Retail Sales Model Excuse any errors as I'm fairly new to STATA. I'm aiming to generate a retail promotional sales model (Multiple Linear Regression Model) whereby my y-variable is volume of sales at time t, and my independent variables are:


*

*number of TV ads

*number of print ads

*number of radio ads

*average promotion price for brand i

*average promotion price for all brands in category


Can you provide me with an identification of what assumptions of time series analysis I may not abide by/need to look out for? Especially while including so many exp-variables.
 A: There are many possible ways to address this question from a methodological POV. With two years of weekly, store-level information, you are not limited in terms of the options.
Some guys with UCLA's Marketing Science department have been pathfinders in terms of functional forms and models. In particular, the several editions of Dominique Hanssens' (Chair of the department and past President of the MSI) book Market Response Models: Econometric and Time Series Analysis is widely considered the go-to bible for questions like this. Among the suggestions Hanssens' makes are VAR (vector autoregression models) as well as the various flavors of ARIMA. VAR is particularly attractive, though rigorous to implement, as noted in the Wiki discussion of it, "The only prior knowledge required is a list of variables which can be hypothesized to affect each other intertemporally."
That said, Lee Cooper's (Emeritus at UCLA) book Market Share Analysis (available for free download here ... http://www.anderson.ucla.edu/faculty/lee.cooper/MCI_Book/BOOKI2010.pdf) advocates a somewhat different and even more flexible approach integrating panel data models, kind of like a dummy variable model which captures features related to the cross-sections (brands, stores, etc.) and time periods. Cooper relies heavily on analyses of the elasticities and cross-elasticities, deriving several functional forms depending on the type of underlying relationship one assumes between sales and the marketing instruments. Forget about the fact that it's focused on market share since it's simply an excellent introduction to marketing mix models.
The list of model options is endless, really. These are just a few of the broad avenues one can pursue. 
A: Your model should have a set of residuals that can be represented by a random process. These residuals should have a constant mean i.e. no pulses/no mean shifts/no trend and a constant error variance over time . These residuals should not be predictable by either contemporaneous or lag effects of any of your user specified variables. Multiple Linear Regression is never a good choice when you have time series data unless your resultant model generates errors/residuals that reflect a random process.
EDITED TO SUGGEST THE SUGGESTED SCRIPT:
I would use Transfer Function Identification using cross-correlations (pre-whitening to adjust for auto-correlation within each predictor series for identification purposes) to form a possible contemporaneous and lag effects model. I would then add in 51 weekly dummies in addition to the aforementioned contemporaneous and lag effects. I would examine the tentative residuals for pulses/level shifts/local time trends and augment the tentative model appropriately. I would estimate this model and delete (slowly !) any and all insignificant variables. I would then review the acf of the newly formed tentative error process and augment the current model with an appropriate ARIMA structure. I would then (again) delete any and all non-significant structure yielding a minimally sufficient ( and possibly useful !) model.
If this is too much trouble or work or beyond your software's capabilities then
just assume a textbook model and pray ....  
