## Time series clustering based on nonparametric multidimensional forecast densities.(English)Zbl 1336.62197

Summary: A new time series clustering method based on comparing forecast densities for a sequence of $$k>1$$ consecutive horizons is proposed. The unknown $$k$$-dimensional forecast densities can be nonparametrically approximated by using bootstrap procedures that mimic the generating processes without parametric restrictions. However, the difficulty of constructing accurate kernel estimators of multivariate densities is well known. To circumvent the high dimensionality problem, the bootstrap prediction vectors are projected onto a lower-dimensional space using principal components analysis, and then the densities are estimated in this new space. Proper distances between pairs of estimated densities are computed and used to generate an initial dissimilarity matrix, and hence a standard hierarchical clustering is performed. The clustering procedure is examined via simulation and is applied to a real dataset involving electricity prices series.

### MSC:

 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62M20 Inference from stochastic processes and prediction 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62G07 Density estimation 62G09 Nonparametric statistical resampling methods 62H25 Factor analysis and principal components; correspondence analysis

### Software:

R; clusfind; TRAMO
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