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I am working on a time series forecasting problem.As I came to know that I was not considering structural changes and seasonal dummies and was building a simple ARIMA that was causing a very poor fit. I added monthly and day dummies and provided them as exogenous variable in seasonal ARIMA (SARIMAX) ,which improved the model somewhat.

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with respect to the the ARIMA model-

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I want to ask how to add the effect of change points in ARIMAX/SARIMAX in python and I also want to understand the conceptual understanding of after adding these change points how does the cost function/parameter estimation of the of the model changes ?

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  • $\begingroup$ You say "I added monthly and day dummies and provided them as exogenous variable in seasonal ARIMA (SARIMAX) ,which improved the model somewhat." . I say "not so much" as there is no daily effect JUST day 1 and there are no level shifts in the out-of-sample so your level shifts make little sense and represent your specification for this problem. Cost function/parameter estimation is not a familiar statistical concept to me . Is it machine language speak ? $\endgroup$
    – IrishStat
    Commented Mar 20, 2019 at 16:12
  • $\begingroup$ There is an effect for JUST 2 months of the year (september & october) based upon the first 413 values. It appears that you have inserted/assumed a Jan/Feb effect $\endgroup$
    – IrishStat
    Commented Mar 20, 2019 at 17:40
  • $\begingroup$ yes, I added a dummy for each month and provided them as exogenous variable. From the first comment - yes Cost function/parameter estimation is word from machine learning ,what I wanted to ask is the how adding the effect of different change points affects the model performance for future points(test points) , like for the exogenous variables I read that there is regression model with ARMA errors. $\endgroup$
    – A.kumar
    Commented Mar 20, 2019 at 18:58
  • $\begingroup$ stats.stackexchange.com/questions/398489/… for stuff on the ARMAX model. The Model I developed for your data is an example of that $\endgroup$
    – IrishStat
    Commented Mar 20, 2019 at 19:23

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