Formulas like this taken from here:
Log_Demand_A = constant + b1*log_Price_A + b2*log_Price_B + b3*Promo_1 + b4*Promo_2 + b5*log_Price_A*Promo_1 + b6*log_Price_A*Promo_2
can be easily fitted with common linear regression algorithms in R or SAS. The parameter b1 can also be directly interpreted as price elasticity of product A and the parameter b2 as cross elasticity.
In theory, the fitted model can also be used to predict demand but demand is not only affected by price but also by other factors (e.g. time of the year). A crude way to incorporate time would be to use, for example, week of the year as dummy variable. However, I think this is too simplistic, as demand usually has a trend, seasonality etc. So this requires sophisticated time series models (AR, MA, ARMA, ARIMA etc.). I reckon these models will be fairly good in predicting demand. However, can such models still contain these components:
And most importantly, can b1 and b2 still be interpreted as price elasticity and cross elasticity respectively? Any feedback and pointers to existing publications/(commercial) solutions would be very much appreciated.