On a spectral density estimator based similarity test for correlated time series
Bouni Nora, Medkour Tarek · Communication in Statistics- Theory and Methods · 2025
In this article, we present a novel method for testing the similarity of two time series by comparing their spectral density functions, without assuming independence between the series. Our hypothesis testing framework builds on a previous result that assessed the similarity of two time series using the multitaper cross-spectrum estimator at a specific frequency, where the test statistic was shown to follow a Beta distribution. By generalizing this approach, we enable comparisons without requiring prior knowledge of the covariance structure. Under the assumption of spectral similarity, the proposed test statistic is distributed as a product of beta random variables. The effectiveness of our method is demonstrated through a comprehensive simulation study. The new test is employed to evaluate whether each pair of time series for commodity price data shares the same underlying processes.