A 2-phase prediction of a non-stationary time-series by Taylor series and reinforcement learning

Prediction of a non-stationary time-series is hard as the frequency components and their amplitudes in the series vary randomly over time. This paper proposes a 2-phase approach for prediction of such non-stationary time-series. The first phase employs Taylor series to approximately predict the next time-point value in the series from its current and last two preceding sample values. The Taylor series based prediction, however, presumes that the time-series is locally stationary. The second phase employs reinforcement learning to refine the Taylor series based prediction further, particularly at the juncture of structural changes in the time-series. The reinforcement learning based prediction is realized with the help of an adaptive probabilistic learning matrix that evolves to encode the mapping between current prediction error and the error-compensation for the next sample. On convergence of the matrix, the saved probabilities are used to determine the error-compensation for the next sample from the estimated error at the current sample. The additive error-compensation is then utilized to rectify the results of prediction obtained by Taylor series. Experiments undertaken confirm that the proposed 2-phase prediction outperforms the state-of-the-art prediction techniques by a significant margin of prediction accuracy.