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Research output: Contribution to Journal/Magazine › Journal article › peer-review
Research output: Contribution to Journal/Magazine › Journal article › peer-review
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TY - JOUR
T1 - Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗
AU - Douc, R.
AU - Fokianos, K.
AU - Moulines, E.
PY - 2017
Y1 - 2017
N2 - We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson based models for count time series or duration models. However, the proposed approach is more general and covers a variety of time series models including the ordinary GARCH model which has been studied extensively in the literature. We provide general conditions under which quasi-maximum likelihood estimators can be analyzed for this class of time series models and we prove that these estimators are consistent and asymptotically normally distributed regardless of the true data generating process. We illustrate our results using classical examples of quasi-maximum likelihood estimation including standard GARCH models, duration models, Poisson type autoregressions and ARMA models with GARCH errors. Our contribution unifies the existing theory and gives conditions for proving consistency and asymptotic normality in a variety of situations.
AB - We study a general class of quasi-maximum likelihood estimators for observation-driven time series models. Our main focus is on models related to the exponential family of distributions like Poisson based models for count time series or duration models. However, the proposed approach is more general and covers a variety of time series models including the ordinary GARCH model which has been studied extensively in the literature. We provide general conditions under which quasi-maximum likelihood estimators can be analyzed for this class of time series models and we prove that these estimators are consistent and asymptotically normally distributed regardless of the true data generating process. We illustrate our results using classical examples of quasi-maximum likelihood estimation including standard GARCH models, duration models, Poisson type autoregressions and ARMA models with GARCH errors. Our contribution unifies the existing theory and gives conditions for proving consistency and asymptotic normality in a variety of situations.
KW - Asymptotic normality
KW - consistency
KW - count time series
KW - duration models
KW - GARCH models
KW - Kullback-Leibler divergence
KW - maximum likelihood
KW - stationarity
U2 - 10.1214/17-EJS1299
DO - 10.1214/17-EJS1299
M3 - Journal article
VL - 11
SP - 2707
EP - 2740
JO - Electronic Journal of Statistics
JF - Electronic Journal of Statistics
SN - 1935-7524
IS - 2
ER -