## Electronic Journal of Statistics

### Feasible invertibility conditions and maximum likelihood estimation for observation-driven models

#### Abstract

Invertibility conditions for observation-driven time series models often fail to be guaranteed in empirical applications. As a result, the asymptotic theory of maximum likelihood and quasi-maximum likelihood estimators may be compromised. We derive considerably weaker conditions that can be used in practice to ensure the consistency of the maximum likelihood estimator for a wide class of observation-driven time series models. Our consistency results hold for both correctly specified and misspecified models. We also obtain an asymptotic test and confidence bounds for the unfeasible “true” invertibility region of the parameter space. The practical relevance of the theory is highlighted in a set of empirical examples. For instance, we derive the consistency of the maximum likelihood estimator of the Beta-$t$-GARCH model under weaker conditions than those considered in previous literature.

#### Article information

Source
Electron. J. Statist., Volume 12, Number 1 (2018), 1019-1052.

Dates
First available in Project Euclid: 15 March 2018

https://projecteuclid.org/euclid.ejs/1521079462

Digital Object Identifier
doi:10.1214/18-EJS1416

Mathematical Reviews number (MathSciNet)
MR3776279

Zentralblatt MATH identifier
06864484

#### Citation

Blasques, Francisco; Gorgi, Paolo; Koopman, Siem Jan; Wintenberger, Olivier. Feasible invertibility conditions and maximum likelihood estimation for observation-driven models. Electron. J. Statist. 12 (2018), no. 1, 1019--1052. doi:10.1214/18-EJS1416. https://projecteuclid.org/euclid.ejs/1521079462

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