Maximum-Entropy Scattering Models For Financial Time Series

Modeling time series with complex statistical properties such as heavy-tails, long-range dependence, and temporal asymmetries remains an open problem. In particular, financial time series exhibit such properties. Existing models suffer from serious limitations and often rely on high-order moments. We introduce a wavelet-based maximum entropy model for such random processes, based on new scattering and phase-harmonic moments. We analyze the model's performance with a synthetic multifractal random process and real-world financial time series. We show that scattering moments capture heavy tails and multifractal properties without estimating high-order moments. Further, we show that additional phase-harmonic terms capture temporal asymmetries.