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I have a modelling dilemma. I am creating a model that attempts to predict demand (leads not sales) based upon the correlation to advertising spend. We know that without advertising spend, demand is driven by seasonality. So our models include seasonal factors like month of the year and even day of the week. If I were building a regular linear regression model, I would fit a linear regression model to a training dataset, to get estimates of the coefficients of the seasonal factors and advertising spend to demand. In order to get an estimate of future baseline demand, I would forecast demand using all the coefficients from the model and then I would estimate a baseline by setting adspend equal to zero. For ARIMA models, there are additional factors such as AR and MA terms. Would I estimate my baseline the same way by just setting the coefficient on advertising spend equal to zero? Thanks for any thoughts.

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No. you have to deal with an issue called endogeneity. the problem is that your ad spend may depend on sales or leads. It's totally plausible to assume that when sales/leads were lower the ad spend next month was increased by your marketing folks. This is a nasty issue, and it can ruin your model. You have to figure out what to do with it before running any models of the sorts you described.

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If you were forecasting where adv spends = 0 then as you suggested you would specify the future values as zero. Care should be taken when estimating coefficients that unusual values or level shifts be detected and remedies be incorporated otherwise you run the serious risk of having coefficients that are incorrect.

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