Comparison of time series with unequal length

Abstract

The comparison and classification of time series is an important issue in practical time series analysis. For these purposes, various methods have been proposed in the literature, but all have shortcomings, especially when the observed time series have different sample sizes. In this paper, we propose spectral domain methods for handling time series of unequal length. The methods make the spectral estimates comparable, by producing statistics at the same frequency. A first sensible approach may consist on zero-padding the shorter time series in order to increase the corresponding number of periodogram ordinates. We show that this works well provided the sample sizes are not very different, but does not give good results in case the time series lengths are very unbalanced. For this latter case, we study some periodogram-based comparison methods and construct a test. Both the methods and the test display reasonable properties for series of any lengths. Additionally and for reference, we develop a parametric comparison method. The procedures are assessed by a Monte Carlo simulation study. As an illustrative example, a periodogram method is used to compare and cluster industrial production series of some developed countries.