That was exactly my thought. Thanks for validating!

Thanks for the comment. I got my answer for the 1st question. For the 2nd one, can you please elaborate a bit and mention what does the two terms on right hand side mean? Is is possible if you can add a visual graph that exhibits this behaviour?

Thanks for the comment but this does not answer my question of how a window of 5 corresponds to a lag of 3. Also, I believe you and this Wikipedia section, are talking about Moving Average (MA) model. I am referring to the Moving Average Smoothing model which has no connection to the MA model.

Thanks for your answer. Is this what happens at the backend of an ARIMA model where we supply certain degrees of differencing a.k.a integrations?

Thanks. Also, is it fine to test logit linearity of continuous variables with the categorical predictors excluded (just for testing purposes)?

I didn't realize the interpretation is going to be different. Btw, how safe is it to build a model with assumption violated apart from becoming less generalized?