Out-of-Sample Forecast Performance as a Test for Nonlinearity in Time Series

Abstract

This article uses a local-information, near-neighbor forecasting methodology as a prediction test for evidence of a noisy, chaotic data-generating process underlying the Divisia monetary-aggregate series. Using a nonparametric method known to perform well with low-dimensional chaotic processes infected by noise, accompanied by a robust test of forecast performance evaluation, we compare out-of-sample forecasting accuracy from the local-information method to forecasting accuracy from the best fitting global linear model. Our results fail to substantiate previous claims for determinism in the Divisia monetary-aggregate series because the degree of forecast improvement obtained by the local-information method is not consistent with the hypothesis of a low-dimensional attractor underlying the Divisia data.