Comparison of time series with unequal length

This paper deals with classi…cation and clustering analysis for independent time series with unequal length. A periodogram-based statistic is used to determine whether the time series at hand are generated by the same stochastic mechanism. To deal with the problem of di¤erent lengths and consequently that the periodograms compared are calculated at di¤erent Fourier frequencies, an interpolation method is proposed. This method consists of a linear interpolation of the individual periodogram ordinates at Fourier frequencies. Nonparametric and parametric test statistics are proposed to test the hypothesis that the two series are generated by the same stochastic mechanism and their random behavior under null are investigated. The performance of the methods is investigated by a Monte Carlo simulation study. As an illustrative example, the interpolated periodogram method is applied to classify industrial production indices series of European and some developed countries. Keywords: Classi…cation; Cluster analysis; Euclidean metric; Periodogram; Spectral analysis; Time series.