# Regression or time series?

I need to predict the sales of a product P2.

I have access to:

1. 7 months of sales history
2. 26 months of sales history of another product P1

I assume the sales trends are similar because the products are similar.

The problems are:

1. The sales are really impacted by the christmas period.
2. The products are not launched in the same month of the year

Question : what is the best way to predict the sales of P2 (orange curve) ?

1. A regression (learnt from P1 and applied on P2):

log(sales) = bo +b1*Aging of the product +b2*DecemberFlag ?

Problem: after the Christmas effect, sales never recover the previous trend, i.e the sales stay higher. This is why maybe time series fit more with this problem.

1. A time series (learnt from P1 and applied on P2):

How will it manage the seasonality since I don't have a full period for P2? i.e. how can the model predict the sales of P2 in December 2015 since it can't recover the sales in December 2014

• If the products really are similar, I'd expect some kind of substitution effect, i.e,, sales for P1 and P2 should be correlated. But then you can't transfer knowledge from P1 to P2, as the P1 model ought to behave differently after March 2015. On the other hand, if P1 and P2 are not correlated (as the plots suggest) then your entire approach is flawed. Exponential smoothing can be used, and you might be able to estimate a "christmas effect" from the data of P1 and apply that to the christmas sales for P2, but even that estimate will be rough since you only have two christmases to work with. Aug 6, 2015 at 15:32

## 1 Answer

Ok here is an idea: You can do the forecast for both the series(You can use ARIMA, as it is robust for modeling seasonality and other trend). Then you can assign weights for all 12 months for the product1 forecast and adjust the value of forecast of series 2 based on that. That way you will assign more weight to the months you expect seasonality or similar trend for product1.