A stochastic context-free grammar model for time series analysis

We propose a stochastic context-free grammar model whose structure can alternatively be viewed as a graphical model, and use it to model time series, We use the inside-outside algorithm to estimate the model parameters. We assume that the time series is a finite-order Markov process generated by our model, and develop an algorithm to forecast the conditional variance of the process. We use this algorithm to forecast the volatility of the S&P 500 index, achieving results that outperform both standard and more recent approaches.