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Necessary and sufficient conditions for the identifiability of observation‐driven models
Author(s) -
Douc Randal,
Roueff François,
Sim Tepmony
Publication year - 2021
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12559
Subject(s) - identifiability , mathematics , poisson distribution , bernoulli's principle , bivariate analysis , autoregressive conditional heteroskedasticity , integer (computer science) , series (stratigraphy) , estimator , vector autoregression , consistency (knowledge bases) , autoregressive model , econometrics , statistics , computer science , discrete mathematics , volatility (finance) , paleontology , engineering , biology , programming language , aerospace engineering
In this contribution we are interested in proving that a given observation‐driven model is identifiable. In the case of a GARCH( p , q ) model, a simple sufficient condition has been established in Berkes I, Horváth L, Kokoszka P. (2003). Bernoulli 9: 201–227 for showing the consistency of the quasi‐maximum likelihood estimator. It turns out that this condition applies for a much larger class of observation‐driven models, that we call the class of linearly observation‐driven models. This class includes standard integer valued observation‐driven time series such as the Poisson autoregression model and its numerous extensions. Our results also apply to vector‐valued time series such as the bivariate integer valued GARCH model, to nonlinear models such as the threshold Poisson autoregression or to observation‐driven models with exogenous covariates such as the PARX model.