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

Area of Science:

• Statistics
• Econometrics
• Financial Modeling

Background:

• Stochastic volatility models are crucial for financial analysis.
• Estimating parameters in these models, especially with complex distributions like SMN, is computationally challenging.
• Existing methods often struggle with the high-dimensional integrals involved in likelihood calculation.

Purpose of the Study:

• To introduce a novel likelihood-based estimation method for the stochastic volatility in mean (SVM) model incorporating scale mixtures of normal (SMN) distributions.
• To demonstrate the efficacy of hidden Markov models (HMMs) in approximating the likelihood function for SVM-SMN models.
• To simplify parameter estimation, forecasting, and residual analysis in SVM models.

Main Methods:

• Utilizing the hidden Markov model (HMM) framework to approximate the likelihood of SVM models with SMN distributions.
• Building upon the methodology proposed by Langrock et al. (2012) to link HMMs and SVM models.
• Implementing numerical maximum likelihood estimation facilitated by the HMM approximation.

Main Results:

• The proposed HMM-based method provides an accurate and computationally feasible approximation of the likelihood function.
• The approach simplifies the process of maximum likelihood estimation for SVM-SMN models.
• Enables straightforward computation of forecast distributions, residuals, and volatility estimation (decoding).

Conclusions:

• The HMM approximation offers a practical and efficient solution for likelihood-based estimation in SVM models with SMN distributions.
• This method overcomes the traditional challenges associated with high-dimensional integrals in stochastic volatility modeling.
• The approach enhances the applicability and utility of SVM models in various analytical contexts.