Prediction of Long-Range Dependent Time Series Data with Performance Guarantee

Modelling and predicting long-range dependent time series data can find important and practical applications in many areas such as telecommunications and finance. In this paper, we consider Fractional Autoregressive Integrated Moving Average (FARIMA) processes which provide a unified approach to characterising both short-range and long-range dependence. We compare two linear prediction methods for predicting observations of FARIMA processes, namely the Innovations Algorithm and Kalman Filter, from the computational complexity and prediction performance point of view. We also study the problem of Prediction with Expert Advice for FARIMA and propose a simple but effective way to improve the prediction performance. Alongside the main experts (FARIMA models) we propose to use some naive methods (such as Least-Squares Regression) in order to improve the performance of the system. Experiments on Publicly available datasets show that this construction can lead to great improvements of the prediction system. We also compare our approach with a traditional method of model selection for the FARIMA model, namely Akaike Information Criterion.