To properly understand the effects of non-Gaussian noise one cannot rely on the R2 score which is the second moment of the distribution. Kurtosis and skewness needs to calculated. From a more theoretical viewpoint one needs to build a model based on generalized Langevin equation (GLE) with fractional Gaussian noise having a correlator depending on Hurst exponent and solve for the full probability distribution if possible analytically. The solution will have the Hurst exponent as a fitting parameter for the market data. As you know, Hurst exponent is a measure of persistency and anti-persistency of a time series. It’s value is related to the effects of memory on the time series. That’s what we do in academia but firms may have their own fancy tools and Algorithms for HFT in which I have developed some interests lately. Thanks for the article and let me know if you are interested in my theoretical approach. May be we can learn something from each other.
There are other approaches as well using subordinated stochastic proccesses to model non-Gaussian and non-stationary time series.
