# Time intervals for modeling

Suppose we have weekly data for some attribute (e.g. housing prices). Say that we have $500$ weeks worth of housing price data. Suppose some major event happened on week $256$. If we want to detect any significant changes in housing prices after week $256$ versus before week $256$, would it be better to use a longer time scale? Maybe convert weeks into months? What other models would you suggest?

Damien, When you know the date /time of the INTERVENTION , this is called Intervention Modelling. When you don't know the date/time one does INTERVENTION DETECTION prior to Intervention Modelling. In your case I would build an ARIMA Model or a Transfer Function if you have some potential cause series AND then add a 0/1 variable reflecting the known intervention 0,0,0.0 etc and 1's starting at period 256. The problem /opportunity with this specification is that the impact may have been prior or after the true/known date AND/OR the duration may not be infinite. Also the effect may be the incorporation of a trend NOT simply a Level/Step Shift. Furthermore the intervention may have changed not only the expected value BUT the variability of the error process. All of these things have to be considered in forming a final conclusion about the impact of the change.