Numerical demodulation of a Gaussian white noise modulated in amplitude by a deterministic volatility

The Gaussian white noise modulated in amplitude is defined as the product of a Gaussian white noise and a slowly varying signal with strictly positive values, called volatility. It is a special case of the superstatistical systems with the amplitude as the single parameter associated to the environm...

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Bibliographic Details
Published inThe European physical journal. B, Condensed matter physics Vol. 86; no. 4
Main Authors VAMOS, Călin, CRACIUN, Maria
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer-Verlag 01.04.2013
EDP Sciences
Springer
Subjects
Algorithms
Complex Systems
Condensed Matter Physics
Exact sciences and technology
Fluctuation phenomena, random processes, noise, and brownian motion
Fluid- and Aerodynamics
Noise
Physics
Physics and Astronomy
Regular Article
Solid State Physics
Statistical physics, thermodynamics, and nonlinear dynamical systems
Statistical and Nonlinear Physics
Monte Carlo methods
Gaussian noise
Deterministic model
Time series
White noise
Real time
Optimization
Demodulation
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Summary:The Gaussian white noise modulated in amplitude is defined as the product of a Gaussian white noise and a slowly varying signal with strictly positive values, called volatility. It is a special case of the superstatistical systems with the amplitude as the single parameter associated to the environment variations. If the volatility is deterministic, then the demodulation, i.e., the separation of the two components from a measured time series, can be achieved by a moving average with the averaging window length optimized by the condition that the absolute values of the estimated white noise are uncorrelated. Using Monte Carlo experiments we show that the large scale deterministic volatility can be accurately numerically determined. The artificial deterministic volatilities have a variety of shapes comparable with those occurring in real financial time series. Applied to the daily returns of the S&P500 index, the demodulation algorithm indicates that the most part of the financial volatility is deterministic.
ISSN:1434-6028
1434-6036
DOI:10.1140/epjb/e2013-31072-x