Discontinuous and Intermittent Signal Forecasting: A Hybrid Approach

A constructive methodology for shaping a neural model of a non-linear process, supported by results and prescriptions related to the Takens-Mañé theorem, has been recently proposed. Following this approach, the measurement of the first minimum of the mutual information of the output signal and the estimation of the embedding dimension using the method of global false nearest neighbors permit to design the input layer of a neural network or a neuro-fuzzy system to be used as predictor. In this paper we present an extension of this prediction methodology to discontinuous or intermittent signals. As the Universal function approximation theorems for neural networks and fuzzy systems requires the continuity of the function to be approximate, we apply the Singular-Spectrum Analysis (SSA) to the original signal, in order to obtain a family of time series components that are more regular than the original signal and can be, in principle, individually predicted using the mentioned methodology. On the basis of the properties of SSA, the prediction of the original series can be recovered as the sum of those of all the individual series components. We show an application of this prediction approach to a hydrology problem concerning the forecasting of daily rainfall intensity series, using a database collected for a period of 10 years from 135 stations distributed in the Tiber river basin. Chapter