Parameter estimation and forecasting for multiplicative log-normal cascades
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comunitat-uji-handle2:10234/8643
comunitat-uji-handle3:10234/8644
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Título
Parameter estimation and forecasting for multiplicative log-normal cascadesFecha de publicación
2012Editor
American Physical SocietyISSN
1539-3755; 1550-2376Tipo de documento
info:eu-repo/semantics/articleVersión
info:eu-repo/semantics/publishedVersionDescripción
We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian
and log normally distributed random variables yields time series with intermittent bursts of activity. Due ... [+]
We study the well-known multiplicative log-normal cascade process in which the multiplication of Gaussian
and log normally distributed random variables yields time series with intermittent bursts of activity. Due to
the nonstationarity of this process and the combinatorial nature of such a formalism, its parameters have been
estimated mostly by fitting the numerical approximation of the associated non-Gaussian probability density
function to empirical data, cf. Castaing et al. [Physica D 46, 177 (1990)]. More recently, alternative estimators
based upon various moments have been proposed by Beck [Physica D 193, 195 (2004)] and Kiyono et al.
[Phys. Rev. E 76, 041113 (2007)]. In this paper, we pursue this moment-based approach further and develop
a more rigorous generalized method of moments (GMM) estimation procedure to cope with the documented
difficulties of previous methodologies. We show that even under uncertainty about the actual number of cascade
steps, our methodology yields very reliable results for the estimated intermittency parameter. Employing the
Levinson-Durbin algorithm for best linear forecasts, we also show that estimated parameters can be used for
forecasting the evolution of the turbulent flow. We compare forecasting results from the GMM and Kiyono
et al.’s procedure via Monte Carlo simulations.We finally test the applicability of our approach by estimating the
intermittency parameter and forecasting of volatility for a sample of financial data from stock and foreign exchange
markets. [-]
Publicado en
Physical Review E, Volume 85, Issue 4, AprilDerechos de acceso
©2012 American Physical Society
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