How can I isolate the effect of an event on a sequence of sales numbers? I have a sequence of integers that represent total sales of my product for each day. From time to time, we have large press or marketing events that increase sales on the day of the event and for a few days after that but then eventually taper down to the long-run average. Here's some made-up numbers showing what I mean:
34, 40, 35, 36, 150, 110, 140, 107, 80, 68, 75, 50, 45, 35, 38, 41, 42,...
                ^^^                                   ^^^
          event occurs here                        reversion to mean

I have limited experience with statistics, so I'm looking for some guidance on statistical methods that I could use to determine:


*

*how much of the sales on the event day and the following days should be attributed to the event

*whether the press or marketing event contributes to a permanently higher sales average, even after its initial effect has worn off.

 A: To answer your question , one would be advised to build a single equation model which captured day-of-the-week effects (6 dummy indicators) and an indicator for the "event". Software exists to capture any lead, contemporaneous and.or lag effects around known event. In the absence of such software you might try and "roll your own" in order to identify the "window of response" around your event variable. In addition you might want to include week-of-the-year and/or month-of-the-year variables to handle annual seasonality. Furthermore since this is daily data you might want to include other events such as the Holidays and also incorporating any required "window of response" around these Holidays. You should also try to identify "particular days of the month" irrespective of what day of the week they fall on as important contributors to explaining daily demand such as the end-of-the-month or the day seniors get their social security checks et al . Other factors that might be important in the "discovery model phase" might be the empirical identification of mean shifts and/or local time trends. Before congratulating yourself for either writing such a "tour de force" you might (should !) validate that neither the model parameters of the error variance have changed over time. By sharing your data and inviting the list to provide quality analysis of your data we could all learn what others are doing in a precise manner. Upon completion of the modelling phase one could then eliminate the event variables effect , essentially scrubbing the data by obtaining a realization of the daily sales series without the events coefficients/effects being incorporated. The difference between the originally observed series and this scrubbed series provides an estimate of the events effects.This recommended approach uses all of the data as compared to the incorrect approach of trying to forecast data values at a point prior to the events effects which of course is the unknown ( but to be found ) point in time where the effect "starts". 
