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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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Bibliografia

I riferimenti della bibliografia possono essere cercati con Cerca la citazione di AIRE, copiando il titolo dell'articolo (o del libro) e la rivista (se presente) nei campi appositi di "Cerca la Citazione di AIRE".
Le url contenute in alcuni riferimenti sono raggiungibili cliccando sul link alla fine della citazione (Vai!) e tramite Google (Ricerca con Google). Il risultato dipende dalla formattazione della citazione.

W. Feller (1951). 'The asymptotic distribution of the range of sums of independent random variables'. Ann. Mat. Statist, 22, 427{432 Cerca con Google

B.B. Mandelbrot and J.W. Van Ness (1968). 'Fractional brownian motions, fractional noises and applications'. Soc. Ind. Appl. Math. Rev., 10, 422{437 Cerca con Google

M. Eneva (1994). 'Monofractal of multifractal: a case study of spatial distribution of mining induced seismic activity'. Nonlinear Processes in Geophysics, 1, 182{190 Cerca con Google

T. Aste, M.M. Dacorogna and T. Di Matteo (2005). 'Long-term memories of developed and emerging markets: using the scaling analysis to characterize their stage of development'. Journal of Banking & Finance, 29, 827{851 Cerca con Google

A.V. Chechkin and V.Y. Gonchar (2000). 'Self and spurious multi-anity of ordinary Levy motion, and pseudo-Gaussian relations'. Chaos Solitons & Fractals, 11, 2379{2390 Cerca con Google

B. LeBaron (2001). 'Stochastic volatility as a simple generator of apparent nancial power laws and long memory'. Quantitative Finance, 1, 621{631 Cerca con Google

R.N. Mantegna and H.E. Stanley (1994). 'Stochastic Process with Ultraslow Convergence to a Gaussian: The Truncated Levy Flight'. Physical Review Letters, 23, 2946{2949 Cerca con Google

B.V. Gnedenko and A.N. Kolmogorov (1954). 'Limit distributions for sums of independent random variables'. Addison Wesley Cerca con Google

K. Falconer (1990). 'Fractal geometry - mathematical foundations and applications'. John Wiley & Sons Cerca con Google

R. Toral and A. Chakrabarti (1993). 'Generation of Gaussian distributed random numbers by using a numerical inversion method'. Computer Physics Communications, 74, 327{334 Cerca con Google

J.P. Bouchaud and M. Potters (2003). 'Theory of nancial risk and derivative pricing'. Cambridge University Press Cerca con Google

B.V. Gnedenko (1968). 'The theory of probability'. Chelsea Pub. Co. Cerca con Google

J.W. Kantelhardt (2008). 'Fractal and Multifractal Time Series'. ArXiv: physics.data-an 0804.0747v1 Cerca con Google

L. Bachelier (1900). 'Theorie de la speculations'. Annales de l'ecole Normale superieure, 17, 21{86 Cerca con Google

D. Sornette (1998). 'Large deviations and Portfolio optimization'. Physica A, 256, 251{283 Cerca con Google

N.J. Higham (1990). 'Analysis of the Cholesky decomposition of a semi-denite matrix'. In 'Reliable numerical computation' Oxford University Press, 161{185 Cerca con Google

T. Lux (2001). 'The multi-fractal model of asset returns: simple moment and GMM estimation'. Cerca con Google

T. Lux and M. Marchesi (1999). 'Scaling and criticality in a stochastic multiagent model of a nancial market'. Nature, 397 Cerca con Google

J.F. Muzy, D. Sornette, J. Delour and A. Arneodo (2001). 'Multifractal returns and Hierarchical Portfolio Theory'. Quantitative Finance, 1, 131{148 Cerca con Google

A. Arneodo, J.F. Muzy and D. Sornette (1998). 'Direct causal cascade in the stock market'. The European Physical Journal B, 2, 277{282 Cerca con Google

L. Calvet, A. Fisher and B. Mandelbrot (1997). 'Large Deviations and the Distribution of Price Changes'. Cowles Foundation, 1165 Cerca con Google

B.B. Mandelbrot, A. Fisher and L. Calvet (1997). 'A Multifractal Model of Asset Returns'. Working Paper Cerca con Google

B.B. Mandelbrot (2001). 'Scaling in nancial prices: IV. Multifractal concentration'. Quantitative Finance, 1, 641{649 Cerca con Google

F. Baldovin and A.L. Stella (2007). 'Central limit theorem for anomalous scaling due to correlations'. Physical Review E, 75 Cerca con Google

F. Baldovin and A.L. Stella (2007). 'Scaling and eciency determine the irreversible evolution of a market'. Proc. Nat. Acad. Sci., 104, 19741{19744 Cerca con Google

S. Ghashghaie, W. Breymann, J. Peinke, P. Talkner and Y. Dodge (1996). 'Turbulent cascades in foreign exchange markets'. Nature, 381, 767{770 Cerca con Google

R.N. Mantegna and H.E. Stanley (1997). 'Stock market dynamics and turbulence: parallel analysis of uctuation phenomena'. Physica A, 239, 255{266 Cerca con Google

R.N. Mantegna and H.E. Stanley (1996). 'Turbulence and nancial markets'. Nature, 383, 587{588 Cerca con Google

T. Bollerslev (1986). 'Generalized autoregressive conditional heteroscedasticity'. Journal of Econometrics, 31, 307{327 Cerca con Google

R.F. Engle (1982). 'Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom in ation'. Econometrica, 50, 987{1008 Cerca con Google

B. Podobnik, P.C. Ivanov, I. Grosse, K. Matia and H.E. Stanley (2004). 'Arch- Garch approaches to modeling high-frequency nancial data'. Physica A, 344, 216{220 Cerca con Google

R. Engle (2001). 'Garch 101: the use of Arch/Garch models in applied econometrics'. Journal of Economic Perspectives, 15, 157{168 Cerca con Google

D.B. Nelson (1991). 'Conditional heteroskedasticity in asset returns: a new approach'. Econometrica, 59, 347{370 Cerca con Google

R.F. Engle, D.M. Lilien and R.P. Robins (1987). 'Estimating time varying risk premia in the term structure: the Arch-M model'. Econometrica, 55, 391{407 Cerca con Google

R.T. Baillie, T. Bollerslev and H.O. Mikkelsen (1996). 'Fractionally integrated generalized autoregressive conditional heteroskedasticity'. Journal of Econometrics, 74, 3{30 Cerca con Google

R.A. Velasco Fuentes. 'Arch-type models'. Cerca con Google

R.F. Engle (1983). 'Estimates of the variance of U.S. In ation based upon the Arch model'. Econometrica, 15, 286{301 Cerca con Google

T. Bollerslev and H.O. Mikkelsen (1996). 'Modeling and pricing long memory in stock market volatility'. Journal of Econometrics, 73, 151{184 Cerca con Google

R.F. Engle and T. Bollerslev (1986). 'Modelling the persistence of conditional variances'. Econometric Reviews, 5, 1{50 Cerca con Google

J.M. Maheu (2002). 'Can Garch models capture the long-range dependence in nancial market volatility?'. Cerca con Google

R. Cont (2001). 'Empirical properties of asset returns: stylized facts and statistical issues'. Quantitative Finance, 1, 223{236 Cerca con Google

A.W. Lo (1991). 'Long-term memory in stock market prices'. Econometrica, 59, 1279{1313 Cerca con Google

V. Teverovsky, M.S. Taqqu and W. Willinger (1999). 'A critical look at Lo's modied R/S statistic'. Jour. of stat. planning and inference, 80, 211{227 Cerca con Google

H.E. Stanley and V. Plerou (2001). 'Scaling and universality in economics: empirical results and theoretical interpretation'. Quantitative Finance, 1, 563{ 567 Cerca con Google

R. Cont (2005). 'Volatility clustering in nancial markets: empirical facts and agent-based models'. Cerca con Google

B.M. Hill (1975). 'A simple general approach to inference about the tail of a distribution'. The Annals of Statistics, 3, 1163{1174 Cerca con Google

S. Resnick and C. Starica (1996). 'Tail index estimation for dependent data'. Annals of Applied Probability, 8, 1156{1183 Cerca con Google

H. Drees, L. de Hann and S. Resnick (2000). 'How to make a Hill plot'. The Annals of Statistics, 1, 254{274 Cerca con Google

E. Carlstein, K.A. Do, P. Hall, T. Hesterberg and H.R. Kunsch (1998). 'Matched-block bootstrap for dependent data'. Bernoulli, 4, 305{328 Cerca con Google

B. Efron (1979). 'Bootstrap Methods: Another Look at the Jackknife'. The Annals of Statistics, 7, 1{26 Cerca con Google

B. Efron and R. Tibshirani (1986). 'Bootstrap Methods for Standard Errors, Condence Intervals, and Other Measures of Statistical Accuracy'. Statistical Science, 1, 54{75 Cerca con Google

H.R. Kunsch (1989). 'The Jackknife and the Bootstrap for General Stationary Observations'. The Annals of Statistics, 17, 1217{1241 Cerca con Google

A. Carbone, G. Castelli and H.E. Stanley (2004). 'Time-dependent Hurst exponent in nancial time series'. Physica A, 344, 267{271 Cerca con Google

C.J.G. Evertsz (1995). 'Fractal Geometry of Financial Time Series'. Fractals, 3, 609{616 Cerca con Google

J.P. Bouchaud, M. Potters and M. Meyer (2000). 'Apparent multifractality in nancial time series'. The European Physical Journal B, 13, 595{599 Cerca con Google

Z.Q. Jiang and W.X. Zhou (2008). 'Multifractality in stock indexes: Fact or Fiction?'. Physica A, 387, 3605{3614 Cerca con Google

J. Fillol (2003). 'Multifractality: Theory and Evidence an Application to the French Stock Market'. Economics Bulletin, 31, 1{12 Cerca con Google

F. Schmitt, D. Schertzer and S. Lovejoy (2000). 'Multifractal uctuations in nance'. International Journal of Theoretical and Applied Finance, 3, 361{364 Cerca con Google

K. Matia, Y. Ashkenazy and H.E. Stanley (2003). 'Multifractal properties of price uctuations of stocks and commodities'. Europhysics Letters, 61, 422{428 Cerca con Google

L. Calvet, A. Fisher and B. Mandelbrot(). 'Multifractality of Deutschemark / US dollar exchange rates'. Cerca con Google

V.I. Belinicher, V.S. L'vov, A. Pomyalov and I. Procaccia (1998). 'Computing the scaling exponents in Cerca con Google

uid turbulence from rst principles: demonstration of multiscaling'. Journal of Statistical Physics, 93, 797{832 Cerca con Google

V.S. L'vov, E. Podivilov and I. Procaccia (1997). 'Temporal multiscaling in hydrodynamic turbulence'. Physical Review E, 55, 7030{7036 Cerca con Google

J. Herweijer and W. van der Water (1995). 'Universal shape of scaling functions in turbulence'. Physical Review Letters, 74, 4651{4655 Cerca con Google

M.H. Jensen (1999). 'Multiscaling and Structure functions in turbulence: an alternative approach'. Physical Review Letters, 83, 76{80 Cerca con Google

Z.S. She and E. Leveque (1994). 'Universal scaling laws in fully developed turbulence'.Physical Review Letters, 72, 336{340 Cerca con Google

E. Bonnet, O. Bour, N.E. Odling, P. Davy, I. Main, P. Cowie and B. Berkowitz (2001). 'Scaling of fracture systems in geological media'. Reviews of Geophysics, 39, 347{383 Cerca con Google

Y. Xu and P.W. Burton (2006). 'Time varying seismicity in Greece: Hurst's analysis and Monte Carlo simulation applied to a new earthquake catalogue for Greece'. Tectonophysics, 423, 125{136 Cerca con Google

L. Tennekoon, M.C. Boufadel, D. Lavallee and J. Weaver (2003). 'Multifractal anisotropic scaling of the hydraulic conductivity'. Water Resources Research, 39, 1193{1205 Cerca con Google

A. Montanari (2001). 'Dipendenza a lungo termine ed eetto di Hurst nelle serie temporali idrologiche' Cerca con Google

H.E. Hurst (1951). 'Long-term storage capacity of reservoirs'. American Society of Civil Engineers Cerca con Google

N.C. Matalas and C.S. Huzzen (1967). 'A property of the range of partial sums'. Proc. Int. Hydrol. Symp., 1, 252{257 Cerca con Google

H.E. Hurst (1957). 'A suggested statistical model of some time series which occur in nature'. Nature, 180 Cerca con Google

R.N. Bhattacharya, V.K. Gupta and E. Waymire (1983). 'The Hurst eect under trends'. J. Appl. Probab., 20, 649{662 Cerca con Google

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