Glue time series back together

I have a long time series whose distribution I don't know. I take snapshot of a fix window at random places of the time series to get a set of equal length shorter time series. Now without the help of the longer time series, what are some of the methods that can help me glue the time series back together ? assume the set of short time series covers all points of the long one, and there are overlaps between the short time series.

• Do you have the time indices from which the "segments" were recorded? E.g. if you recorded between years 5 and 10, do you know those years are 5, 6, 7, 8, 9, 10 or would you not know if it was 5-10 or, say, 0-5, or 30-35? Oct 13 '14 at 3:01
• This does not sound like a statistical problem. Assembling a series of segments based on overlaps among them amounts to finding a Hamiltonian path (in a graph whose nodes are the segments and edges are the overlaps), a problem that is NP-complete. (The best known algorithms have computational effort that is exponential in the number of segments.) If this is a statistical problem, then please edit the question to point out what its statistical nature is.
– whuber
Oct 13 '14 at 5:41
• @whuber, your point makes the problem much clearer to me. If the action of take a window of the long time series introduces white noise to short time series, how can I compute the overlapping of the edge? Thank you Oct 13 '14 at 13:49
• I was wondering whether that might be the case. Could you please edit the question to explain how you are windowing and how such "white noise" might appear as a result? In some sense it is beginning to sound like you might have a (very interesting) probabilistic analog of the Hamiltonian path problem for an edge-weighted graph, where the objective is to find a path that visits each vertex exactly once and maximizes the sum of the weights (equal to log probabilities) of its edges.
– whuber
Oct 13 '14 at 16:10
• This is very similar to problem solved in bioinformatics of putting scanned segments of cromosomes back together ... Oct 7 '18 at 2:11