New methodological contributions in time series clustering

Abstract

his thesis presents new procedures to address the analysis cluster of time series. First of all a two-stage procedure based on comparing frequencies and magnitudes of the absolute maxima of the spectral densities is proposed. Assuming that the clustering purpose is to group series according to the underlying dependence structures, a detailed study of the behavior in clustering of a dissimilarity based on comparing estimated quantile autocovariance functions (QAF) is also carried out. A prediction-based resampling algorithm proposed by Dudoit and Fridlyand is adjusted to select the optimal number of clusters. The asymptotic behavior of the sample quantile autocovariances is studied and an algorithm to determine optimal combinations of lags and pairs of quantile levels to perform clustering is introduced. The proposed metric is used to perform hard and soft partitioning-based clustering. First, a broad simulation study examines the behavior of the proposed metric in crisp clustering using hierarchkal and PAM procedure. Then, a novel fuzzy C-mcdoids algorithm based on the QAF-dissimilarity is proposed. Three different robust versions of this fuzzy algorithm are also presented to deal with data containing outlier time series. Finally, other ways of soft clustering analysis are explored, namely probabilistic 0-clustering and clustering based on mixture models.