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I'm building a model involving a few times series, let's call them A and B. I removed seasonality from A using a function with a linear trend, days of the week and statistically significant months. However, for the series B days of the week don't have any effect and different months are statistically significant.
Is there any reason why using different seasonality functions would for different time series in the same model would be a bad idea? Intuitively it shouldn't be a problem, the end product are deseasonalised time series and we don't need to care how we got them - but I'm not sure.

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Essentially the idea is to use a common seasonal filter to IDENTIFY the way y and x relate since the original cross-correlation defies analysis due to auto-correlative structure. The reason for the common filter is to not distort the IDENTIFICATION of the underlying predictive effect/model between the two original series. .

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  • $\begingroup$ I don't think I understand. So what you're saying is that I shouldn't use different seasonalities, because then I won't be able to identify the relation between x and y? Why is that the case? $\endgroup$ – Paula Aug 8 '17 at 14:49
  • $\begingroup$ To clarify we make X and Y stationary by applying the appropriate differencing operator which MIGHT BE NOT THE SAME . After this step then build and ARMA model for the stationary X use use that on the stationary Y . You now have two new series to cross-correlate to IDENTIFY the relationship between the original Y and X $\endgroup$ – IrishStat Aug 8 '17 at 14:59

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