Artificial neural network forecasting of nonlinear Markov processes

Abstract

I assessed the performance characteristics of the feed-forward artificial neural network (ANN) as a first-order nonlinear Markov modelling technique. The ability to recover the underlying structure of five synthetic random time series was first tested. The method was then applied to an observed geophysical time series, and the results were compared against external empirical constraints and a simple representation of the underlying physics. The Monte Carlo experiments suggested that the ANN–Markov technique: (i) yields good prediction skill; (ii) in general, accurately retrieves the form of the iterative mapping, even for extremely noisy data; (iii) accomplishes the foregoing without any need to consider or adjust for the distributional characteristics of the data or driving noise; and (iv) accurately estimates the distribution of the strictly stochastic signal component. Application to a historical river-flow record again showed good forecast skill. Moreover, the robustness, flexibility, and simplicity of the method permitted easy identification of the fundamental nonlinear physical dynamics of this environmental system directly from the time series data, perhaps belying the common perception of ANNs as a strictly black-box prediction technique. The ANN–Markov technique may thus serve as a valuable data-driven tool for guiding the development of both process-based and parameteric statistical models. The lack of specific distributional assumptions and requirements notwithstanding, it was also found that manual distributional transformations may permit the method to be tuned to particular applications by emphasizing or de-emphasizing certain features of the data. Drawbacks to the method include substantial data-set length requirements, a general limitation of ANNs, as well as an inconsistent but potentially troubling tendency to partially imprint the form of the ANN activation function upon the estimated recursion relationship. PACS Nos.: 02.50.Ga, 05.10.–a, 05.45.Tp, 07.05.Mh, 02.50.Ey, 92.40.Fb