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The question is pretty self-explanatory. I'm trying to compare the similarity of two time-series, in terms of the distribution of their values. I've already performed a qualitative assessment by studying histogram plots, and am aware that most statistical tests for comparing distributions require independence of samples, which is not possible in time-series data.

I used this video to understand KLD, and feel it can be used for time-series data that comes from two independent processes. I'm a beginner so I can be wrong, in that case do feel free to share more comprehensive resources from where I can study.

Thank you!

Haris Naveed
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K-L divergence could indeed be used to compare the two distributions of values. However, I usually prefer the Kolmogorov-Smirnov test, which has nice properties.

When you do that, you are taking the time out of the time series. It would not notice the relationship between these two:

1,1,2,1,2
3,3,4,3,4

but perhaps that is not what you care about.

chrishmorris
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I'm going to assume that determining whether two time series' data has the same distribution truly is the only thing that matters here, and that there's no other question being asked. You need to assume that your time series has a stationary solution. This means that despite there being potential dependence in the observations, there is a distribution that can describe any observation's potential value at any point in time (not conditioning on any other observation in the time series' value), and this distribution does not change over time. If the time series is stationary, then yes, you can compare the distribution of the two time series, via K-L or any other functional of the (empirical) distribution of the observations.

cgmil
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  • Yes, I'm already using DTW and autocorrelation plots to assess how well the temporal relationship was maintained between the true and generated time-series, I am hoping the KLD might give me more insight into how similar the two series are. So if I stationarize the two time series via differencing, I can use the KL - Divergence with no theoretical problems right? Thank you! – Haris Naveed Aug 19 '21 at 11:53