Why there is a gap when generating lags in time series?

Question

I just started heading into time series forecasting, and a friend of mine who is doing this for several years showed me one of his projects. In his project, he was forecasting monthly sales quantity for a shop, and he had 3 or 4 years of historic data to work with. Howewer, what he did was generate lags in a range between 12 and 24. So basically he generated monthly lags for the second year, and skipped the past year? If so, why is that? And he told me about some kind of backtesting, which is equivalent to validating a model? And when predicting, the model must not see the past-year's lags? Furthermore, he is predicting one year ahead, so as far as I got it, he must generate 12 monthly lags at least? What happens if he got less lags?

There is so much confusion and questions in my head right now. I read/did lots of beginner/starting time series courses, but in practice its way harder. So I would be very thankful and would highly appreciate it if somebody could clarify these things for me. :')

Answer 1

Say you are forecasting some quantity as a function of its 1-month lag among other things, i.e.:

$Y_{t} = \alpha + \beta Y_{t-1} + ...$

Your forecast 1 month into the future ($\widehat{Y_{t+1}}$) will require that quantity for the current month ($Y_{t}$), which you know. Your forecast 2 months into the future ($\widehat{Y_{t+2}}$) will require that quantity 1 month into the future ($Y_{t+1}$), which you already don't know. Of course you can just use the forecasted value you obtained at the previous step ($\widehat{Y_{t+1}}$) in place of the real value ($Y_{t+1}$), but doing so iteratively for a considerably lengthy forecast will degrade the quality quickly due to accumulation of errors (i.e. your forecast 2 months into the future will carry not only the model error from the current forecasting step, but also from the previous step since you used its forecast in place of the real value, and so on).

In your friend's case, if he wants to forecast 12 months ahead, 12-month lag is the minimal lag he can include if he wants to avoid using forecasted values in place of real values.