I am trying to model a multi variate time series model. (i.e. Multivariate ARIMA). The general format of the model is in the shape of a budget model like:

W(t) = f [ X(t), Y(t), Z(t), T(t) ]

were W(t) shows the jump and drop that I mentioned. There is jump and a following drop in the historical dependent variable (i.e. Output). But this record is not just on one data and records seem to persist on this behavior for a medium period (i.e. several years after jump and then a following drop). I have attached the diagram of the time series to this post. As soon as the independent variables spouse to cause or track down the jump and drop; and since I am going to make  them independent from each other. Do I have to remove the jump from the data or not?

I think changes in input variables should track or result in that jump and drop and it is not proper to remove the jump and the drop.

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