We discuss a model for simulating a long-time memory in time series characterized in addition by a stochastic variance. The model is based on a combination of fractional Brownian motion (FBM) concepts, for dealing with the long-time memory, with an autoregressive scheme with conditional heteroskedasticity (ARCH), responsible for the stochastic variance of the series, and is denoted as FBMARCH. Unlike well-known fractionally integrated autoregressive models, FBMARCH admits finite second moments. The resulting probability distribution functions have power-law tails with exponents similar to ARCH models. This idea is applied to the description of long-time autocorrelations of absolute returns ubiquitously observed in stock markets. © 2008 World Scientific Publishing Company.

Roman, H., Porto, M. (2008). Fractional Brownian motion with stochastic variance: Modeling absolute returns in stock markets. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 19(8), 1221-1242 [10.1142/S0129183108012820].

Fractional Brownian motion with stochastic variance: Modeling absolute returns in stock markets

Roman H. E.;
2008

Abstract

We discuss a model for simulating a long-time memory in time series characterized in addition by a stochastic variance. The model is based on a combination of fractional Brownian motion (FBM) concepts, for dealing with the long-time memory, with an autoregressive scheme with conditional heteroskedasticity (ARCH), responsible for the stochastic variance of the series, and is denoted as FBMARCH. Unlike well-known fractionally integrated autoregressive models, FBMARCH admits finite second moments. The resulting probability distribution functions have power-law tails with exponents similar to ARCH models. This idea is applied to the description of long-time autocorrelations of absolute returns ubiquitously observed in stock markets. © 2008 World Scientific Publishing Company.
Articolo in rivista - Articolo scientifico
Fractional Brownian motion; Stochastic variance; Stock markets
English
2008
19
8
1221
1242
none
Roman, H., Porto, M. (2008). Fractional Brownian motion with stochastic variance: Modeling absolute returns in stock markets. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 19(8), 1221-1242 [10.1142/S0129183108012820].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/326543
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