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Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients

Author

Listed:
  • Abdelkamel Alj
  • Rajae Azrak
  • Christophe Ley
  • Guy Melard

Abstract

This paper is about vector autoregressive-moving average (VARMA) models with time-dependent coefficients to represent non-stationary time series. Contrary to other papers in the univariate case, the coefficients depend on time but not on the series’ length n. Under appropriate assumptions, it is shown that a Gaussian quasi-maximum likelihood estimator is almost surely consistent and asymptotically normal. The theoretical results are illustrated by means of two examples of bivariate processes. It is shown that the assumptions underly- ing the theoretical results apply. In the second example the innovations are marginally heteroscedastic with a correlation ranging from −0.8 to 0.8. In the two examples, the asymptotic information matrix is obtained in the Gaussian case. Finally, the finite-sample behavior is checked via a Monte Carlo simulation study for n from 25 to 400. The results confirm the validity of the asymptotic properties even for short series and the asymptotic information matrix deduced from the theory.

Suggested Citation

  • Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Melard, 2016. "Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients," Working Papers ECARES ECARES 2016-41, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:eca:wpaper:2013/241623
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    Cited by:

    1. Abdelkamel Alj & Rajae Azrak & Christophe Ley & Guy Melard, 2016. "Technical Appendix to Asymptotic Properties of QML Estimators for VARMA Models with Time-Dependent Coefficients," Working Papers ECARES ECARES 2016-42, ULB -- Universite Libre de Bruxelles.

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    Keywords

    non-stationary process; multivariate time series; time-varying models;

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