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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?

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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.

Some answers to questions:

Damien, If it only lasts 1 day then as Wayne suggests simply code a pulse variable ( all zeroes except for 1 period ) BUT as he also intimated there could be a lead, contemporaneous and lag response around the one period.

Wayne, Thanks for reflecting on AUTOBOX , a piece of software that can be useful for time series.

Danien, If you wish to post the data , I will try and respond.

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  • $\begingroup$ Thanks for the answer. I know the exact date when the event happened. Also the event occurs for only 1 day. Also what would a cause series be? The event was a news event (e.g the CEO retired). Would the cause series be the housing prices after the event happened? $\endgroup$ – Damien Jul 13 '12 at 17:39
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    $\begingroup$ @Damien: The issue is, while the event is one day, you are asking about its effect. IrishStat's suggestion of 0's through time 255 and 1's afterwards addresses the case where the event has a permanent effect after it takes place. As he then says, it's possible that the effect started before the event (say rumors were swirling), or to not kick in until after the event (say the resignation was Friday after the close of business), and that the effect could trail off over time. $\endgroup$ – Wayne Jul 13 '12 at 18:41
  • $\begingroup$ A cause series would be some other variable that has a causal effect on the (in this case) housing prices, for example, mortgage rates (although there's causality going both ways and with some lag, esp. on a weekly basis, so this wouldn't be simple to model - I give it just as an illustration.) $\endgroup$ – jbowman Jul 13 '12 at 18:55
  • $\begingroup$ @Wayne: Thanks for the response. So if you are given a time series and want to fit an ARIMA model. how do you know whether to fit an ARIMA(1,1) model, etc..? $\endgroup$ – Damien Jul 13 '12 at 18:55
  • $\begingroup$ @Damien: For ARIMA, there's a whole methodology called the Box Jenkins method (en.wikipedia.org/wiki/Box–Jenkins), which takes some training/experience to properly apply. There are some automated procedures (R has auto.arima in the forecast package). IrishStat's company's product has automated procedures. The bottom line is that time series are tricky, as Irish alludes, and there are many landmines to step on. $\endgroup$ – Wayne Jul 13 '12 at 19:35

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