{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,14]],"date-time":"2026-05-14T02:43:18Z","timestamp":1778726598700,"version":"3.51.4"},"reference-count":39,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2021,5,30]],"date-time":"2021-05-30T00:00:00Z","timestamp":1622332800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100004281","name":"Narodowe Centrum Nauki","doi-asserted-by":"publisher","award":["UMO-2018\/31\/B\/HS4\/00730"],"award-info":[{"award-number":["UMO-2018\/31\/B\/HS4\/00730"]}],"id":[{"id":"10.13039\/501100004281","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>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 \u201clocality\u201d 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 \u201cnon-standard\u201d financial time series with repeating zero returns, as well as more \u201ctypical\u201d data on the S&amp;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.<\/jats:p>","DOI":"10.3390\/e23060689","type":"journal-article","created":{"date-parts":[[2021,5,31]],"date-time":"2021-05-31T00:22:15Z","timestamp":1622420535000},"page":"689","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["A Locally Both Leptokurtic and Fat-Tailed Distribution with Application in a Bayesian Stochastic Volatility Model"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4111-0866","authenticated-orcid":false,"given":"\u0141ukasz","family":"Lenart","sequence":"first","affiliation":[{"name":"Department of Mathematics, Cracow University of Economics, ul. Rakowicka 27, 31-510 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5643-0649","authenticated-orcid":false,"given":"Anna","family":"Pajor","sequence":"additional","affiliation":[{"name":"Department of Mathematics, Cracow University of Economics, ul. Rakowicka 27, 31-510 Krak\u00f3w, Poland"},{"name":"Department of Financial Mathematics, Jagiellonian University in Krak\u00f3w, ul. Prof. Stanis\u0142awa \u0141ojasiewicza 6, 30-348 Krak\u00f3w, Poland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-0420-7589","authenticated-orcid":false,"given":"\u0141ukasz","family":"Kwiatkowski","sequence":"additional","affiliation":[{"name":"Department of Econometrics and Operations Research, Cracow University of Economics, ul. Rakowicka 27, 31-510 Krak\u00f3w, Poland"}]}],"member":"1968","published-online":{"date-parts":[[2021,5,30]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"99","DOI":"10.1111\/j.2517-6161.1974.tb00989.x","article-title":"Scale mixture of normal distribution","volume":"36","author":"Andrews","year":"1974","journal-title":"J. R. Stat. Soc. Ser. B"},{"key":"ref_2","doi-asserted-by":"crossref","unstructured":"Fang, K.T., Kotz, S., and Ng, K.W. (1990). Symmetric Multivariate and Related Distributions, Chapman and Hall.","DOI":"10.1007\/978-1-4899-2937-2"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"511","DOI":"10.1086\/296519","article-title":"The Variance Gamma (V.G.) Model for Share Market Returns","volume":"63","author":"Madan","year":"1990","journal-title":"J. Bus."},{"key":"ref_4","unstructured":"Romanowski, M. (1979). 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