Eur. Phys. J. B 27, 197-200 (2002)
https://doi.org/10.1140/epjb/e20020150

Second-order moving average and scaling of stochastic time series

¹ 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 acarbone@polito.it

Received: 31 December 2001
Published online: 15 May 2002

Abstract

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 N_max is the dimension of the stochastic series. It is shown that, using an appropriate computational procedure, the function varies as n^H 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.