vol. 126(C), pages 176-180.
    5. Lieberman, Offer & Phillips, Peter C.B., 2017. "A multivariate stochastic unit root model with an application to derivative pricing," Journal of Econometrics, Elsevier, vol. 196(1), pages 99-110.
    6. Marine Carrasco & Liang Hu & Werner Ploberger, 2014. "Optimal Test for Markov Switching Parameters," Econometrica, Econometric Society, vol. 82(2), pages 765-784, March.
    7. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    8. Granger, Clive W. J. & Swanson, Norman R., 1997. "An introduction to stochastic unit-root processes," Journal of Econometrics, Elsevier, vol. 80(1), pages 35-62, September.
    9. Alexander Aue & Lajos Horváth & Josef Steinebach, 2006. "Estimation in Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 61-76, January.
    10. Corradi, Valentina & Swanson, Norman R., 2006. "The effect of data transformation on common cycle, cointegration, and unit root tests: Monte Carlo results and a simple test," Journal of Econometrics, Elsevier, vol. 132(1), pages 195-229, May.
    11. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    12. Marc Hallin & Abdelhadi Akharif, 2003. "Efficient detection of random coefficients in AR(p) models," ULB Institutional Repository 2013/2121, ULB -- Universite Libre de Bruxelles.
    13. Abdelhadi Akharif & Marc Hallin, 2003. "Efficient detection of random coefficients in autoregressive models," ULB Institutional Repository 2013/127956, ULB -- Universite Libre de Bruxelles.
    14. Holger Dette & Dominik Wied, 2016. "Detecting relevant changes in time series models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 78(2), pages 371-394, March.
    15. Christian Francq & Jean‐Michel Zakoïan, 2012. "Strict Stationarity Testing and Estimation of Explosive and Stationary Generalized Autoregressive Conditional Heteroscedasticity Models," Econometrica, Econometric Society, vol. 80(2), pages 821-861, March.
    16. Distaso, Walter, 2008. "Testing for unit root processes in random coefficient autoregressive models," Journal of Econometrics, Elsevier, vol. 142(1), pages 581-609, January.
    17. Lieberman, Offer & Phillips, Peter C.B., 2020. "Hybrid stochastic local unit roots," Journal of Econometrics, Elsevier, vol. 215(1), pages 257-285.
    18. Leybourne, S J & McCabe, B P M & Tremayne, A R, 1996. "Can Economic Time Series Be Differenced to Stationarity?," Journal of Business & Economic Statistics, American Statistical Association, vol. 14(4), pages 435-446, October.
    19. Ramanathan, R. V. & Rajarshi, M. B., 1994. "Rank tests for testing the randomness of autoregressive coefficients," Statistics & Probability Letters, Elsevier, vol. 21(2), pages 115-120, September.
    20. Nagakura, Daisuke, 2009. "Asymptotic theory for explosive random coefficient autoregressive models and inconsistency of a unit root test against a stochastic unit root process," Statistics & Probability Letters, Elsevier, vol. 79(24), pages 2476-2483, December.
    21. McCabe,B.P.M. & Tremayne,A.R., 1995. "Testing a Time-Series for Difference Stationarity," Cambridge Working Papers in Economics 9420, Faculty of Economics, University of Cambridge.
    22. Phillips, Peter C.B. & Magdalinos, Tassos, 2007. "Limit theory for moderate deviations from a unit root," Journal of Econometrics, Elsevier, vol. 136(1), pages 115-130, January.
    23. Offer Lieberman & Peter C. B. Phillips, 2014. "Norming Rates And Limit Theory For Some Time-Varying Coefficient Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(6), pages 592-623, November.
    24. S. Y. Hwang & I. V. Basawa, 2005. "Explosive Random‐Coefficient AR(1) Processes and Related Asymptotics for Least‐Squares Estimation," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(6), pages 807-824, November.
    25. repec:hal:journl:hal-00870795 is not listed on IDEAS
    26. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    27. Jonathan Hill & Liang Peng, 2014. "Unified Interval Estimation For Random Coefficient Autoregressive Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(3), pages 282-297, May.
    28. Aue, Alexander, 2008. "Near-Integrated Random Coefficient Autoregressive Time Series," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1343-1372, October.
    29. István Berkes & Lajos Horváth & Shiqing Ling, 2009. "Estimation in nonstationary random coefficient autoregressive models," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 395-416, July.
    30. Davidson, James, 1993. "The Central Limit Theorem for Globally Nonstationary Near-Epoch Dependent Functions of Mixing Processes: The Asymptotically Degenerate Case," Econometric Theory, Cambridge University Press, vol. 9(3), pages 402-412, June.
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    Cited by:

    1. Barigozzi, Matteo & Trapani, Lorenzo, 2020. "Sequential testing for structural stability in approximate factor models," Stochastic Processes and their Applications, Elsevier, vol. 130(8), pages 5149-5187.
    2. Lorenzo Trapani & Emily Whitehouse, 2020. "Sequential monitoring for cointegrating regressions," Papers 2003.12182, arXiv.org.
    3. Matteo Barigozzi & Giuseppe Cavaliere & Lorenzo Trapani, 2020. "Determining the rank of cointegration with infinite variance," Discussion Papers 20/01, University of Nottingham, Granger Centre for Time Series Econometrics.

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    Keywords

    Random Coefficient AutoRegression; WLS estimator; randomised test.;
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