1. A computer-implemented system for forecasting realized volatility via wavelets and non-linear dynamics, the system comprising: a computing device comprising one or more physical processors configured to: compute a volatility time series that includes daily volatility values associated with a security over a previous time period; decompose the volatility time series into a wavelet series, wherein the wavelet series decomposed from the volatility time series includes multiple wavelets that can be summed to reproduce the volatility time series; discover a time delay value, a Theiler value, and an embedding dimension value associated with each wavelet in the wavelet series; use the discovered time delay value and the discovered embedding dimension value to calculate maximum likelihood estimators associated with an autoregressive integrated moving average model and project volatility values associated with each wavelet in the wavelet series from the maximum likelihood estimators; and sum the projected volatility values associated with each wavelet in the wavelet series to produce a volatility prediction associated with the security.