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A Note on the QMLE Limit Theory in the Non-stationary ARCH(1) Model

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  • Arvanitis Stelios
  • Louka Alexandros

    (Department of Economics, Athens University of Economics and Business, P.O. Box 10434, Patision Str. 80, Athens, Greece)

Abstract

In this note we extend the standard results for the limit theory of the popular quasi-maximum likelihood estimator (QMLE) in the context of the non-stationary autoregressive conditional heteroskedastic ARCH(1) model by allowing the innovation process not to possess fourth moments. Depending on the value of the index of stability, we either derive α$\alpha $-stable weak limits with non-standard rates or inconsistency and non-tightness. We obtain the limit theory by the derivation of a limit theorem for multiplicative “martingale” transforms with limit mixtures of α$\alpha $-stable distributions for any α∈0,2$\alpha \in \left({0,2} \right]$.

Suggested Citation

  • Arvanitis Stelios & Louka Alexandros, 2016. "A Note on the QMLE Limit Theory in the Non-stationary ARCH(1) Model," Journal of Time Series Econometrics, De Gruyter, vol. 8(1), pages 21-39, January.
    • Handle: RePEc:bpj:jtsmet:v:8:y:2016:i:1:p:21-39:n:3
    DOI: 10.1515/jtse-2014-0034
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    References listed on IDEAS

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    1. Abadir, Karim & Magnus, Jan, 2004. "03.6.1 The Central Limit Theorem for Student's Distribution—Solution," Econometric Theory, Cambridge University Press, vol. 20(6), pages 1261-1263, December.
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