On the connection between ARCH time series and non-extensive statistical mechanics

Sı́lvio M. Duarte Queirós

Physica A: Statistical Mechanics and its Applications, 2004, vol. 344, issue 3, 619-625

Abstract: The ARCH(1) is a generator of stochastic discrete time series, {εt}, widely used in finance and characterised by conditional time-varying (and correlated) second-order moment. It involves a parameter, β and a noise, η. In this work one presents, through an analytical result, that ARCH(1) stationary distributions are well approached by the distributions that maximise the entropy, Sq=1−∫[p(x)]qdx1−q. Using the generalised Kullback–Leibler relative entropy, Iq, one also quantifies the degree of dependence between variables εt and εt′ and shows that the degree of dependence increases with parameter β.

Keywords: Econophysics; Nonextensive statistical mechanics (search for similar items in EconPapers)
Date: 2004
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:phsmap:v:344:y:2004:i:3:p:619-625

DOI: 10.1016/j.physa.2004.06.041

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