Eur. Phys. J. B 64, 607-614 (2008)
https://doi.org/10.1140/epjb/e2008-00244-4

The non-random walk of stock prices: the long-term correlation between signs and sizes

¹ Santa Fe Institute, 1399 Hyde Park Road, Santa Fe, NM 87501, USA
² LUISS Guido Carli, Viale Pola 12, 00198 Roma, Italy
³ Dipartimento di Fisica e Tecnologie Relative, Viale delle Scienze 90128 Palermo, Italy

Corresponding author: ^a glaspada@luiss.it

Received: 27 November 2007
Revised: 29 April 2008
Published online: 25 June 2008

Abstract

We investigate the random walk of prices by developing a simple model relating the properties of the signs and absolute values of individual price changes to the diffusion rate (volatility) of prices at longer time scales. We show that this benchmark model is unable to reproduce the diffusion properties of real prices. Specifically, we find that for one hour intervals this model consistently over-predicts the volatility of real price series by about , and that this effect becomes stronger as the length of the intervals increases. By selectively shuffling some components of the data while preserving others we are able to show that this discrepancy is caused by a subtle but long-range non-contemporaneous correlation between the signs and sizes of individual returns. We conjecture that this is related to the long-memory of transaction signs and the need to enforce market efficiency.