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Locally Stationary Multiplicative Volatility Modeling

Lookup NU author(s): Dr Chris WalshORCiD

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Abstract

In this article, we study a semiparametric multiplicative volatility model, which splits up into a nonparametric part and a parametric GARCH component. The nonparametric part is modeled as a product of a deterministic time trend component and of further components that depend on stochastic regressors. We propose a two-step procedure to estimate the model. To estimate the nonparametric components, we transform the model and apply a backfitting procedure. The GARCH parameters are estimated in a second step via quasi maximum likelihood. We show consistency and asymptotic normality of our estimators. Our results are obtained using mixing properties and local stationarity. We illustrate our method using financial data. Finally, a small simulation study illustrates a substantial bias in the GARCH parameter estimates when omitting the stochastic regressors.

Publication metadata

Author(s): Walsh C, Vogt M

Publication type: Article

Publication status: Published

Journal: Journal of Business & Economic Statistics

Year: 2023

Volume: 41

Issue: 2

Pages: 497-508

Online publication date: 16/03/2022

Acceptance date: 01/01/2022

ISSN (print): 0735-0015

ISSN (electronic): 1537-2707

Publisher: Taylor & Francis

URL: https://doi.org/10.1080/07350015.2022.2036612

DOI: 10.1080/07350015.2022.2036612

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