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Information Technology and Management Science

The Journal of Riga Technical University

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Wavelet Transform Modulus Maxima Approach for World Stock Index Multifractal Analysis

Andrejs Puckovs / Andrejs Matvejevs
Published Online: 2013-01-31 | DOI: https://doi.org/10.2478/v10313-012-0016-5

Abstract

This paper describes an approach that is able to fix difference in multifractal behaviour of various World Stock Indexes. The approach is beneficial for the forecasting and simulations of the most European and Asian stock indexes. Multifractal analysis is provided using the so-called Wavelet Transform Modulus Maxima approach, which involves two basic aspects: Wavelet aspect (Direct Continuous Wavelet Transform, Skeleton construction) and Multifractal formalism (Fractal Partition Function calculation, Moment Generating Function calculation, Multifractal Spectrum estimation).

Šī raksta mērķis ir nodrošināt pieeju, kas spēj izpētīt atšķirības pasaules akciju indeksu multifraktāļu spektros. Šī pieeja ir spējīga noteikt atšķirības multifraktāļu uzvedībā dažādiem pasaules akciju indeksiem. Šī pieeja ir piemērota Eiropas un Āzijas akciju indeksu prognozēšanai un imitācijas modelēšanai. Multifraktālā analīze ir īstenota, izmantojot tā saucamo veivlet pārveidojumu moduļu maksimumu pieeju, kas ietver sevī divus galvenos aspektus: veivlet analīzi un multifraktāļu algoritmu. Veivlet pārveidojumu moduļu maksimumu pieeja ir metode, kas atklāj signāla fraktāļu mēru. Šī raksta secība ir sekojoša: vispirms ir aplūkotas pasaules akciju indeksu multifraktalitātes pamati un konstruēts aktīvu ienesīguma multifraktāļu modelis, otrajā solī ir izklāstīta sākotnējo datu apstrādes procedūra, pēc tam tiek aplūkoti divi veivlet pārveidojumu moduļu maksimumu pieejas aspekti (veivlet analīze un multifraktāļu algoritms). Pēc tam veivlet pārveidojumu moduļu maksimumu pieeja ir izklāstīta saistībā ar pasaules akciju indeksiem uz Vācijas DAX30 akciju indeksa piemēra. Par eksperimenta objektiem ir kļuvuši 12 pasaules akciju indeksi: IBEX35 index, DAX30 index, Swiss Market Index, CAC40 index, FTSE100 index, Dow Jones Industrial index, Amsterdam Exchange index, Hang Seng index, NIKKEI225 index, Straits Times Index {Singapore}, Philippines Stock Exchange Index, BSE India Sensex 30 Index. Indeksi ir analizēti par pēdējiem 20 gadiem. Pēc akciju indeksu multifraktāļu analīzes rezultātiem, visi pētāmie objekti demonstrē stingri izteiktu multifraktāļu uzvedību, kas norāda uz dažādu fraktāļu mēru esamību. Pētījumā tika atklāti tipiskie fraktāļu mēri, kā arī multifraktāļu spektru nobīdes. Tāpat ir izpētīta akciju indeksu multifraktāļu spektru korelācija. Pētāmā metode ļauj atklāt indeksu līdzīgu uzvedību, kas nozīmē spēju fiksēt, turēt un glabāt tirgus informāciju "noteiktā veidā".

Данная статья призвана определить лучший подход, который будет способен выявить разницу в мультифрактальных спектрах различных биржевых индексов. Данный подход должен быть применим для мультифрактального анализа и имитационного моделирования азиатских и европейских биржевых индексов. Мультифрактальный анализ осуществлён с использованием так называемого метода модулей максимумов вейвлет коэффициентов (Wavelet Transform Modulus Maxima), который включает в себя два основных аспекта: вейвлет анализ (прямое непрерывное вейвлет преобразование и построение скелетона) и мультифрактальный алгоритм (функция обобщенной статистической суммы, функция масштабирования, функция мультифрактального спектра). Метод модулей максимумов вейвлет коэффициентов является методом для определения фрактальной размерности сигнала. В статье изложение результатов осуществляется следующим образом: прежде всего, освещаются основы мультифрактальности биржевых индексов, строится модель мультифрактальной доходности активов, после чего излагается процедура начальной обработки биржевых индексов, затем

Keywords : Wavelet Transform Modulus Maxima approach; Direct Continuous Wavelet Transform; Skeleton; Multifractal formalism; Fractal Partition Function; Moment Generating Function; Multifractal Spectrum; Stock indexes

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About the article

Andrejs Puckovs

Andrejs Puckovs was born in Riga in 1985. He graduated from Riga Technical University (Latvia), where he received his Bachelor Degree in Management in 2007. He has the Qualification of Economist and Professional Master Degree in Economics (Financial analysis). Andrejs Puckovs is currently completing his research for a Doctoral Degree at Riga Technical University in the field of Mathematical Statistics and its Applications. From 2008 to 2010 he worked as a Fund Administrator in Custody and Correspondent Banking Department, JSC Swedbank. Contact data: Chair of the Probability Theory and Mathematical Statistics, Riga Technical University.

Andrejs Matvejevs

Andrejs Matvejevs is a Doctor of Technical Sciences in Information Systems. Until 2009 he was a Chief Actuary at the insurance company “BALVA”. For more than 25 years he has taught at Riga Technical University and Riga International College of Business Administration, Latvia. His previous research was devoted to solving of dynamical systems with random perturbation. His current professional research interests include applications of Markov chains to actuarial technologies: mathematics of finance and security portfolio. He is the author of about 40 scientific publications, two textbooks and numerous conference papers. Contact data: Chair of the Probability Theory and Mathematical Statistics, Riga Technical University


Published Online: 2013-01-31

Published in Print: 2012-12-01


Citation Information: Information Technology and Management Science, Volume 15, Issue 1, Pages 76–86, ISSN (Online) 2255-9094, ISSN (Print) 2255-9086, DOI: https://doi.org/10.2478/v10313-012-0016-5.

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