Stable processes in econometric time series: Are prices made out of noise?

If the rules that regulate a market allow speculation then prices in that market become volatile. It is possible to model the fluctuations in these prices as random variables. The empirical distributions of these random variables are unusual; they are distinctly non-Gaussian. They belong to a class of distributions called Levy stable distributions and have paradoxical properties. The processes that generate these unusual distributions must also have special properties. One possible hypothesis is that markets are self organised critical systems. The discussion provides a brief history of these ideas and identifies some of the unsolved problems in the application of the theory of the Levy process to economics.