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Bovina, Dario (2009) Scaling and modelization of financial time series. [Ph.D. thesis]

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Abstract (english)

This thesis is devoted to the characterization of the invariance under rescaling of financial time series. Our main result is that the multiscaling observed until now in many financial time series could be a spurious effect. We proved that a probabilistic mechanism working in the empirical statistical analysis of a single time series and based on the power law tails of the density function of the returns, can affect the outcoming Hurst exponent and leads to a strong spurious multiscaling even for a strictly simple scaling underlying process. Since this effect is due only to the availability of a single empirical time series and to the presence of extreme events whose distribution follows a power law, we cannot exclude that our results could be relevant to fields of complex systems physics different from finance.

Abstract (italian)

Questa tesi è dedicata allo studio dell'invarianza di scala delle serie temporali finanziarie. Il nostro risultato principale è che il multiscaling osservato sinora in molte serie temporali finanziarie potrebbe essere solo un effetto spurio. Abbiamo dimostrato che un meccanismo probabilistico può influire sul calcolo dell'esponente di Hurst e portare ad un multiscaling fittizio anche per serie temporali provenienti da processi strettamente simple scaling. Tale meccanismo interviene nell'analisi statistica di una singola serie empirica ed è basato sulle code a potenza della PDF dei ritorni. Siccome questo effetto si deve solamente alla presenza di eventi estremi che seguono una legge a potenza e alla disponibilità di un'unica serie temporale, non possiamo escludere che il nostro risultato abbia rilevanza in campi della fisica dei sistemi complessi diversi dalla finanza.

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EPrint type:Ph.D. thesis
Tutor:Stella, Attilio
Supervisor:Baldovin, Fulvio
Ph.D. course:Ciclo 21 > Scuole per il 21simo ciclo > FISICA
Data di deposito della tesi:02 February 2009
Anno di Pubblicazione:2009
Key Words:Stochastic processes, Stock market indexes, Financial time series Hurst exponent analysis, Multiscaling
Settori scientifico-disciplinari MIUR:Area 02 - Scienze fisiche > FIS/02 Fisica teorica, modelli e metodi matematici
Struttura di riferimento:Dipartimenti > Dipartimento di Fisica e Astronomia "Galileo Galilei"
Codice ID:1953
Depositato il:02 Feb 2009
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