Second-order moving average and scaling of stochastic time series
Metronome-Ricerca sui Mercati Finanziari, via Bogino 23, 10123 Torino, Italy
2 Istituto Nazionale per la Fisica della Materia (INFM) and Dipartimento di Fisica, Politecnico di Torino, Corso Duca degli Abruzzi 24, 10129 Torino, Italy
Corresponding author: a email@example.com
Published online: 15 May 2002
Long-range correlation properties of stochastic time series y(i) have been investigated by introducing the function , where is the moving average of y(i), defined as , n the moving average window and Nmax is the dimension of the stochastic series. It is shown that, using an appropriate computational procedure, the function varies as nH where H is the Hurst exponent of the series. A comparison of the power-law exponents obtained using respectively the function and the Detrended Fluctuation Analysis has been also carried out. Interesting features denoting the existence of a relationship between the scaling properties of the noisy process and the moving average filtering technique have been evidenced.
PACS: 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 05.45.Tp – Time series analysis
© EDP Sciences, Società Italiana di Fisica, Springer-Verlag, 2002