Maximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.

TitleMaximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.
Publication TypeJournal Article
Year of Publication2017
AuthorsAbanto-Valle, Carlos A., Roland Langrock, Ming-Hui Chen, and Michel V. Cardoso
JournalAppl Stoch Models Bus Ind
Volume33
Issue4
Pagination394-408
Date Published2017 Jul-Aug
ISSN1524-1904
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 (Abanto-Valle et al., 2012). 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. The method is based on the proposal of Langrock et al. (2012) and makes explicit the useful link between HMMs and SVM models 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, i.e., estimating the volatility of the process.

DOI10.1002/asmb.2246
Alternate JournalAppl Stoch Models Bus Ind
Original PublicationMaximum likelihood estimation for stochastic volatility in mean models with heavy-tailed distributions.
PubMed ID28970740
PubMed Central IDPMC5621483
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States
R01 GM070335 / GM / NIGMS NIH HHS / United States