A big FMCG company sells "paper napkins" of various sizes and pack size ( say pack of 10 or a pack of 20) through retail outlets in eastern India/ western India/ southern India / northern India. Paper napkin of a particular size and pack size form a distinct item and is labeled with a Universal Product Code (UPC). They aggregate the units sold across all retail outlets in a weekly basis and collect that data. We have 2 years data from them for each of the geographical regions. Their sales show an increase over a "baseline sales" whenever they carry out trade promotions where they put $ x for a week. There are four kinds of trade promotions viz
a) Display promotion ( where they spend money by spending on the displays of the paper napkin belonging to a UPC in various retail outlets in say eastern India )
b) Feature Promotion ( where they spend money by advertising on features of the product in newspapers and electronic media )
c) Display and Feature Promotion ( both of the above simultaneously )
d) Price discount promotion ( where they spend money to reduce prices to drive up sales units ).
Usually, only one kind of promotion will run in one week for a UPC in one geography ( say eastern India )
We will have a dataset for each UPC which will look as follows :
Product ID Week no | Sales_units | Display($) | Feature ($) | Display and Feature ($) | Price_discount ($)
xxxxxx 1 70 0 0 0 0
xxxxxx 2 90 60 0 0 0
xxxxxx 3 75 0 0 0 0
xxxxxx 4 100 0 0 0 50
xxxxxx 5 32 0 0 0 0
xxxxxx 6 65 0 0 0 0
xxxxxx 7 100 0 40 0 0
xxxxxx 8 70 0 0 0 0
xxxxxx 9 i15 0 0 75 0
xxxxxx 10 65 0 0 0 0
Now it is clearly required to build model with moving average and auto-regressive terms and the "causal" variables to fit a prediction of sales_units in future weeks.
Please can any one suggest me what algorithm i will used for the same. If any soultion is there please tell me.