Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process

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Polish Statistical Association

Central Statistical Office of Poland

Subject: Economics , Statistics & Probability

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VOLUME 21 , ISSUE 2 (June 2020) > List of articles

Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process

Piotr Szczepocki

Keywords : Ornstein–Uhlenbeck  process, stochastic volatility, iterated filtering

Citation Information : Statistics in Transition New Series. Volume 21, Issue 2, Pages 173-187, DOI: https://doi.org/10.21307/stattrans-2020-019

License : (CC BY-NC-ND 4.0)

Received Date : 04-March-2019 / Accepted: 31-January-2020 / Published Online: 01-June-2020

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ABSTRACT

Barndorff-Nielsen and Shephard (2001) proposed a class of stochastic volatility models in which the volatility follows the Ornstein–Uhlenbeck process driven by a positive Levy process without the Gaussian component. The parameter estimation of these models is challenging because the likelihood function is not available in a closed-form expression. A large number of estimation techniques have been proposed, mainly based on Bayesian inference. The main aim of the paper is to present an application of iterated filtering for parameter estimation of such models. Iterated filtering is a method for maximum likelihood inference based on a series of filtering operations, which provide a sequence of parameter estimates that converges to the maximum likelihood estimate. An application to S&P500 index data shows the model perform well and diagnostic plots for iterated filtering  ensure convergence iterated filtering to maximum likelihood estimates.  Empirical application is accompanied by a simulation study  that   confirms the validity of the approach in the case of Barndorff-Nielsen and Shephard’s stochastic volatility models.

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