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

Abstract

In the paper, we begin with introducing a novel scale mixture of normal distribution such that its leptokurticity and fat-tailedness are only local, with this “locality” being separately controlled by two censoring parameters. This new, locally leptokurtic and fat-tailed (LLFT) distribution makes a viable alternative for other, globally leptokurtic, fat-tailed and symmetric distributions, typically entertained in financial volatility modelling. Then, we incorporate the LLFT distribution into a basic stochastic volatility (SV) model to yield a flexible alternative for common heavy-tailed SV models. For the resulting LLFT-SV model, we develop a Bayesian statistical framework and effective MCMC methods to enable posterior sampling of the parameters and latent variables. Empirical results indicate the validity of the LLFT-SV specification for modelling both “non-standard” financial time series with repeating zero returns, as well as more “typical” data on the S&P 500 and DAX indices. For the former, the LLFT-SV model is also shown to markedly outperform a common, globally heavy-tailed, t-SV alternative in terms of density forecasting. Applications of the proposed distribution in more advanced SV models seem to be easily attainable.

Using search trends to analyze web-based users’ behavior profiles connected with COVID-19 in mainland China: infodemiology study based on hot words and Baidu Index

“…To solve the above problem, this study replaced BI values with the occurrence frequency of subordinate hot words to explore the temporal relationship ( Wang et al, 2021 ). The occurrences of subordinate hot words (domains) was defined as their occurrence frequencies of peak BI values (kurtosis >3, critical value of leptokurtic and fat-tailed distribution ( Lenart, Pajor & Kwiatkowski, 2021 ) to compute their sum of occurrence frequencies per week. Additionally, our study took “Month” as the minimum time unit of temporal relationship analysis instead of “Day” for avoiding possible data redundancy problems ( Garland, James & Bradley, 2014 ) and exploring the secular trends of domains.…”