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M-Estimation in GARCH Models in the Absence of Higher-Order Moments

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M-Estimation in GARCH Models in the Absence of Higher-Order Moments. / Hallin, Marc; Liu, Hang; Mukherjee, Kanchan.
Research papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi. 1. ed. Singapore: Springer, 2023. p. 195-219.

Research output: Contribution in Book/Report/Proceedings - With ISBN/ISSN › Chapter

Harvard

Hallin, M, Liu, H & Mukherjee, K 2023, M-Estimation in GARCH Models in the Absence of Higher-Order Moments. in Research papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi. 1 edn, Springer, Singapore, pp. 195-219. <https://link.springer.com/book/10.1007/978-981-99-0803-5>

APA

Hallin, M., Liu, H., & Mukherjee, K. (2023). M-Estimation in GARCH Models in the Absence of Higher-Order Moments. In Research papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi (1 ed., pp. 195-219). Springer. https://link.springer.com/book/10.1007/978-981-99-0803-5

Vancouver

Hallin M, Liu H, Mukherjee K. M-Estimation in GARCH Models in the Absence of Higher-Order Moments. In Research papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi. 1 ed. Singapore: Springer. 2023. p. 195-219

Author

Hallin, Marc ; Liu, Hang ; Mukherjee, Kanchan. / M-Estimation in GARCH Models in the Absence of Higher-Order Moments. Research papers in Statistical Inference for Time Series and Related Models: Essays in Honor of Masanobu Taniguchi. 1. ed. Singapore : Springer, 2023. pp. 195-219

Bibtex

@inbook{f3fffb7b0d184978a0c2946dfc81c9aa,
title = "M-Estimation in GARCH Models in the Absence of Higher-Order Moments",
abstract = "We consider a class of M-estimators of the parameters of a GARCH(p,q) model. These estimators are asymptotically normal, depending on score functions, under milder moment assumptions than the usual quasi maximum likelihood, which makes them more reliable in the presence of heavy tails. We also consider weighted bootstrap approximations of the distributions of these M-estimators and establish their validity. Through extensive simulations, we demonstrate the robustness of these M-estimators under heavy tails and conduct a comparative study of the performance (biases and mean squared errors) of various score functions and the accuracy (confidence interval coverage probabilities) of their bootstrap approximations. In addition to the GARCH(1,1) model, our simulations also involve higher-order models such as GARCH(2,1) and GARCH(1,2) which so far have received relatively little attention in the literature. We also consider the case of order-misspecified models. Finally, we analyze two real financial time series datasets by fitting GARCH(1,1) or GARCH(2,1) models with our M-estimators.",
keywords = "M-Estimation, GARCH models, Higher-Order moments",
author = "Marc Hallin and Hang Liu and Kanchan Mukherjee",
year = "2023",
month = jun,
day = "1",
language = "English",
isbn = "9789819908028",
pages = "195--219",
booktitle = "Research papers in Statistical Inference for Time Series and Related Models",
publisher = "Springer",
edition = "1",

}

RIS

TY - CHAP

T1 - M-Estimation in GARCH Models in the Absence of Higher-Order Moments

AU - Hallin, Marc

AU - Liu, Hang

AU - Mukherjee, Kanchan

PY - 2023/6/1

Y1 - 2023/6/1

N2 - We consider a class of M-estimators of the parameters of a GARCH(p,q) model. These estimators are asymptotically normal, depending on score functions, under milder moment assumptions than the usual quasi maximum likelihood, which makes them more reliable in the presence of heavy tails. We also consider weighted bootstrap approximations of the distributions of these M-estimators and establish their validity. Through extensive simulations, we demonstrate the robustness of these M-estimators under heavy tails and conduct a comparative study of the performance (biases and mean squared errors) of various score functions and the accuracy (confidence interval coverage probabilities) of their bootstrap approximations. In addition to the GARCH(1,1) model, our simulations also involve higher-order models such as GARCH(2,1) and GARCH(1,2) which so far have received relatively little attention in the literature. We also consider the case of order-misspecified models. Finally, we analyze two real financial time series datasets by fitting GARCH(1,1) or GARCH(2,1) models with our M-estimators.

AB - We consider a class of M-estimators of the parameters of a GARCH(p,q) model. These estimators are asymptotically normal, depending on score functions, under milder moment assumptions than the usual quasi maximum likelihood, which makes them more reliable in the presence of heavy tails. We also consider weighted bootstrap approximations of the distributions of these M-estimators and establish their validity. Through extensive simulations, we demonstrate the robustness of these M-estimators under heavy tails and conduct a comparative study of the performance (biases and mean squared errors) of various score functions and the accuracy (confidence interval coverage probabilities) of their bootstrap approximations. In addition to the GARCH(1,1) model, our simulations also involve higher-order models such as GARCH(2,1) and GARCH(1,2) which so far have received relatively little attention in the literature. We also consider the case of order-misspecified models. Finally, we analyze two real financial time series datasets by fitting GARCH(1,1) or GARCH(2,1) models with our M-estimators.

KW - M-Estimation

KW - GARCH models

KW - Higher-Order moments

M3 - Chapter

SN - 9789819908028

SP - 195

EP - 219

BT - Research papers in Statistical Inference for Time Series and Related Models

PB - Springer

CY - Singapore

ER -