First, I would like to make sure I fully understand your current approach. You were trying to capture trend and seasonality using month number and week number, right? So I guess the week number you used is actually the week id instead of 1 to 52, right? Otherwise, it will be nested within the month number, and there is no variable to capture the trend. If this is the case, you are using this week id to capture the trend and month number to capture the seasonality, which assumes the seasonality to be 12.
My understanding is that you want to do a 3-step process:
1. Estimate the trend and seasonality, and forecast trend and seasonality
2. Estimate the de-trend and de-seasonlized series
3. Combine the forecast from the previous 2 steps.
By "adding“, there might be additive model and multiplicative model. I'm just assuming additive model for simplicity, you can apply the same logic to multiplicative model too.
1. There are many ways to estimate the trend and seasonality. For example, you can run regression models just on trend and seasonality term, i.e. run regression y=t+s or y=t+t^2+s or whatever model you like. Here, the t is your time id, and s is the seasonal indices you want to use.
2. To compute the de-trend and de-seaonalized series, you can just take the estimates y^ from from your last model, and compute the residual. For additive model, it just means compute z=sales-y^. Then you can run your regression model on this residual.
3. With the model in step 1 and step 2, you can easily score the forecast for the historical period and future, and "add" them together.
... View more