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An indirect proof for the asymptotic properties of VARMA model estimators

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  • Mélard, Guy

Abstract

Strong consistency and asymptotic normality of a Gaussian quasi-maximum likelihood estimator for the parameters of a causal, invertible, and identifiable 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 coefficients, 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

  • Mélard, Guy, 2022. "An indirect proof for the asymptotic properties of VARMA model estimators," Econometrics and Statistics, Elsevier, vol. 21(C), pages 96-111.
    • Handle: RePEc:eee:ecosta:v:21:y:2022:i:c:p:96-111
    DOI: 10.1016/j.ecosta.2020.12.004
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