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I have just started to learn about forecasting. I thought it would be easy to create forecast models for a daily time series but have encountered a number of difficulties. Firstly most examples and available datasets are either in months or quarters. It is rare to find examples for weeks and days. Secondly it also appears difficult to create a timeseries object for days (365) and weeks (52) as these vary between years. This may just be the way the timeseries object works in R. I have had to use Zoo. I also have a concern that my data may not be properly modeled for use in packages like Forecast and HTS.

I am interested in how best to approach this problem. Any examples of forecasting to daily events that may cycle across years would be greatly appreciated.

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Daily data is often impacted by 1) day-of-the-week-profiles and changes in these profiles ; 2) week of the year ; 3) Time trends ( note the plural ) ; 4) Level Shifts ; 5) monthly effects ; 6) particular days of the month E.G. the first,15th etc ; 7) Lead, contemporaneous and lag effects around known events e.g Christmas , JUly4th etc ) ; 8) Unusual values ; 9)Long weekends around events ; 10) particular week in month effects ; ARIMA structure reflecting unspecified stochastic input series

That should be enough to start with.

When you think that your equation deals effectively with the above then start to consider the impact of parmeters that change over time and an error variance that may change over time.

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  • $\begingroup$ How do I model these things eg public holidays and weekends as an initial start to try to forecast at the daily level. My data has a seasonal trend that goes for a year, then there is a weekly trend with weekends needed to be zero and public holidays also needing to be zero. The dates for these events are known. I am not sure how to model ARIMA or ETS to take these events into consideration. Do I use xreg? It is very hard to find any useful articles or tutorials on doing this on the web. Any pointers in the correct direction would be appreciated. $\endgroup$ – orbital May 16 '13 at 13:37
  • $\begingroup$ You would start with a model that 6 indicators for the day of the week , 11 indicators for the month of the year , 14-15 indicators reperesenting the major holidays and then either use commercially avialable software like AUTOBOX/SAS/SPSS to detect the specific window of response around each holiday/event, the presence of level shifts and or local time trends , dynamic changes un the day-of-the-week effects , pulse effects , parameter change effects over tome and carinace change effects over time OR spend a lot of time yourself with free tools which don't exist. $\endgroup$ – IrishStat May 17 '13 at 17:45

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