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I'm having some difficulty applying concepts I'm learning about Transfer Functions into useful equations. I've read a couple of the related posts, and perhaps I need to learn by example... I have two examples below, which are output from made-up data in SPSS Time Series modeler. As I am simply trying to learn the mechanics of Time Series, and how the equations work, I would like it if someone could walk me through translating the output into an equation I could understand and manipulate in Excel. I understand that SPSS produces the forecasts automatically, but I'm trying to better understand the mechanics. Any help is appreciated.

Here is one example, with one predictor... enter image description here

This is another example, with 2 predictors. enter image description here

SD_Data_Scientist
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1 Answers1

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One of the thorniest issues in transfer function modelling is the lack of clarity when the results are presented. AUTOBOX takes the final model and expresses the forecast in "regression-like terms) i.e. an explicit equation showing an understandable ( to the layman ) presentation. This is a uniqueenter image description here feature and is referred to as RHSIDE.TXT for your second example.

For your first example ..using data you had provided in ARIMA with independent variables I obtained for RHSIDE.TXT a presentation that expressed the forecast in terms of the Y and the one input and the history of errors. This was obtained by multiplying through by the denominator structure for X where VAR1 is your APPLES.

enter image description here

I suggest that you ask SPSS to provide this useful report for you and others struggling with understanding the model in simple terms. Note that the re-expression can get "complicated" with either denominator transfer function structure structure or arima model structure ... which perhaps is why SPSS doesn't present it.

IrishStat
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  • What I'm looking for is a bit of a worked example, something that I could manage in Excel that will help illustrate how it works - I suppose similar to putting a logistic regression equation in excel and modifying the values of the significant predictors. I understand Time Series is not logistic regression. However, I think it would be helpful to students who are trying to learn these concepts, like me. In the example I provided, It indicates that Apples and Bananas are significant predictors of "Sales." So, what happens to the forecast for different values of apples and bananas? – SD_Data_Scientist Sep 25 '18 at 15:16
  • Updating comments to clarify - I'm looking to port the SPSS output of parameter estimates into Excel and manually compute the ARIMAX forecasts. It seems that is possible, at least Rob Hyndman's online book seems to suggest it. https://otexts.org/fpp2/lagged-predictors.html

    I located another stackexchange post discussing this topic. https://stats.stackexchange.com/questions/191413/how-can-i-transfer-an-armax-model-in-excel-in-order-to-forecast-future-values.

    I would be interested to hear from anyone who has had success manually calculating ARIMX forecasts from SPSS parameter estimates

     – SD_Data_Scientist Sep 27 '18 at 15:10
  • In a very specific case i.e .IF no denominator structure in the transfer function i.e. no dynamc structure AND no autoregressive structure in the ARIMA component AND no differencing of the output series one can use the estimated coefficients in an excel file to compute the forecast ...... OTHERWISE not so much. – IrishStat Sep 27 '18 at 19:06
  • tu for the acceptance of my reflections . – IrishStat Oct 12 '18 at 20:09