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I'm looking for some algorithms that detect statistical anomaly in time series.

For example, Google Trend automatically detects peaks of a specific search query in time, and associates those peaks with most popular news stories at that time. See this for example:

I'm looking for this kind of algorithms that detect those peaks, or just anomaly in general.

I can think of a simple way to do it, i.e. using short-run EMA minus long-run EMA as a signal. But I'm sure people have done more comprehensive analysis of tasks of this kind, and I want to learn more about that. Thanks for any pointers!

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