Volume 69, Number 6, March 2005
|Page(s)||893 - 899|
|Published online||18 February 2005|
Bridging a paradigmatic financial model and nonextensive entropy
Centro Brasileiro de Pesquisas Físicas - Rua Dr. Xavier Sigaud 150 22290-180, Rio de Janeiro-RJ, Brazil
2 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
Accepted: 17 January 2005
Engle's ARCH algorithm is a generator of stochastic time series for financial returns (and similar quantities) characterised by a time-dependent variance. It involves a memory parameter b ( corresponds to no memory), and a noise currently chosen to be Gaussian. We assume here a generalised noise, namely qn-Gaussian, characterised by an index ( recovers the Gaussian case, and corresponds to tailed distributions). Supported by the recently introduced concept of superstatistics, we match the second and fourth moments of ARCH return distribution with those associated with the q-Gaussian distribution obtained through optimisation of the entropy , basis of nonextensive statistical mechanics. The outcome is an analytic distribution for returns, where a unique corresponds to each pair (q=qn if ). This distribution is compared with numerical results and appears to be remarkably precise. This system constitutes a simple, low-dimensional, dynamical mechanism which accommodates well within the current nonextensive framework.
PACS: 05.90.+m – Other topics in statistical physics, thermodynamics, and nonlinear dynamical systems / 05.40.-a – Fluctuation phenomena, random processes, noise, and Brownian motion / 89.65.Gh – Economics; econophysics, financial markets, business and management
© EDP Sciences, 2005
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.