INAUGURACYJNE POSIEDZENIE ZARZĄDU SEKCJI FENS PTF Wydział Fizyki Politechniki Warszawskiej Warszawa 08 maja 2004 r.

Co w trawie piszczy? Ryszard Kutner Wydział Fizyki, Uniwersytet Warszawski Badania: Szeregi czasowe - dynamika cen akcji i indeksów: korelacje, rozkłady,... - prognozowanie,... Projekty: Modele mikroskopowe kolektywnej dynamiki

Dydaktyka i organizacja - projekt specjalizacji magisterskiej z metod fizyki w ekonomii na Wydziale Fizyki Uniwersytetu Warszawskiego ekonofizyka/

Oczekiwania Lobbing dydaktyczny Baza danych/Archiwum Współpraca z ekonomistami, socjologami, praktykami

ONE OF THE POSSIBLE MECHANISM OF THE NON-LINEAR LONG-TERM AUTOCORRELATIONS IN FINANCIAL TIME SERIES Ryszard Kutner* and Filip Świtała* * Institute of Experimental Physics, Department of Physics, Warsaw University, Hoża 69, Warsaw, Poland Faculty of Economic Sciences, Warsaw University, Długa 44/50, Warsaw, Poland

Content Motivation: power-law, non-linear autocorrelations of volatility in financial time-series present at Stock Markets particularly at Warsaw Stock Exchange (WGPW) Empirical data analysis Extended Continuous-Time Random Walk formalism & Weierstrass hierarchical two-state walk: Analysis of autocorrelations Comparison of empirical results with model predictions: agreement, questions and projects

M. Ausloos, J.-P. Bouchaud, J. Ho Ł yst, J. KERTéSZ, B. Mandelbrot, R. Mantegna, D. Sornette, P. Richmond, H.E. Stanley, G. Weiss,... R. Kutner, F. Świtała, Quant. Finance 3 (2003) R. K., F., Ś., Europ. Phys. J. B 33 (2003) R. K., F., Ś., LNCS 2657 (2003) R. K., Chem Phys. 284 (2002) R. K., Comp. Phys. Comm. 147 (2002) R. K., M. Regulski, Phys. A 264 (1999)

Empirical high-frequency data

|ΔX(t)| vs. trading time

Autocorrelations of price variations

Autocorrelations of absolute price variations Single-session periodicity

Eight trading days periodicity

K(t) after removing single-session periodicity

K(t) in log-log plot

Weierstrass Walk Randomly Intermitted by Localizations (WWRIL): Basic Walk One-Dimensional Continuous-Time Random Walk (CTRW) formalism was extended to cover localized and delocalized states of the walker. Walker moves at a constant velocity between consecutive turning points where he can be occasionally and temporarily localized and then chooses direction at random, walking in principle with an other constant velocity till the next turning point where again a localization event occurs... Weierstrass walk with varying velocity was developed.

Basic densities: waiting-time distributions for localized and delocalized states

Weierstrass Walks Randomly Intermitted by Localizations (WWRIL): The Result

Discretization step is incommensurate with the length of a single step of the continuous-time random walk hence discrete-time random walk is more stiff than the original basic one

Subordinators from Weierstrass walk

We considered one-sided discrete-time (forward) random walk which define a (forward) domino effects or directional autocorrelations hence power-law non-linear autocorrelations were obtained

Conclusions Discretized version of extended CTRW and some stock dynamics present at Warsaw Stock Exchange leads to similar non-linear long-term autocorrelations (even for the Gaussian regime) Extended data analysis is required Subordinates should be extended in this context to cover one-sided Weierstrass walk with varying velocity