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Lets say I want to model weekly grocery store sales.

I have 300 stores. Only 100 remain active during the duration of the modeling period. This is due to some stores opening, some stores closing, and some stores being remodeled etc.

It seems that I have at least two options for modeling.

  1. Exclude all stores that were not active during the time measured (or at least "mostly" active for the year).

  2. Make a variable that is a count of how many stores were active each week.

It seems like option 2 is better because it will allow for more observations. I just wanted to know if there were any issues with this approach or if there was something better.

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    $\begingroup$ What is your aim in modeling? Do you want to forecast total sales? $\endgroup$
    – Stephan Kolassa
    Commented Nov 9, 2017 at 13:24
  • $\begingroup$ Since you asked ... two different models. 1. Forecast total sales, most likely via ARIMA, 2. Inference, what factors have an effect on total sales, most likely via multiple regression. $\endgroup$
    – Alex
    Commented Nov 9, 2017 at 13:26

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  1. For forecasting, it will probably be best to include a count variable or some other way of keeping track of the number of active stores. Otherwise, how will you deal with stores opening and closing during the forecast period?

    In addition, I would recommend that you separately forecast all individual stores, using each store's separate history. Constrain forecasts to be zero if the store closes. Then consolidate the top and bottom level forecasts. (This will change the zero forecasts on the bottom level to be nonzero, but if I understand you correctly, that is not an issue.) People have repeatedly found that this approach improves forecasts on all levels.

  2. If you want to do inference, a count variable may again be useful. Alternatively, use observations from all stores that are active at any given point in time, a kind of panel regression. This should give you better estimates of promotion or other effects.

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  • $\begingroup$ The forecasting part makes a lot of sense. As for the inference you are saying that I can approach the problem in two ways. 1. Multiple regression with a count variable. 2. A longitudinal analysis with only active stores. Am I interpreting that correctly? $\endgroup$
    – Alex
    Commented Nov 9, 2017 at 13:39
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    $\begingroup$ Yes, although you can include all stores - each open store in a given week will just contribute one observation row, so stores that close will simply contribute fewer observations than ones that stayed open throughout. (And thank you, but you may want to un-accept - sometimes other people have other ideas, but fewer people will look at a question with an accepted answer.) $\endgroup$
    – Stephan Kolassa
    Commented Nov 9, 2017 at 13:41

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