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This question is related to this one:

How to determine seasonality of a binary variable?

I have a multivariate binary time series. That is, say I have $y_1 \in$ {0, 1}$^N$, $y_2 \in$ {0, 1}$^N$

I expect that $y_1$ and $y_2$ are correlated.

In the linked question, there is a recommendation to use polynomial smoothing (and the OP has only one binary time series). But I don't understand why polynomial smoothing would be helpful.

Question: How can I determine the seasonality of each of the time series independently, and together?

StatsSorceress
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