Multidimensional Alpha Stable Distribution in Model Parameter Estimation Algorithms

Kód výsledku v IS VaVaI

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Výsledek na webu

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DOI - Digital Object Identifier

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Jazyk výsledku

angličtina

Název v původním jazyce

Multidimensional Alpha Stable Distribution in Model Parameter Estimation Algorithms

Popis výsledku v původním jazyce

Solving optimization problem with a multidimensional objective function is the tra- ditional task of operational research. Both multimodality and nonsmoothness of the objective function are typical difficulties when searching for the global optimum. To improve the search effectiveness in non-adaptive algorithms as well as the ability to leap away from local optima, the so called Levy flights are often used. The Levy flights are random non-Gaussian step sizes following alpha stable distribution. How- ever, this random variable is very difficult to be generated in the multivariatal case, the step size generation procedure has never been treated accordingly so far. To examine the effectiveness of the general usage of this possibility, the goal of this paper is to introduce the multivariate alpha stable random variable step size generation technique into several novel optimization algorithms. Our approach then is used to estimate pa- rameters of generalized hyperbolic distribution with the use of maximum likelihood estimation method for returns of Czech stock market index PX from 2000 to 2017. As this task is almost unsolvable for traditional optimization methods, the results we obtained are quite promising.

Název v anglickém jazyce

Multidimensional Alpha Stable Distribution in Model Parameter Estimation Algorithms

Popis výsledku anglicky

Solving optimization problem with a multidimensional objective function is the tra- ditional task of operational research. Both multimodality and nonsmoothness of the objective function are typical difficulties when searching for the global optimum. To improve the search effectiveness in non-adaptive algorithms as well as the ability to leap away from local optima, the so called Levy flights are often used. The Levy flights are random non-Gaussian step sizes following alpha stable distribution. How- ever, this random variable is very difficult to be generated in the multivariatal case, the step size generation procedure has never been treated accordingly so far. To examine the effectiveness of the general usage of this possibility, the goal of this paper is to introduce the multivariate alpha stable random variable step size generation technique into several novel optimization algorithms. Our approach then is used to estimate pa- rameters of generalized hyperbolic distribution with the use of maximum likelihood estimation method for returns of Czech stock market index PX from 2000 to 2017. As this task is almost unsolvable for traditional optimization methods, the results we obtained are quite promising.

Druh

D - Stať ve sborníku

CEP obor

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OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

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Návaznosti

S - Specificky vyzkum na vysokych skolach<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2017

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Mathematical Methods in Economics MME 2017

ISBN

978-80-7435-678-0

ISSN

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e-ISSN

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Počet stran výsledku

6

Strana od-do

384-389

Název nakladatele

Univerzita Hradec Králové

Místo vydání

Hradec Králové

Místo konání akce

Hradec Králové

Datum konání akce

13. 9. 2017

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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