期刊
ELECTRONIC JOURNAL OF STATISTICS
卷 12, 期 1, 页码 1019-1052出版社
INST MATHEMATICAL STATISTICS
DOI: 10.1214/18-EJS1416
关键词
Consistency; invertibility; maximum likelihood estimation; observation-driven models; stochastic recurrence equations
资金
- Center for Research in Econometric Analysis of Time Series, CREATES - Danish National Research Foundation [DNRF78]
- ANR network AMERISKA [ANR 14 CE20 0006 01]
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-LARCH model under weaker conditions than those considered in previous literature.
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