Abstract
The problem of comparison of several multivariate time series via their spectral properties is discussed. A pairwise comparison between two independent multivariate stationary time series via a likelihood ratio test based on the estimated cross-spectra of the series yields a quasi-distance between the series. A hierarchical clustering algorithm is then employed to compare several time series given the quasi-distance matrix. For use in situations where components of the multivariate time series are measured in different units of scale, a modified quasi-distance based on a profile likelihood based estimation of the scale parameter is described. The approach is illustrated using simulated data and data on daily temperatures and precipitations at multiple locations. A comparison between hierarchical clustering based on the likelihood ratio test quasi-distance and a quasi-distance described in Kakizawa et al. (J Am Stat Assoc 93:328–340, 1998) is interesting.
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Ravishanker, N., Hosking, J.R.M. & Mukhopadhyay, J. Spectrum-Based Comparison of Stationary Multivariate Time Series. Methodol Comput Appl Probab 12, 749–762 (2010). https://doi.org/10.1007/s11009-010-9180-0
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DOI: https://doi.org/10.1007/s11009-010-9180-0