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I would like to know what is the difference between synchrony and similarity w.r.t time series data. Upon research I get the below explanation.

"Synchrony and similarity are two different concepts in time series data analysis. Synchrony refers to the degree of temporal coordination between two or more time series, while similarity refers to the degree of resemblance between two or more time series.

For example, consider two time series that represent the stock prices of two different companies. If the stock prices of the two companies rise and fall at the same time, then the two time series are said to be synchronous 1. On the other hand, if the stock prices of the two companies are similar in shape but do not rise and fall at the same time, then the two time series are said to be similar but not synchronous "

However, I see that the methods to find both are same, for eg, Dynamic Time Warping DTW.

If I apply DTW on two equal length time series data without any lag , the output is a measure of Synchrony or similarity? or these are interchangeably used terms?

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Synchronous means that it happens at the very exact time. Similarity means that there are common patterns (potentially lagged in time). Since dtw is not enforcing focus on synchrony it is more a measure of similarity. Note that one main plus point for dtw is that you can apply it to time series which are unequally spaced. Then synchrony is hard to evaluate and you may prefer similarity

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