I'm working on a time series model which predicts daily sales. The model is based on seasonal-trend decomposition by Loess, basically. (I'm using an R package similar to Prophet by facebook.)
Since the time series I want to model has large PACF for lag 1, I added 1st-order lagged variable to this stl-based model.
To summarize, my model has the following form.
Today's Sales ~ trend + seasonality + some indicator variables + Yesterday's Sales + error
This 'some indicator variables' mean dummy variables whose values are 1 when a specific kind of marketing campaign is ON, 0 when OFF.
I want to interpret the regression coefficients of these dummy variables as the average effect of a marketing campaign category on Sales.
Then there arises a problem. The coefficients are much smaller when I put Yesterday's Sales to the model. (about 1/3 ~ 1/4) But the sign and relative size of these coefficients (compared to the coefficients of the other dummies) remains almost the same.
Yesterday's Sales (lag 1 variable) is highly significant(p<0.0000001) and the coefficient of this lagged variable is about 0.6.
Is it OK to maintain this lagged variable in my model? Is it reasonable to interpret the coefficients of the indicator variables as the campaign effect?
Thanks in advance.