Leitura do dia - Comparison of time series with unequal length

Comparison of time series with unequal length

Jorge Caiado Nuno Crato and Daniel Peña

Department of Economics and Management, School of Business Administration,
Polytechnic Institute of Setubal, Campus do IPS, Estefanilha, 2914-503 Setúbal,
Portugal. Tel.: +351 265 709 438. Fax: +351 265 709 301. E-mail: jcaiado@esce.ips.pt
Department of Mathematics, School of Economics and Business, Technical University
of Lisbon, Rua do Quelhas 6, 1200-781 Lisboa, Portugal. Tel.: +351 213 925 846.
E-mail: ncrato@iseg.utl.pt
Department of Statistics, Universidad Carlos III de Madrid, Calle Madrid 126, 28903
Getafe, Spain. Tel.: +34 916 249 806. Fax.: +34 916 249 849. E-mail:
dpena@est-econ.uc3m.es

Abstract: This paper deals with classification 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 different lengths and consequently that the periodograms compared are calculated at different 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: Classification; Cluster analysis; Euclidean metric; Periodogram; Spectral
analysis; Time series.


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