Feasible invertibility conditions and maximum likelihood estimation for observation-driven models
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Feasible invertibility conditions and maximum likelihood estimation for observation-driven models. / Blasques, Francisco; Gorgi, Paolo; Koopman, Siem Jan; Wintenberger, Olivier.
I: Electronic Journal of Statistics, Bind 12, Nr. 1, 2018, s. 1019-1052.Publikation: Bidrag til tidsskrift › Tidsskriftartikel › Forskning › fagfællebedømt
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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
VL - 12
SP - 1019
EP - 1052
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
IS - 1
ER -
ID: 222096680