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 (it's 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 modeling 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.