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I'm working on a time series model which predicts daily sales. The model is based on seasonal-trend decomposition by Loess, basically. (I'm using an R package similar to Prophet by facebook.)

Since the time series I want to model has large PACF for lag 1, I added 1st-order lagged variable to this stl-based model.

To summarize, my model has the following form.

Today's Sales ~ trend + seasonality + some indicator variables + Yesterday's Sales + error

This 'some indicator variables' mean dummy variables whose values are 1 when a specific kind of marketing campaign is ON, 0 when OFF.

I want to interpret the regression coefficients of these dummy variables as the average effect of a marketing campaign category on Sales.

Then there arises a problem. The coefficients are much smaller when I put Yesterday's Sales to the model. (about 1/3 ~ 1/4) But the sign and relative size of these coefficients (compared to the coefficients of the other dummies) remains almost the same.

Yesterday's Sales (lag 1 variable) is highly significant(p<0.0000001) and the coefficient of this lagged variable is about 0.6.

Is it OK to maintain this lagged variable in my model? Is it reasonable to interpret the coefficients of the indicator variables as the campaign effect?

Thanks in advance.

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  • $\begingroup$ It looks like yesterday's sales is an important predictor whose effect is not otherwise captured in your model, this strongly hints that it needs to be included. @IrishStat's answer points to various ways you can account for yesterday's sales effect on today's sales. $\endgroup$
    – Antoine Vernet
    Commented Jul 3, 2018 at 9:50

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Yes if you have also accounted for level shifts in the series as compared to only dealing with trends. Also if you have identified and incorporated indicator variables to deal with 1 time amomalies. Also if you have incorporated the lead and lag structure around holidays .

Care must also be taken to deal with parameters that are transient over time or error variance that changes at specific points in time.

Another variation of this model might be more effective if you introduced a SARIMA component rather than just a lag of the endogenous (output) series.

Only a comprehensive analysis of your data could expose possible flaws in your current approach. http://autobox.com/cms/index.php/afs-university/intro-to-forecasting/doc_download/53-capabilities-presentation slide 51 is an example in this regard.

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  • $\begingroup$ Thank you for your answer, IrishStat. It helped me a lot. I have incorporated level shifts, one time anomalies, etc. I'm still confused with the dramatic decrease in the value of the coefficients when I include this lagged variable. Does it mean that without this lagged variable, the coefficients of the campaign dummies is NOT controlled for this lagged variable, so it can be overestimated? I have to choose between the model with or without lag, but the coefficients differ significantly(about 3 ~ 4 times higher in absolute value when the lag is not included in the model). $\endgroup$
    – th-ahn
    Commented Jul 4, 2018 at 7:12
  • $\begingroup$ I am a data guy . For me to help you with your question I need to see your data and your models. If it is proprietary and you don't want to share it with the list then email it to me and I will treat it confidentially. $\endgroup$
    – IrishStat
    Commented Jul 4, 2018 at 9:44

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