Let's say I'm constructing a linear model with the intention of predicting automobile sales volume. Let's say that the consumer auto purchasing cycle takes 4 months, and so we'd 'lag' each observation by four data points. So if out data was monthly, out data may end up looking like the following

month   lag_month     sales      visits       gas price
april    jan           500        50000        3.55
may      feb           550        45000        3.87

Given the lag in consumer shopping behavior, I want/'need' to lag the variables. However, I also feel like I have to lag the variables for the sake of prediction. Let's say I run a regression using this data and get the following estimates, I could input feb numbers to prediction sales four months from now, yes/no?

sales = -0.05 + 2*(visits) + .0.35*(gas)
sales = -0.05 + 2*(550) + .0.35*(3.87)  - four month lag to predict four months from now

The question I have relates to the process. This process seems incredibly poor (statistically unsound) and I'm wondering what are the problems with utilizing such an approach (four month lag). What are alternatives to lagging when the goal is prediction?

  • $\begingroup$ Running models on lagged data is the essence of predictive modeling. If your data are lagged 4 months, you need to take that into account. Just make sure your output corresponds to the predicted, non-lagged value when you are calibrating your model. $\endgroup$ – user31668 Jan 22 '14 at 0:38
  • $\begingroup$ I know this doesn't answer your question (sorry), but have you tried a univariate time series? How far into the future do you want to predict? $\endgroup$ – charles Jan 22 '14 at 2:37

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