Clustering Time Series Based on Forecast Distributions Using Kullback-Leibler Divergence

One of the key tasks in time series data mining is to cluster time series. However, traditional clustering methods focus on the similarity of time series patterns in past time periods. In many cases such as retail sales, we would prefer to cluster based on the future forecast values. In this paper, we show an approach to cluster forecasts or forecast time series patterns based on the Kullback-Leibler divergences among the forecast densities. We use the same normality assumption for error terms as used in the calculation of forecast confidence intervals from the forecast model. So the method does not require any additional computation to obtain the forecast densities for the Kullback-Leibler divergences. This makes our approach suitable for mining very large sets of time series. A simulation study and two real data sets are used to evaluate and illustrate our method. It is shown that using the Kullback-Leibler divergence results in better clustering when there is a degree of uncertainty in the forecasts.