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Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models

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Abstract

It is well known that moment matrices play a very important rôle in econometrics and statistics. Liu and Heyde (Stat Pap 49:455–469, 2008) give exact expressions for two-moment matrices, including the Hessian for ARCH models under elliptical distributions. In this paper, we extend the theory by establishing two additional moment matrices for conditional heteroskedastic models under elliptical distributions. The moment matrices established in this paper implement the maximum likelihood estimation by some estimation algorithms like the scoring method. We illustrate the applicability of the additional moment matrices established in this paper by applying them to establish an AR-ARCH model under an elliptical distribution.

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Authors and Affiliations

  1. Faculty of Information Sciences and Engineering, University of Canberra, Canberra, ACT, 2601, Australia

    Shuangzhe Liu

  2. Department of Statistics, Columbia University, New York, NY, USA

    Chris C. Heyde

  3. Mathematical Sciences Institute, Australian National University, Canberra, ACT, 0200, Australia

    Chris C. Heyde

  4. Department of Economics and Institute for Computational Mathematics, Hong Kong Baptist University, Hong Kong, China

    Wing-Keung Wong

Authors
  1. Shuangzhe Liu
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  2. Chris C. Heyde
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  3. Wing-Keung Wong
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Correspondence to Shuangzhe Liu.

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Liu, S., Heyde, C.C. & Wong, WK. Moment matrices in conditional heteroskedastic models under elliptical distributions with applications in AR-ARCH models. Stat Papers 52, 621–632 (2011). https://doi.org/10.1007/s00362-009-0272-2

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