Model Identification and Data Analysis

3Prediction

3.1 Introduction

We can now tackle the problem posed at the beginning of the book, namely the problem of estimating the future value of a signal from the observation of its past. We shall indicate with the symbol or, simply, as , the optimal predictor at time , given the observations up to time . Integer is the prediction horizon.

The derivation is based on the fundamental assumption that the process is stationary, so that we can rely on the theory seen in Chapter 1. To be precise, we assume to know the dynamical representation of the process as the output of a system with a given transfer function fed by white noise, as discussed in Section 1.16. The derivation of such representation from experimental data is postponed to the subsequent chapter on identification.

The prediction method we present is mainly owed to the studies of two masters of the past century, Andrey Kolmogorov ...