A Nearest Neighbor Approach to Forecast Nonlinear Time Series

Abstract

In this chapter, we will concentrate on a forecasting algorithm suggested by Sugihara, Grenfell and May [1990], based on previous work of Farmer and Sidorowich [1987], to improve the short term prediction of nonlinear chaotic processes. The idea underlying their forecasting algorithm is as follows: For a nonlinear low-dimensional process, a state space reconstruction of the observed time series exhibits “spatial” correlation, which can be exploited to improve short term forecasts by means of local linear approximations. Still, the important question of evaluating the forecast perfomance is very much an open one, if the researcher is confronted with data that are additionally disturbed by stochastic noise. To account for this problem, a nonparametric test to accompany the algorithm is suggested here. To demonstrate its practical use, the methodology is applied to the observed agricultural price series. It is found that the short term predictability of the best fitting linear model can be improved upon significantly by this method.