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

Abdelkamel Alj, Rajae Azrak, Christophe Ley and Guy Melard

Working Papers ECARES from ULB -- Universite Libre de Bruxelles

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.

Keywords: non-stationary process; multivariate time series; time-varying models (search for similar items in EconPapers)
Pages: 35 p.
Date: 2016-12
New Economics Papers: this item is included in nep-ecm and nep-ets
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Citations: View citations in EconPapers (1)

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