On Surrogate Data Testing for Linearity based on the Periodogram

TL;DR

This paper critiques existing surrogate data tests based on the periodogram for linearity, revealing their shortcomings and proposing an improved method grounded in linear system theory.

Contribution

It identifies flaws in current periodogram-based tests and introduces a new procedure to correctly determine the test statistic distribution for linearity testing.

Findings

Current tests often mis-specify the test statistic.

Proposed method provides a more accurate distribution of the test statistic.

Discussion of limitations and potential issues of the new approach.

Abstract

The method of surrogate data is a tool to test whether data were generated by some class of model. Tests based on the periodogram have been proposed to decide if linear systems driven by Gaussian noise could have generated a sample time series. We show that this procedure based on the periodogram, in general, misspecifies the test statistic. Based on the theory of linear systems we suggest an alternative procedure to obtain the correct distribution of the test statistic and discuss problems of this approach.