Maximum likelihood estimation for stochastic volatility in mean models with heavy‐tailed distributions. (13th March 2017)

• Record Type: Journal Article
• Authors: Abanto‐Valle, Carlos A.; Langrock, Roland; Chen, Ming‐Hui; Cardoso, Michel V.
• Is Part Of: Applied stochastic models in business and industry. Volume 33:Number 4(2017)
• Page Start: 394
• Page End: 408
• Publication Date: 2017-03-13
• Subjects: feedback effect -- non‐Gaussian and nonlinear state‐space models -- scale mixture of normal distributions -- value‐at‐risk; Stochastic analysis -- Periodicals; Stochastic processes -- Periodicals; Business mathematics -- Periodicals; Finance -- Mathematical models -- Periodicals; Industrial management -- Mathematical models -- Periodicals; 338.00151923
• DOI: 10.1002/asmb.2246
• Languages: English
• ISSNs: 1524-1904

Abstract

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.