A CASCADE FORM PREDICTOR OF NEURAL AND FIR FILTERS AND ITS MINIMUM SIZE ESTIMATION BASED ON NONLINEARITY ANALYSIS OF TIME-SERIES

Time series prediction is very important technology in a wide variety of fields. The actual time series contains both linear and nonlinear p roperties. The amplitude of the time series to be predicted is usually continuous value. For these reasons, we combine nonlinear and linear predictors in a cascade form. The nonlinear prediction problem is redu ced to a pattern classification. A set of the past samples x(n-1),..., x(n-N) is transformed into the output, which is the prediction of the next coming sample x(n). So, we employ a multi-layer neural network wi th a sigmoidal hidden layer and a single linear output neuron for the nonlinear prediction. II is called a Nonlinear Sub-Predictor (NSP). Th e NSP is trained by the supervised learning algorithm using the sample rc(n) as a target. However, it is rather difficult to generate the co ntinuous amplitude and to predict linear property. So, we employ a lin ear predictor after the NSP. An FIR filter is used for this purpose, w hich is called a Linear Sub-Predictor(LSP). The LSP is trained by the supervised learning algorithm using also x(n) as a target. In order to estimate the minimum size of the proposed predictor, we analyze the n onlinearity of the time series of interest. The prediction is equal to mapping a set of past samples to the next coming sample. The multi-la yer neural network is good for this kind of pattern mapping. Still, di fficult mappings may exist when several sets of very similar patterns are mapped onto very different samples. The degree of difficulty of th e mapping is closely related to the nonlinearity. The necessary number of the past samples used for prediction is determined by this nonline arity. The difficult mapping requires a large number of the past sampl es. Computer simulations using the sunspot data and the artificially g enerated discrete amplitude data have demonstrated the efficiency of t he proposed predictor and the nonlinearity analysis.