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maybe it is a bit trivial, but I would like to ask how can I do weekly demand forecasting when I have got daily demand? the thing is that every year has 12 months, but does not have exactly 52 weeks. Therefore, I do not know how to handle it.

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    $\begingroup$ If you have historical demands by day, you can simply aggregate these in weekly buckets. Can you be a little more specific what the problem is? $\endgroup$ – Stephan Kolassa Oct 31 '17 at 19:29
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    $\begingroup$ I believe his problem is that weekly data is not technically periodic. $\endgroup$ – AnscombesGimlet Oct 31 '17 at 20:57
  • $\begingroup$ The issue is that the year in my historical demand data starts on Tuesday, but does not finish on Monday. In other words, one year does not have 52 weeks, but 52.14 (or 52.29) weeks. I have got historical data with daily demand and the task is to make weekly and monthly forecast. I have done monthly, but I`m not sure how to deal with weekly forecast. Thank you for your reply. $\endgroup$ – peterT Oct 31 '17 at 21:39
  • $\begingroup$ a lot of your problems will vanish when you use daily data as opportunities arise... $\endgroup$ – IrishStat Nov 1 '17 at 21:29
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If you have daily data you can detect daily effects . weekly effects , monthly effects , lead and lag holiday effects , long-weekend effects , week-of-the-month effects , day-of-the-month effects, level shifts , local time trends , pulse effects, changes in day-of-the-week effects , end-of-month-effects..et al . You can then aggregate your daily forecasts to higher aggregates and even compute probabilities of making weekly/monthly/quarterly totals as you go through the month. Weekly data analysis/models should be studiously avoided because weekly totals are effected by a number of factors thus leading to distortion .

Daily data is less "smooth" than higher aggregates but that is not a problem as anomaly detection can be used to render the affect/distortion of "unusual observations" providing robustification.

By resampling the residuals from a model using monte carlo methods one can obtain a family of forecasts for each forecast period. Then one can create a distribution of the aggregate of these forecasts. This easily extends to allowing for identified pulses to play a role in the family/distribution of forecasts which were necessary to get robust model parameter estimates . If one doesn't allow for pulses to be possible in the forecasts one obtains naive tight limits due to the smaller variance of the errors. Finally the idea of MC is applicable to any level of temporal forecasting .

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  • $\begingroup$ In the belief that "aggregating" daily data to weekly data by summing them up is so obvious that the OP surely is aware of that option, I have interpreted this thread as inquiring about the much more challenging problem of erecting prediction limits around an aggregate of such forecasts--that, after all, is what distinguishes a statistical analysis from other types of forecasts. Would you have any constructive advice to give about that? $\endgroup$ – whuber Oct 31 '17 at 21:30
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    $\begingroup$ By resampling the residuals from a model using monte carlo methods one can obtain a family of forecasts for each forecast period. Then one can create a distribution of the sum of these aggregate forecasts . This easily extends to allowing for identified pulses to play a role in the family/distribution of forecasts which were necessary to get robust model parameter estimates . If one doesn't allow for pulses to be possible in the forecasts one obtains naive tight limits due to the smaller variance of the errors. The idea of MC is applicable to any level of temporal forecasting ..... $\endgroup$ – IrishStat Oct 31 '17 at 22:29
  • $\begingroup$ "Then one can create a distribution of the aggregate of these forecasts" $\endgroup$ – IrishStat Nov 1 '17 at 10:30
  • $\begingroup$ Thank you--that comment greatly enhances the usefulness of your answer. Perhaps you could incorporate it directly within the text? $\endgroup$ – whuber Nov 1 '17 at 13:12

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