Comparing spectral densities of stationary time series with unequal sample sizes

TL;DR

This paper develops a theoretical framework for comparing spectral densities of stationary time series with unequal sample sizes, including hypothesis testing and applications to clustering financial data.

Contribution

It introduces a new testing approach for spectral density equality with proven asymptotic normality, applicable to multivariate cases and practical data clustering.

Findings

Asymptotic normality of the test statistic is established under null and alternative hypotheses.

Simulation studies demonstrate the finite sample performance of the proposed method.

Application to financial data shows effectiveness in clustering time series with different lengths.

Abstract

This paper deals with the comparison of several stationary processes with unequal sample sizes. We provide a detailed theoretical framework on the testing problem for equality of spectral densities in the bivariate case, after which the generalization of our approach to the m dimensional case and to other statistical applications (like testing for zero correlation or clustering of time series data with different length) is straightforward. We prove asymptotic normality of an appropriately standardized version of the test statistic both under the null and the alternative and investigate the finite sample properties of our method in a simulation study. Furthermore we apply our approach to cluster financial time series data with different sample length.