Formulation of a Nonlinear Predictor

Abstract

The classical linear prediction problem has received much attention both theoretically and empirically in the past few decades and a great deal is known about it (though there remain important open questions). See, e.g., discussions and lists of references in Parzen (1969) and Rozanov (1967). The nonlinear prediction problem is much more difficult and much less is known about it. See, e.g., Masani and Wiener (1959). We reduce a certain type of nonlinear prediction problem to the multiple linear prediction problem, see Wiener (1956) and Van Ness (1966). We can then take advantage of theoretical results and computational techniques which have been developed to solve the linear problem. The methods are applied to both real and generated data using an iterative method due to Parzen and fast Fourier transform techniques on a small computer (an IBM 1130).