This paper proposes an online framework to characterize demand response (DR) over time. The proposed framework facilitates obtaining and updating the daily consumption patterns of customers. The essential concept of response profile class (RPC) is introduced for characterization and complemented by the measure of the variability in customer behavior. This paper uses a modified version of the incremental clustering by fast search and find of density peaks (CFSFDP) algorithm for daily profiles, considering the multivariate normal kernel density estimator and incremental forms of the Davies-Bouldin (iDB) and Xie-Beni (iXB) validity indices. Case studies conducted using real-world and simulated daily profiles of residential and commercial Chilean end-users have demonstrated how the proposed framework can continuously characterize DR. The proposed framework is proven to achieve realistic customer models for effective energy management by estimating the customer response to price signals at the distribution system operator (DSO) level.