A Test for Non‐linearity of Prediction in Time Series

Abstract

A test for non-linearity of prediction in time series is suggested; the test makes use of the partial correlation between a series and its square, eliminating linear terms. The distribution of partial correlation estimates is considered both theoretically and by simulation. Extensions of the test to include partial correlations with other nonlinear functions of the observed data are suggested. The nature of optimum predictors for some particular non-linear time series is described, and the performance of the test when used with simulated non-linear series is investigated.