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An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators

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  • Guy Melard

Abstract

Strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters of a causal, invertible, and identiable vector autoregressive-moving average (VARMA) model are established in an indirect way. The proof is based on similar results for a much wider class of VARMA models with time-dependent coecients, hence in the context of non-stationary and heteroscedastic time series. For that reason, the proof avoids spectral analysis arguments and does not make use of ergodicity. The results presented are also applicable to ARMA models.

Suggested Citation

  • Guy Melard, 2020. "An Indirect Proof for the Asymptotic Properties of VARMA Model Estimators," Working Papers ECARES 2020-10, ULB -- Universite Libre de Bruxelles.
    • Handle: RePEc:eca:wpaper:2013/304272
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    Keywords

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