Noise levels in time series subsequence data are typically very high, and properties of the noise differ from those of white noise. The proposed algorithm incorporates a continuous random-walk noise model into kernel-density-based clustering. Evaluation is done by testing to what extent the resulting clusters are predictive of the process that generated the time series. It is shown that the new algorithm not only outperforms partitioning techniques that lead to trivial and unsatisfactory results under the given quality measure, but also improves upon other density-based algorithms. The results suggest that the noise elimination properties of kernel-density-based clustering algorithms can be of significant value for the use of clustering in preprocessing of data.