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I am attempting to build a model to forecast attendance in a given week in the current year based on this year's attendance values up until the present, and data from two previous years. My data looks like this:

   Week 11-12 Cumulative ADA    12-13 Cumulative ADA    13-14 Cumulative ADA
   1    0.9941                  0.9941                  0.9914
   2    0.9907                  0.991                   0.989
   3    0.9888                  0.9888                  0.9879
   4    0.9877                  0.987                   0.9869
   5    0.9869                  0.9865                  0.9867
   6    0.9862                  0.985                   0.9859
   7    0.9856                  0.9842                  0.9857
   8    0.9856                  0.984                   NA
   9    0.9852                  0.9839                  NA
   10   0.9848                  0.9834                  NA

Any guidance on how to predict the three NAs based on the past two years data and this year's values would be much appreciated.

Thanks!

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    $\begingroup$ check out the forecast package - it's great. $\endgroup$ – Fernando Oct 16 '13 at 14:17
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Forecasting weekly data using weekly history is problematic as what we do in say week 4 is probably not what we did in week 4 last year whereas what we do in month 4 is probably systematic with what we did in month 4 last year ,save special effects such as Easter or Thanksgiving. Furthermore the different number of weeks in a year can throw a monkey-wrench into the analysis. More importantly the effect of holidays on weekly sums can be quite dependent on when the holiday occurs thus effectively distorting pattern. I have seen very few examples of where weekly data is consistent/predictable and can be used reliably to obtain weekly forecasts.

With the development of statistically aggressive daily models taking into account the window of response around each holiday/event, day-of-the-week effects,day-od-the-month effects,month-of-the-year effects,level shifts and or local time trends... users are now developing daily models to obtain weekly predictions. Additionally they can compute probabilities of making month-end numbers or of meeting a plan/goal number.

THe other item dealing with missing values is easily handled by Intervention Detection schemes which would identify pulses for the missing values and effectively replace the missing value with an imputed value based upon the full model.

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  • $\begingroup$ We've actually counteracted the issue of weeks not lining up by munging the weeks to line up. For example, this year there would actually be an additional week so the first week's information includes 8 weekdays instead of 5. It's not a perfect system but the holiday weeks should match up, the final week should roughly correspond every year, and so on. What I'm interested in is, is there a good method to build a model based on the trends from previous years to apply to this year's data? $\endgroup$ – n8sty Oct 16 '13 at 15:28
  • $\begingroup$ Yes there is a good method to develop this structure. It is a combibation or ARIMA and regressor variables which can include all that I mentioned above. If tou wish you can contact me at my email address and I will try and give you more details. Just click on my name and you can get my email address. Alyternatively post your data and I will analyse it and show you precisely what can be done. Do not post the cumulative but do post the actual daily values. $\endgroup$ – IrishStat Oct 19 '13 at 16:37

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