Student-t Stochastic Volatility Model With Composite Likelihood EM-Algorithm

Embargo End Date
2023-05-06

Type
Article

Authors
Sundararajan, Raanju R.
Barreto-Souza, Wagner

KAUST Department
Statistics Program

Preprint Posting Date
2021-05-27

Online Publication Date
2022-05-24

Print Publication Date
2023-01

Date
2022-05-24

Abstract
A new robust stochastic volatility (SV) model having Student-t marginals is proposed. Our process is defined through a linear normal regression model driven by a latent gamma process that controls temporal dependence. This gamma process is strategically chosen to enable us to find an explicit expression for the pairwise joint density function of the Student-t response process. With this at hand, we propose a composite likelihood (CL) based inference for our model, which can be straightforwardly implemented with a low computational cost. This is a remarkable feature of our Student-t process over existing SV models in the literature that involve computationally heavy algorithms for estimating parameters. Aiming at a precise estimation of the parameters related to the latent process, we propose a CL Expectation-Maximization algorithm and discuss a bootstrap approach to obtain standard errors. The finite-sample performance of our composite likelihood methods is assessed through Monte Carlo simulations. The methodology is motivated by an empirical application in the financial market. We analyze the relationship, across multiple time periods, between various US sector Exchange-Traded Funds returns and individual companies' stock price returns based on our novel Student-t model. This relationship is further utilized in selecting optimal financial portfolios. Generalizations of the Student-t SV model are also proposed.

Citation
Sundararajan, R. R., & Barreto-Souza, W. (2022). Student-t Stochastic Volatility Model With Composite Likelihood EM-Algorithm. Journal of Time Series Analysis. Portico. https://doi.org/10.1111/jtsa.12652

Acknowledgements
We thank the two referees for their insightful comments and suggestions that lead to an improvement of the paper. W. Barreto-Souza would like to acknowledge the financial support from the KAUST Research Fund.

Publisher
Wiley

Journal
Journal of Time Series Analysis

DOI
10.1111/jtsa.12652

arXiv
2105.13081

Additional Links
https://onlinelibrary.wiley.com/doi/10.1111/jtsa.12652

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