A computational bootstrap procedure to compare two dependent time series

ABSTRACT

It is an important problem to compare two time series in many applications. In this paper, a computational bootstrap procedure is proposed to test if two dependent stationary time series have the same autocovariance structures. The blocks of blocks bootstrap on bivariate time series is employed to estimate the covariance matrix which is necessary in order to construct the proposed test statistic. Without much additional effort, the bootstrap critical values can also be computed as a byproduct from the same bootstrap procedure. The asymptotic distribution of the test statistic under the null hypothesis is obtained. A simulation study is conducted to examine the finite sample performance of the test. The simulation results show that the proposed procedure with the bootstrap critical values performs well empirically and is especially useful when time series are short and non-normal. The proposed test is applied to an analysis of a real data set to understand the relationship between the input and output signals of a chemical process.

KEYWORDS:

• Autocorrelation
• blocks of blocks
• order selection test
• spectral density

Acknowledgments

The authors wish to thank the Associate Editor and a referee for their helpful comments and suggestions that have led to a much improved version of this paper.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This research was supported in part by the Simons Foundation Mathematics and Physical Sciences - Collaboration Grants for Mathematicians Program Award 499650. Li Cai would like to thank the China Scholarship Council (CSC) for providing the financial support to visit Texas A&M University.