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Unified Interval Estimation For Random Coefficient Autoregressive Models

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  • Jonathan Hill
  • Liang Peng

Abstract

type="main" xml:id="jtsa12064-abs-0001"> The consistency of the quasi-maximum likelihood estimator for random coefficient autoregressive models requires that the coefficient be a non-degenerate random variable. In this article, we propose empirical likelihood methods based on weighted-score equations to construct a confidence interval for the coefficient. We do not need to distinguish whether the coefficient is random or deterministic and whether the process is stationary or non-stationary, and we present two classes of equations depending on whether a constant trend is included in the model. A simulation study confirms the good finite-sample behaviour of our resulting empirical likelihood-based confidence intervals. We also apply our methods to study US macroeconomic data.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:35:y:2014:i:3:p:282-297
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    File URL: http://hdl.handle.net/10.1111/jtsa.12064
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    Cited by:

    1. Horváth, Lajos & Trapani, Lorenzo, 2019. "Testing for randomness in a random coefficient autoregression model," Journal of Econometrics, Elsevier, vol. 209(2), pages 338-352.
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    3. Tao, Yubo & Phillips, Peter C.B. & Yu, Jun, 2019. "Random coefficient continuous systems: Testing for extreme sample path behavior," Journal of Econometrics, Elsevier, vol. 209(2), pages 208-237.
    4. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).
    5. Horváth, Lajos & Trapani, Lorenzo, 2016. "Statistical inference in a random coefficient panel model," Journal of Econometrics, Elsevier, vol. 193(1), pages 54-75.
    6. Proïa, Frédéric & Soltane, Marius, 2021. "Comments on the presence of serial correlation in the random coefficients of an autoregressive process," Statistics & Probability Letters, Elsevier, vol. 170(C).
    7. Mikihito Nishi, 2023. "Testing for Coefficient Randomness in Local-to-Unity Autoregressions," Papers 2301.04853, arXiv.org, revised Jan 2023.

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