  Financial time series exhibit a number of interesting properties that are
difficult to explain with simple models. These properties include fat-tails in
the distribution of price fluctuations (or returns) that are slowly removed at
longer timescales, strong autocorrelations in absolute returns but zero
autocorrelation in returns themselves, and multifractal scaling. Although the
underlying cause of these features is unknown, there is growing evidence they
originate in the behavior of volatility, i.e., in the behavior of the magnitude
of price fluctuations. In this paper, we posit a feedback mechanism for
volatility that closely reproduces the non-trivial properties of empirical
prices. The model is parsimonious, contains only two parameters that are easily
estimated, fits empirical data better than standard models, and can be grounded
in a straightforward framework where volatility fluctuations are driven by the
estimation error of an exogenous Poisson rate.
