Forecasting Using Locally Stationary Wavelet Processes

Locally stationary wavelet (LSW) processes, built on non-decimated wavelets, can be used to analyze and forecast non-stationary time series, and they have proved useful in the analysis of financial data. In this paper we first carry out a sensitivity analysis, then propose some practical guidelines for choosing the wavelet bases for these processes. The existing forecasting algorithm is found to have no protection from outliers and a new algorithm, imposing restrictions on the predictor coefficients, is proposed. These algorithms are tested on real data. The volatility forecasting ability of LSW modeling based on our new algorithm is then discussed and is shown to be competitive with traditional GARCH models when applied to S&P500 return series