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I have a time series "A" and another one "B". I would like to find occurrences of "B" inside "A". Typically, "A" is much bigger (magnitude: millions of points) than "B" (magnitude: hundreds of points)

  • I don't necessarily want exact matching (obviously, since the values we deal are real numbers not, say, text) The values are preferably close, though.
  • Trends/shapes are more important than exact time matching (i.e. somehow Dynamic Time Warping could be useful)
  • With regards to the first two points, what happens if I don't care about the absolute values at all but just the shape (maybe taking a log of the values?)
  • What happens if I would like to scale the number of points to billions from millions? How to scale the system? How do I index a time series? (maybe use Mahout, Lucene, somehow?)

What's inside above parentheses are the results of my short research, not necessarilly correct. All in all, what kind of an approach should I take? What are your general suggestions/tips? I'd like to develop a system, so any practical examples/suggestions are even more welcome.

Thanks!

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    $\begingroup$ Can you provide a simple example w/ data for time-series A & B that would demonstrate what you mean? $\endgroup$
    – gung - Reinstate Monica
    Commented Jul 22, 2014 at 14:46
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    $\begingroup$ A clear and quantitative description of what it would mean for $A$ to be "close" to a subsequence of $B$ is essential. For some meanings--for instance, where "close" means strongly correlated--there are extremely efficient and effective solutions. For other meanings the problem will be impossible to solve without an exhaustive search. $\endgroup$
    – whuber ♦
    Commented Jul 22, 2014 at 15:11
  • $\begingroup$ Let's assume we're talking about temperature values: from -100 to 1000 celcius, real numbers. $\endgroup$
    – kolistivra
    Commented Jul 22, 2014 at 15:21
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    $\begingroup$ That does not clarify what it means for two time series of values to be "close". Although the question refers to "the shape," this could mean many things, especially in light of the mysterious reference to "absolute values" (which, although that has a well-defined mathematical meaning, does not seem to be what you wanted to say). $\endgroup$
    – whuber ♦
    Commented Jul 23, 2014 at 22:14

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Such a shorter series is known as motif. Think of music: a motif is a subsequence that appears at multiple times, and even in different compositions.

With Time Series Motifs you will find plenty of literature.

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