Random Effects Mixture Models for Clustering Time Series
Min Tsao
Department of Mathematics & Statistics
University of Victoria
Abstract
In this talk, I discuss a new mixture model based clustering method for a
large collection of long time series. This research was motivated by a data
set of load series, long time series of hourly rates of electricity consumption
of individual customers, from BC Hydro, a public utility company in
Vancouver, British Columbia, Canada.
For purposes such as rate setting and long-term capacity planning, utility
companies such as BC Hydro are interested in dividing their customers into
homogeneous groups or clusters in terms of their electricity demand profiles
as represented by the load series. There are two technical difficulties for
clustering long time series such as the load series: firstly, they are of very
high dimensions and secondly they may have complicated but important
covariance structures. Existing methods for cluster analysis are unable to
handle these difficulties, and I propose a random effects mixture model
based method which is particularly effective for clustering such long time
series. The random effects mixture models are based on a hierarchical model
for individual components. They employ highly flexible antedependence
models for the covariance of the time series. I discuss the construction of
such mixture models, the estimation of model parameters and the application
of the estimated models for clustering analysis.
This is a typical example of an “application driven’’ research in statistics in
the sense that a statistical method was developed to solve a specific problem
arising from the industry.