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 an interactive HTML5 applet, using which one can reproduce
burst statistics of certain stochastic model.