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I have two time series. One that measures sales data, and the other that measures foot traffic. Both series have some correlated seasonal components, e.g. both are higher around around Christmas. I also suspect that there is some non-seasonal correlation between the two series, e.g. sales are largely driven by foot traffic.

Is it valid to regress the two series against each other, and if so how should I go about doing it?

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  • $\begingroup$ Hello @GreeTreePython, what are you trying to achieve? Short answer is yes you can do that and you can use time series regression techniques like ARIMA or VARMA or state space models. $\endgroup$ – forecaster Mar 15 '16 at 21:17
  • $\begingroup$ Thanks @forecaster. What I ultimately want to learn is if I can predict what the sales data is going to be like by measuring the foot traffic data. I.e. if I count X people, the sales revenue is most likely to be $Y. $\endgroup$ – Gree Tree Python Mar 15 '16 at 21:23
  • $\begingroup$ It would make sense to either seasonally adjust the variables in advance (and remember to add back the seasonal components in the process of forecasting later on) or allow for seasonal patterns when modelling the relationship between the two series (such as by including seasonal dummies in the model). $\endgroup$ – Richard Hardy Mar 16 '16 at 8:21
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You will want to use a Transfer Function model. Regression ignores the component of time (ie autoregression). You will want to include holiday variables. Chapter 10 of Box-Jenkins text book is called "Transfer Function" models. These are the guys that created the methodology called ARIMA(univariate) and the this methodology. The idea is to create a model for each of the causals (ie prewhitening) and then take those residuals to find correlations against the Y variable. You can read more about "time series" methods here http://www.itl.nist.gov/div898/handbook/toolaids/pff/pmc.pdf

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