I am coming from a genomics background, so when I read about sliding window on time series data, I think about sliding window approach on regions of genome sequences.
The ultimate point of doing this clustering is to find repetitive sub-sequences in the series. This is also something we do commonly in the genomics field (repeatmasker/repeatmodeler software for example).
Something we can look at in genomes is a "k-mer coverage". A k-mer is just a k-lengthed sub-sequence (A,T,G,C), analogous to a k-length sub-sequence of a time series.
By scanning the genome, we can tally up how many times a k-mer appears in the genome. With this tally, we can determine a k-mer coverage for a region on the genome. This gives us an idea how many times we see this same region on the rest of the genome.
Maybe this approach can be adapted somehow? The only problem is that in genomics, we have four discrete classes (A,G,T,C), making finding exact matching relatively easy. In time-series, we have continuous data, making finding matches a lot tougher to do and define.