Multivariate Local Linear Regression in the Prediction of ARFIMA Processes

Long memory processes are widely used in many scientific fields, such as bioinformatics, economics and engineering. In this paper, we use the multivariate local linear estimator to predict the ARFIMA(p,d,q) processes. Using the C-C method to choose the appropriate delay time and the embedding dimension, we reconstruct the time series and use multivariate local linear estimator to directly predict ARFIMA processes, we also obtain the MSE of this estimator, which is not same as for short memory or i.i.d data. Simulation results show that this estimator is better than some parameter methods, such as the GPH and banded MLE.