st: Question Time varying parameters (Master thesis Marketing Research)

[jeroenvanvugt <jeroenvanvugt1987@gmail.com>]

Dear Statalist,

At the moment I got a wonderful assignment for my Master Thesis Marketing
Research at a retailer. They want to know the effects of various promotions
on sales in units (for various product lines). A return on investment
analysis.

Excited as I was, I already started looking for the method I would use. What
I noticed:

1.	The sales is evolving for most of the products. 

2.	The effect of some promotions changes.

3.	The promotions can have a lasting effect (hysteresis). 

I have three questions: 

1. It seems reasonable to use a regression model with time varying
parameters for the promotions. In STATA I found two options: ARIMAX models
or state space models. I prefer ARIMA because it’s easier to use. What
syntax should I use and what literature should I read? I don't want to use
the OLS regression: 
Y(t)=constant+B1X1(t)+B2X2(t)+B3time+B4X1(t)*time+B5X2(t)*time… 
because there are many promotions (more than two) and then there is
multicollinearity. 

Depending on your answer:

a. If you say state space models:
Can you indicate what the syntax would be for a state space model where:
y(t)=constant+B1(t)X1(t)+B2(t)X2(t) and B1(t)=B1(t-1) B2(t)=B2(t-1) where
each X# is a different promotion

b. I you say ARIMA:
Can you help me with the adjustments to the syntax and finding good and easy
to understand literature?

2. What is the best way to estimate the long run effect (hysteresis) and the
direct effects? Should I use two separate models (one with positive and
negative cumulative effects per promotion and one with direct effects) or
can it all be estimated in one model? 

3. Can I estimate ARIMA models for non stationary time series or should I
use state space in which the time series is decomposed into various elements
(trend etc.). What should I change in the model (what are the syntax
adjustments).

If you can help me with pointing me towards a final overall answer then that
would be great! 

I have looked in various books and the stata manual but I'm still puzzled on
how to implement this in Stata. Keep in mind that I’m not an econometrician. 

Jeroen




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