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Testing for a random walk in random coefficient autoregressive models

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  • W Distaso

Abstract

New tests for simple unit root and unit root with a possibly nonzero drift processes are proposed, in the context of a random coefficient autoregressive model. The proposed tests are either univariate on the variance of the autoregressive coefficient random variable, or joint on mean and variance. The asymptotic distribution of the tests are derived, and their properties are investigated through a Monte-Carlo simulation experiment. The tests have good power properties. In many cases they perform better than the competing univariate tests available in the literature, despite testing for a multiple joint hypothesis, because the partially one-sided nature is taken into account. In particular, for moderate to large sample sizes, very small values of the variance of the random coefficient variable are needed in order for the tests to reach some power against roots very close to unity. Finally, the proposed tests are applied to the US GDP series.

Suggested Citation

  • W Distaso, "undated". "Testing for a random walk in random coefficient autoregressive models," Discussion Papers 05/14, Department of Economics, University of York.
    • Handle: RePEc:yor:yorken:05/14
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    Cited by:

    1. Auray, Stéphane & Eyquem, Aurélien & Jouneau-Sion, Frédéric, 2014. "Modeling tails of aggregate economic processes in a stochastic growth model," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 76-94.
    2. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    3. Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    4. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
    5. 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.
    6. Yoon, Gawon, 2016. "Stochastic unit root processes: Maximum likelihood estimation, and new Lagrange multiplier and likelihood ratio tests," Economic Modelling, Elsevier, vol. 52(PB), pages 725-732.

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