I have estimated an intervention model on the log of a seasonally differenced series of sales figures and have used a step function rather than a pulse function. My question is: how do I interpret the intervention effect ? If the coefficient is -0.05 am I correct in saying that the intervention resulted in a 5% decrease in sales? Is that interpretation correct even though the original series to which the intervention was applied is in seasonal differences (its a weekly series)?
Why are you assuming logs and seasonal differencing ? Just because Box and Jenkins applied these transforms doesn't mean that they are applicable to other time series. Meanwhile in a specific answer to your question. If you are taking seasonal differences UP FRONT and modelling the seasonal differences using your assumed level shift variable ( remember that the level shift needed may not be the de jure point ) then the -.05 would reflect a 5% decrement in the logs.