Thursday, December 14, 2006

Another interesting challenge...

...Oldham Athletic will be charging just £2 for adults, and £1 for kids in their next two home matches. These are matches against Brighton and Hove Albion, and Northampton Town, matches which otherwise would not attract a very high attendance at all. It's a great idea, I'm totally for it - get a full house in, hopefully get some kids hooked on Latics, especially if the team can carry on playing as they have recently (unbeaten in nine league home matches, seven wins).

But it creates havoc for modelling and forecasting. On the other hand, it's a known break. One of the biggest problems with forecasting is structural breaks, if the break affects the mean of the time series being forecast. Before the break, it's generally quite hard to predict one will happen, and then if it can be predicted, the size is another matter entirely. If a break happens, next period when forecasting, one needs to know whether this is simply an outlier, measurement error, or an actual break.

So here, I have quite a lot of information: I know something will happen that can only be described as a break - the two previous big discount matches (Grimsby (free) and Torquay (fiver)) have attracted substantially larger attendances. I further know it will only last for two matches, it is not permanent, but it's not a one-off either. And I'll know the reason why the break has occured.

All in all, it makes for an interesting experiment. Will the attendances be as large as the Grimsby or Torquay matches? A method for capturing a break is to add a dummy variable estimated over some observations in the sample, and extend this dummy into the forecast period. Usually in time-series, the dummy is for the last few observations. However, here as we have some idea from these matches how big the break might be, it makes sense to use this information.

Extending the Grimsby dummy gives a forecast of 11,670, and extending the Torquay dummy just 6,856. I think somewhere inbetween these two examples is more likely. A combination, weighting Grimsby at 0.6 since £2 is closer to £0 than £5 gives a forecast of 9,442, but I think a higher weight should be used, since zero prices have wierd effects. A weight of 0.75 on Grimsby provides a forecast of 10,230, which pleases me.

Come on Oldham!

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