Kiel Working Papers, Kiel Institute for World Economics
No 1746:
Parameter Estimation and Forecasting for Multiplicative Lognormal Cascades
Thomas Lux Andrés E. Leövey
Abstract: We study the well-known multiplicative Lognormal cascade
process in which the multiplication of Gaussian and Lognormally distributed
random variables yields time series with intermittent bursts of activity.
Due to the non-stationarity 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 pdf to empirical
data, cf. Castaing et al. [Physica D, 46, 177 (1990)]. More recently, an
alternative estimator based upon qth order absolute moments has been
introduced by Kiyono et al. [Phys. Rev. E 76 41113 (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
Keywords: Random Lognormal cascades, GMM estimation, best linear forecasting, volatility of financial returns; (follow links to similar papers)
JEL-Codes: C20,; G12; (follow links to similar papers)
30 pages, December 2011
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