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Optimal model parameter values are obtained from fits to consecutive daily 2-year period returns of S&amp;P500 index over [1950\u20132016], generating 33-time series estimations. Through an econometric model, the kurtosis of returns distributions is modelled as a function of these parameters. Subsequently an auto-regressive analysis on these parameters advances the modelling and forecasting of kurtosis and returns distributions, providing the accurate shape of returns distributions and measurement of Value at Risk.<\/jats:p>","DOI":"10.1007\/s10479-019-03305-z","type":"journal-article","created":{"date-parts":[[2019,7,23]],"date-time":"2019-07-23T14:17:40Z","timestamp":1563891460000},"page":"1397-1410","update-policy":"https:\/\/doi.org\/10.1007\/springer_crossmark_policy","source":"Crossref","is-referenced-by-count":20,"title":["Modelling and forecasting the kurtosis and returns distributions of financial markets: irrational fractional Brownian motion model approach"],"prefix":"10.1007","volume":"299","author":[{"given":"Gurjeet","family":"Dhesi","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Bilal","family":"Shakeel","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Marcel","family":"Ausloos","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"297","published-online":{"date-parts":[[2019,7,23]]},"reference":[{"key":"3305_CR1","doi-asserted-by":"crossref","first-page":"275","DOI":"10.1093\/jjfinec\/nbj006","volume":"4","author":"K Aas","year":"2006","unstructured":"Aas, K., & Haff, I. 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