Particle Filters for Markov-Switching Stochastic Volatility Models

Abstract

This chapter proposes an auxiliary particle filter algorithm for inference in regime switching stochastic volatility models in which the regime state is governed by a first-order Markov chain. It proposes an ongoing updated Dirichlet distribution to estimate the transition probabilities of the Markov chain in the auxiliary particle filter. A simulation-based algorithm is presented for the method that demonstrates the ability to estimate a class of models in which the probability that the system state transits from one regime to a different regime is relatively high. The methodology is implemented in order to analyze a real-time series, namely, the foreign exchange rate between the Australian dollar and the South Korean won.

Fast smoothing in switching approximations of non-linear and non-Gaussian models

“…The Markov switching stochastic volatility (MSSV) model (see [17,18,19]) reads as follows: where 1l A (.) is the indicator function of the set A, S N 1 is a stationary discrete Markov chain with q states, p s n+1 x n 1 , y n 1 , s n 1 = p (s n+1 |s n ) and γ 1 , .…”

“…, U N , V N are independent standard Gaussian vectors. Following the simulation study in [19], we set q = 2, p 11 = p (s n+1 = 1 |s n = 1) and p 22 = p (s n+1 = 2 |s n = 2). As a random sampling is straightforward within the framework of MSSV [17], our smoothing algorithm remains applicable.…”

“…As a random sampling is straightforward within the framework of MSSV [17], our smoothing algorithm remains applicable. Table 3 shows its results for the MSSV parameters given in [19].…”

“…Since PS (for which (34) is approximated by (30) identifying respective ergodic means of X n ) fails for MSSV model, we propose to compare our method to a switching variant, SPS, of PS which also computes E X n Y n+T 1 for T = 5 with m = 1500 particles (c.f. [19]). In all cases, we note that if K is large enough, the smoothed output of our method is as good as the statistically optimal one, produced by the PS (or SPS).…”

“…SCGOMSM is then used as an approximation of (1), as specified in Section 4. Some experimental results within the context of stochastic volatility [11,12,13,14,15,16,17,18,19] and the dynamic beta regression [20] are presented in Section 5. The last Section exposes conclusions and perspectives.…”