Further Results on Lund's Statistic for Identifying Cluster in a Circular Data Set with Application to Time Series

Abstract

This note investigates the capability of Lund's method in assessing the correct number of clusters and the appropriate group membership for directional data. My simulation results indicate that both tasks are performed satisfactorily if there is an equal number of points in each cluster. Otherwise, Lund's statistic identifies only large clusters. An application is also presented as far as clustering time series, according to their phase spectrum, is concerned. If the phase measurements for a given frequency of interest, that are circular data, are taken to represent each time series, then Lund's method is able to correctly identify their cluster structure.

Keywords:

• Cluster analysis for directional data
• Lund's statistic
• Genetic algorithms
• Time series
• Spectral density function