Comparing spectral densities of stationary time series with unequal sample sizes

2012/07/24 by Philip Preuß, Preuß, Philip, Thimo Hildebrandt +1
Computer Science · Economics, Econometrics and Finance · Mathematics · #Applications (stat.AP) #Complex Systems and Time Series Analysis #FOS: Computer and information sciences #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistics Theory (math.ST) #Time Series Analysis and Forecasting #math.ST #stat.AP #stat.TH

paper · pdf · doi:10.48550/arxiv.1207.5659

arxiv created 2012/07/24 · openalex publication_date 2012/07/24 · arxiv updated 2012/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

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