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Two-Stage Weighted Least Squares Estimation of Nonstationary Random Coefficient Autoregressions

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  • Aknouche Abdelhakim

    (Faculty of Mathematics, University of Science and Technology Houari Boumediene, Algiers, Algeria)

Abstract

This paper proposes a two-stage weighted least squares (2S-WLS) estimate for the autoregressive parameter and the random coefficient variance of a non-(strictly) stationary random coefficient autoregression (RCA). In the first stage, the autoregressive parameter is estimated from the conditional mean equation by a weighted least squares (WLS) method in which the weight is the conditional variance evaluated at any arbitrary known parameter value. In the second stage, based on the estimated conditional variance equation, the random coefficient variance is estimated again using the WLS method, but weighted by the squared conditional variance arbitrarily evaluated. It will be shown that the 2S-WLS estimate is asymptotically Gaussian with the same asymptotic variance as the quasi-maximum likelihood estimate under very mild conditions. Applications to the Gaussian double autoregression and the Markov bilinear model are given.

Suggested Citation

  • Aknouche Abdelhakim, 2013. "Two-Stage Weighted Least Squares Estimation of Nonstationary Random Coefficient Autoregressions," Journal of Time Series Econometrics, De Gruyter, vol. 5(1), pages 25-46, January.
    • Handle: RePEc:bpj:jtsmet:v:5:y:2013:i:1:p:25-46:n:1
    DOI: 10.1515/jtse-2012-0011
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    References listed on IDEAS

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    1. Shiqing Ling & Dong Li, 2008. "Asymptotic inference for a nonstationary double AR (1) model," Biometrika, Biometrika Trust, vol. 95(1), pages 257-263.
    2. Abdelhakim Aknouche, 2012. "Multistage weighted least squares estimation of ARCH processes in the stable and unstable cases," Statistical Inference for Stochastic Processes, Springer, vol. 15(3), pages 241-256, October.
    3. Jensen, Søren Tolver & Rahbek, Anders, 2004. "Asymptotic Inference For Nonstationary Garch," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1203-1226, December.
    4. Paul D. Feigin & Richard L. Tweedie, 1985. "Random Coefficient Autoregressive Processes:A Markov Chain Analysis Of Stationarity And Finiteness Of Moments," Journal of Time Series Analysis, Wiley Blackwell, vol. 6(1), pages 1-14, January.
    5. Abdelhakim Aknouche & Eid Al-Eid, 2012. "Asymptotic inference of unstable periodic ARCH processes," Statistical Inference for Stochastic Processes, Springer, vol. 15(1), pages 61-79, April.
    6. Barr Rosenberg, 1973. "A Survey of Stochastic Parameter Regression," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 2, number 4, pages 381-397, National Bureau of Economic Research, Inc.
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