Forecast (R) with Trend, Seasonality and Promotions (Causals)

Question

I have aggregated sales data along with price discount at month level for two years. There are seasonality, trend and also causals - the impact of price promotions (discount, in percentage). I want to decompose trend, seasonality (as index) and impact of promotions (price elasticity). Each of these components then can be leveraged to generate forecasts.

I tried STL and Decompose using only "Sales" but am losing out on impact of discount (as percentage).

Dataset:

SALES:
      Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
2013  120  130  180  150  200  200  190  150  130  160  220  350
2014  160  250  340  330  380  550  400  300  450  150 1070 1110

DISCOUNT:
      Jan  Feb  Mar  Apr  May  Jun  Jul  Aug  Sep  Oct  Nov  Dec
2013 0.10 0.12 0.13 0.10 0.14 0.15 0.10 0.12 0.15 0.15 0.18 0.23
2014 0.25 0.25 0.25 0.25 0.25 0.30 0.30 0.30 0.40 0.30 0.35 0.4

As an alternative, I tried modeling this in Excel using solver (GRG) with inconsistent results.

Answer 1

I would recommend looking at auto.arima() in the forecast package. You can feed your promotion data into the xreg parameter (this may be helpful). This will fit a regression on your promotion regressor and an ARIMA model on the residuals from that regression, which should take care of seasonality and trend. Note that this is different from an ARIMAX model.

We have quite a few questions on ARIMAX and similar models in the "forecasting" tag. Browsing through them may be helpful.