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Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗

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Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗. / Douc, R.; Fokianos, K.; Moulines, E.
In: Electronic Journal of Statistics, Vol. 11, No. 2, 2017, p. 2707-2740.

Research output: Contribution to Journal/Magazine › Journal article › peer-review

Harvard

Douc, R, Fokianos, K & Moulines, E 2017, 'Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗', Electronic Journal of Statistics, vol. 11, no. 2, pp. 2707-2740. https://doi.org/10.1214/17-EJS1299

APA

Douc, R., Fokianos, K., & Moulines, E. (2017). Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗. Electronic Journal of Statistics, 11(2), 2707-2740. https://doi.org/10.1214/17-EJS1299

Vancouver

Douc R, Fokianos K, Moulines E. Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗. Electronic Journal of Statistics. 2017;11(2):2707-2740. Epub 2017 May 29. doi: 10.1214/17-EJS1299

Author

Douc, R. ; Fokianos, K. ; Moulines, E. / Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗. In: Electronic Journal of Statistics. 2017 ; Vol. 11, No. 2. pp. 2707-2740.

Bibtex

@article{1104f39372db45218aad2c4784fe3ea0,
title = "Asymptotic properties of quasi-maximum likelihood estimators in observation-driven time series models∗",
abstract = "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.",
keywords = "Asymptotic normality , consistency , count time series, duration models , GARCH models, Kullback-Leibler divergence, maximum likelihood , stationarity",
author = "R. Douc and K. Fokianos and E. Moulines",
year = "2017",
doi = "10.1214/17-EJS1299",
language = "English",
volume = "11",
pages = "2707--2740",
journal = "Electronic Journal of Statistics",
issn = "1935-7524",
publisher = "Institute of Mathematical Statistics",
number = "2",

}

RIS

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 -