An indirect proof for the asymptotic properties of VARMA model estimators

Guy Mélard

Econometrics and Statistics, 2022, vol. 21, issue C, 96-111

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.

Keywords: Non-stationary process; Multivariate time series; Time-varying models; Identifiability; ARMA models (search for similar items in EconPapers)
Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:eee:ecosta:v:21:y:2022:i:c:p:96-111

DOI: 10.1016/j.ecosta.2020.12.004

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