Handy sufficient conditions for the convergence of the maximum likelihood estimator in observation-driven models

2015/06/05 by Randal Douc, Douc, Randal, François Roueff +3
Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Distribution Estimation and Applications #Statistical Methods and Inference #Statistics Theory (math.ST) #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.1506.01831

arxiv created 2015/06/05 · openalex publication_date 2015/06/05 · arxiv updated 2015/06/08 · openalex created_date 2019/06/27 · openalex updated_date 2026/07/28

Abstract

This paper generalizes asymptotic properties obtained in the observation-driven times series models considered by \citedou:kou:mou:2013 in the sense that the conditional law of each observation is also permitted to depend on the parameter. The existence of ergodic solutions and the consistency of the Maximum Likelihood Estimator (MLE) are derived under easy-to-check conditions. The obtained conditions appear to apply for a wide class of models. We illustrate our results with specific observation-driven times series, including the recently introduced NBIN-GARCH and NM-GARCH models, demonstrating the consistency of the MLE for these two models.

Citations

• Generalized autoregressive conditional heteroskedasticity
• Theory and Inference for a Class of Observation-driven Models with Application to Time Series of Counts

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