A Test for Nonlinearity of Time Series with Infinite Variance

A heavy tailed time series that can be represented as an infinite moving average has the property that the sample autocorrelation function (ACF) at lag h converges in probability to a constant ρ(h), although the mathematical correlation typically does not exist. For many nonlinear heavy tailed models, however, the sample ACF at lag h converges in distribution to a nondegenerate random variable. In this paper, a test for (non)linearity of a given infinite variance time series is constructed, based on subsample stability of the sample ACF. The test is applied to several real and simulated datasets.