Testing time series linearity via goodness-of-fit methods

Abstract

We consider the problem of testing time series linearity. Existing time domain and spectral domain tests are discussed. A new approach relying on spectral domain properties of a time series under the null hypothesis of linearity is suggested. Under linearity, the normalized bispectral density function Z is a constant. Under the null hypothesis of linearity, properly constructed estimators of 2| Z | 2 have a non-central chi-squared distribution with two degrees of freedom and constant non-centrality parameter 2| Z | 2 . If the null hypothesis is false, the non-centrality parameter is non-constant. This suggests goodness-of-fit tests might be effective in diagnosing non-linearity. Several approaches are introduced.