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I am having some issues explaining to [non-statistician] people that it is natural to revise the parameters of a time series (ARIMA) model if you update the model with new data (add new actual values and move the forecasting point forward).

I say: The model is predicting new values of the series based on recent and older values in the series. If I have new data points and wish to forecast from time t2 rather than point t1 (t2 > t1) then I have to update the model with data between t1 and t2, otherwise I am really forecasting from t1. This is natural for time series.

They say: Your model coefficients have changed value, therefore you have developed a new model. You should keep the coefficients the same even with the new data.

The reason for this debate is that I was instructed not to build a new model. In their opinion, I have built a new model. In my opinion, I have not. Semantics aside, I have three main questions:

(1) Am I wrong? I freely admit that the model may no longer be the "best" model: whether it is the best or most suitable is not at issue. Fundamentally, the question is about when a model should constitute a "new" model.

(2) Is there a practical, not-fundamentally-flawed way to do what they ask, namely to use the time series model with more recent data without changing the coefficients? The only ways I can think of are: (a) just forecast from the original point but use actual data where actual data exists, and (b) chop out the time between t1 and t2, so that the forecast period begins at t1. (I should point out that this is technically an ARIMAX model because I use a forecasted macroeconomic variable as an input.)

(3) Assuming I am not wrong, does anyone have a source that might help explain time series to people who know zero statistics.

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  • $\begingroup$ In my understanding, the updated (only coefficient values changed) model is a new or another model. But it is not new kind or type of model. It is still a semantic question, so "model has changed" is vague; it's better to be specific: either "model refreshed its parameters" or "type of model changed". In time-series, one usually wants the model to remain a good forecaster for considerable time without any update of parameter values; but this wish is often unrealistic. $\endgroup$ – ttnphns May 1 '13 at 4:34
  • $\begingroup$ I must admit I get a bit confused myself. Typically with an exponential smoothing model you would not re-estimate alpha (in fact, with a short time series you might not estimate it in the first place, just "borrow" an alpha from a similar series). Yet with ARIMA models "there are no easy ways to update the parameters of an ARIMA model as new data become available, as there are in some smoothing methods." (Hanke and Wichern, Business Forecasting, 9th ed. p. 444) QUESTION: What about ARIMA models that map to smoothing models, e.g. (0,1,1) without constant and single exponential smoothing? $\endgroup$ – zbicyclist May 2 '13 at 1:28
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The question you raise is quite important. WE have implemented the CHOW Test for constancy of parameters in order to test the hypothesis that the parameters haven't changed significantly at one or more points in time. If we detect a significant change then we can then use the most recent data set to develop a new model. This test requires ( at least for us who know time series ) that any anamolous data points have been rectified/corrected via Intervention Detection procedures ( see R. Tsay's work ). If you want to pursue this topic please feel free to contact me off line and I will try and help you.

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