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 jan feb march 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?