Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions |
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| Authors: | Carlos A Abanto‐Valle Roland Langrock Ming‐Hui Chen Michel V Cardoso |
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| Institution: | 1. Department of Statistics, Federal University of Rio de Janeiro, Rio de Janeiro, Brazil;2. Department of Business Administration and Economics, Bielefeld University, Bielefeld, Germany;3. Department of Statistics, University of Connecticut, Storrs, CT, U.S.A. |
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| Abstract: | In this article, we introduce a likelihood‐based estimation method for the stochastic volatility in mean (SVM) model with scale mixtures of normal (SMN) distributions. Our estimation method is based on the fact that the powerful hidden Markov model (HMM) machinery can be applied in order to evaluate an arbitrarily accurate approximation of the likelihood of an SVM model with SMN distributions. Likelihood‐based estimation of the parameters of stochastic volatility models, in general, and SVM models with SMN distributions, in particular, is usually regarded as challenging as the likelihood is a high‐dimensional multiple integral. However, the HMM approximation, which is very easy to implement, makes numerical maximum of the likelihood feasible and leads to simple formulae for forecast distributions, for computing appropriately defined residuals, and for decoding, that is, estimating the volatility of the process. Copyright © 2017 John Wiley & Sons, Ltd. |
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| Keywords: | feedback effect non‐Gaussian and nonlinear state‐space models scale mixture of normal distributions value‐at‐risk |
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