New Zealand Statistical Association 2024 Conference

Ciprian Doru Giurcăneanu

University of Auckland

Dissimilarity measures for time series

This is joint work with Miaotian Li

The problem of measuring the dissimilarity between time series has been discussed in numerous works. It has risen to prominence during recent years when an impressive amount of time series data became available. Various classifications of the existing methods have been proposed, but for the sake of simplicity, we consider the classification that is based on the domain where the dissimilarity is assessed: time domain, frequency domain or cepstrum domain. It is interesting that the cepstral dissimilarity measures are well known in computer science, signal processing and control engineering, but they are less known in statistics. This motivates us to focus on the formulas of the metrics that involve the cepstral coefficients. There are empirical studies which show that, for example, the clustering of time series improves when some of the cepstral coefficients are replaced with zeros in the formulas mentioned above. In this talk, we present principled methods for cepstral nulling and assess their impact on the evaluation of the cepstral metrics. The presentation encompasses novel theoretical results that are illustrated via numerical examples.