I want to predict my sales using my marketing costs, but my marketing costs data has a lot of zero expenditure days. Both sales and marketing data are daily observe data but I only spend on the marketing side infrequently, i.e., I have zero values on a lot of observed days.
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$\begingroup$ I would imagine that marketing expenditures are for distributed types of results, e.g. pay for an ad that then runs for days or weeks? I am not sure if you need stationarity to do prediction. Some sort of "integrated form" of the marketing costs could be used perhaps? For example, a convolution with an "impulse response" kernel? $\endgroup$– GeoMatt22Commented Oct 12, 2016 at 2:31
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$\begingroup$ Yup, that kind of data, like the pays for ads. I am not sure what you meant with integrated form, though. $\endgroup$– python noviceCommented Oct 12, 2016 at 2:50
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$\begingroup$ I was not certain of the question context, and a lot of econometric time-series questions seem to focus on stationarity and differencing/integrating time series to achieve this. So I crudely meant "integrate" in the sense of "smoothing" the response (vs. differencing, which tends to "roughen"). Really more the idea of a lagged & distributed response though, as in the impulse response link I gave. $\endgroup$– GeoMatt22Commented Oct 12, 2016 at 3:12
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$\begingroup$ Just read the full article, thanks for this. never thought my signal processing course will be this helpful. Thank you. $\endgroup$– python noviceCommented Oct 12, 2016 at 3:17
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$\begingroup$ I just posted an answer summarizing these comments. Hope it helps! $\endgroup$– GeoMatt22Commented Oct 12, 2016 at 3:43
1 Answer
I would imagine that marketing expenditures are for distributed types of results, e.g. you pay for an ad that then runs for days or weeks? This suggests a lagged & distributed respons of sales to a given marketing expenditure. This could perhaps be represented by convolution with an "impulse response" kernel.
Commonly "stationarity" is considered in the context of ARIMA models. This approach should be applicable here, as I believe these models can represent convolutions. However you would have to use the multivariate version. I cannot say what tools would be best to estimate this sort of model, but here is one place to start.
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$\begingroup$ I agree, that is what I would do. +1 $\endgroup$– CarlCommented Oct 12, 2016 at 19:11