Bayesian semiparametric Markov switching stochastic volatility model

Abstract

This paper proposes a novel Bayesian semiparametric stochastic volatility model with Markov switching regimes for modeling the dynamics of the financial returns. The distribution of the error term of the returns is modeled as an infinite mixture of Normals; meanwhile, the intercept of the volatility equation is allowed to switch between two regimes. The proposed model is estimated using a novel sequential Monte Carlo method called particle learning that is especially well suited for state‐space models. The model is tested on simulated data and, using real financial times series, compared to a model without the Markov switching regimes. The results show that including a Markov switching specification provides higher predictive power for the entire distribution, as well as in the tails of the distribution. Finally, the estimate of the persistence parameter decreases significantly, a finding consistent with previous empirical studies.

A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model

“…Depending on the family distribution of the latter, conditional (on the past) expectation of the price simply may not exist (as it happens in the case of y t following a Student's t or slash distribution). However, from (21), it follows that if the conditional distribution of y t is LLFT, then the expectation of the induced price distribution is finite (conditionally on the past price).…”

“…Modifications of the distribution for ε t has been one of the most prolific strands of SV literature (see, e.g., [9][10][11][12][13][14][15][16]). Other typical directions of generalizing the basic SV structure focus on capturing the leverage effect and asymmetry (see, e.g., [12,[17][18][19]) as well as on refining the volatility process by, for example, accommodating realized volatility and long memory (see, e.g., [18,20]), or allowing for discrete, Markov switches of the parameters (see, e.g., [21][22][23]). However, we do not follow these lines of research in our current paper, focusing rather on the construction of a new distribution "from scratch" and its introduction into the basic SV model, thereby contributing to the research area of improving the conditional distribution in SV models.…”

An infinite hidden Markov model with stochastic volatility

“…Our infinite hidden Markov model with stochastic volatility (SV‐IHMM) is related to Virbickaitė and Lopes (2019), which has a two‐state Markov‐switching process affecting the conditional mean of log‐volatility, while log‐squared returns are nonparametrically modeled. The SV‐IHMM allows unbounded states for the conditional mean of log‐volatility but nonparametrically models return innovations without losing the sign information of returns.…”