Time series obtained by solving non-linear stochastic models exhibit rather interesting statistical properties. On Physics of Risk we have already discussed some of these models 1, 2 (ex. stochastic model of return, herding model of financial markets), which are able to reproduce statistical properties of high frequency return (namely spectral density and probability distribution).
In statistical sense model and financial market behavior might be studied in many different manners. One may study probability distributions, moments, spectral densities, autocorrelations and etc., using each of them to obtain vital information on the statistical and dynamical properties of the studied system. It is important to note that new useful information might be provided by the statistical indicators, which are related to the previously used indicators in unambiguous manner. One may also introduce new variables describing system itself or its time series.
There is a group of such variables, which is closely related to the estimation of risk, known as burst statistics 3, 4. In this text we will discuss these variables and their statistical properties. At the end of the text we also present interactive java applet, using which one can reproduce burst statistics of certain stochastic model. Continue reading “Brust statistics in non-linear stochastic models” »