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I run the two logistic regressions on different time windows (let say 1/2015 and 3/2015) and get two sets of parameters estimates. They differ a little.

Is it possible to use any statistical test to find out whether the difference between every respective two parameters (from the first model and the second model) is significant?

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The easiest way is to make sure that both months are in the same dataset (one "stacked" on top of the other) with a variable representing from which month that observation is. Than you estimate one model with interaction effects between month and all your other variables. The significant test reported after each of these interaction effects represent the test whether that coefficient differs between the months and you can create a wald or likelihood ratio test to test whether all coefficients are equal between months

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