Estimation of Stochastic Volatility Models with Heavy Tails and Serial Dependence

Abstract

Financial time series often exhibit properties that depart from the usual assumptions of serial independence and normality. These include volatility clustering, heavy-tailedness and serial dependence. A voluminous literature on different approaches for modeling these empirical regularities has emerged in the last decade. In this paper we review the estimation of a variety of highly flexible stochastic volatility models, and introduce some efficient algorithms based on recent advances in state space simulation techniques. These estimation methods are illustrated via empirical examples involving precious metal and foreign exchange returns. The corresponding Matlab code is also provided.

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“…Next, Step 4 involves a non-linear non-Gaussian measurement equation, and the standard linear Kalman lter can not be applied. To overcome this issue we follow Poon (2017) and make use of the auxiliary mixture sampler developed by Kim et al (1998) along with an ecient sampling algorithm in Chan and Hsiao (2014). The auxiliary mixture sampler uses a seven-Gaussian mixture to convert the non-linear measurement equation in the stochastic volatility model, into a log-linear equation that is conditionally Gaussian.…”

“…Finally, the full conditional distribution in Steps 5 results in non-standard distribution. Sampling is therefore achieved through an independence-chain Metropolis-Hastings Algorithm adapted from the univariate models in Chan and Hsiao (2014). For completeness, we now discuss the derivation of the conditional posterior distribution of each block in the Gibbs sampler.…”

“…To sample h, we follow Poon (2018) and apply the auxiliary mixture sampler from Kim et al (1998) along with the precision sampler from Chan and Hsiao (2014). To this end, note that the measurement equation in (4) can be written as:…”

“…is a truncated normal. Since this conditional distribution is non-standard, we follow Chan and Hsiao (2014) and implement an independence-chain Metropolis-Hastings step with a truncated normal distribution. More precisely,…”

“…s T , and parameter values in Table A.3, the state space model in (A.10) and (9) is linear and conditionally Gaussian, thus standard sampling methods can be used. Instead of adopting traditional Kalman lter based algorithms, we follow Poon (2018) and implement the ecient precision sampling based algorithm in Chan and Jeliazkov (2009); Chan and Hsiao (2014).…”