Nowadays, a huge amount of applications exist that natively adopt a data-streaming model to represent highly dynamic phenomena. A challenging application is constituted by data from the stock market, where the stock prices are naturally modeled as data streams that fluctuate very much and remain meaningful only for short amounts of time. In this paper we present a technique to track evolving clusters of financial time series, with the aim of constructing reliable models for this highly dynamic application. In our technique the clustering over a set of time series is iterated over time through sliding windows and, at each iteration, the differences between the current clustering and the previous one are studied to determine those changes that are "significant" with respect to the application. For example, in the financial domain, if a company that has belonged to the same cluster for a certain amount of time moves to another cluster, this may be a signal of a significant change in its economical or financial situation.