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

## Abstract

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.

## Authors

Călin Vamoş
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

Maria Crăciun
Tiberiu Popoviciu Institute of Numerical Analysis, Romanian Academy

## Keywords

Statistical and Nonlinear Physics; computational methods; superstatistics; volatility; artificial time series; Monte Carlo methods

## Paper coordinates

C. Vamoş, M. Crăciun, Numerical demodulation of a Gaussian white noise modulated in amplitude by a deterministic volatility, Eur. Phys. J. B (2013) 86: 166.
10.1140/epjb/e2013-31072-x

## References

see the expansion block below.

## PDF

##### Journal

The European Physical Journal B

Springer-Verlag

1434-6028

1434-6036