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

Arvanitis Stelios () and Alexandros Louka
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Arvanitis Stelios: Department of Economics, Athens University of Economics and Business, P.O. Box 10434, Patision Str. 80, Athens, Greece

Journal of Time Series Econometrics, 2016, vol. 8, issue 1, 21-39

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]$.

Keywords: α-stable distribution; slow variation; domain of attraction; MLT with mixed limit; non-stationary ARCH(1); QMLE; inconsistency; non-tightness (search for similar items in EconPapers)
Date: 2016
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DOI: 10.1515/jtse-2014-0034

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