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

TY - JOUR

T1 - Feasible invertibility conditions and maximum likelihood estimation for observation-driven models

AU - Blasques, Francisco

AU - Gorgi, Paolo

AU - Koopman, Siem Jan

AU - Wintenberger, Olivier

PY - 2018

Y1 - 2018

N2 - 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.

AB - 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.

KW - Consistency

KW - Invertibility

KW - Maximum likelihood estimation

KW - Observation-driven models

KW - Stochastic recurrence equations

U2 - 10.1214/18-EJS1416

DO - 10.1214/18-EJS1416

M3 - Journal article

AN - SCOPUS:85044216651

SN - 1935-7524

VL - 12

SP - 1019

EP - 1052

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

IS - 1

ER -