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I am working with an ARIMA model using data with hourly resolution and a 24 hour cyclical pattern. When I run an ACF on the data I can see a peak at a lag of 24. Does this mean I set p to 24 or am I missing something. I have found this slow to run.

Shug
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    It sounds like you could use a seasonal ARIMA model, though you should check whether you have seasonality at other time scales too (e.g., day of week, week of year, month). – Isabella Ghement Nov 23 '18 at 00:56
  • Yes there is other seasonality as well. – Shug Nov 23 '18 at 13:48
  • If you have seasonality at multiple time scales, you can try forecasting your time series using the tbats() function in the R forecast package created by Rob Hyndman. See this link for a start: https://robjhyndman.com/hyndsight/seasonal-periods/. – Isabella Ghement Nov 23 '18 at 16:28
  • @Isabella Ghement The particular day that you are forecasting for may depend on the week-of-the-month or a day-of-the-month or the quarter of the year or the month of the year. Thus it is often ( if not always !) important tp construct a model that might need these factors (features) and to use tools that pay attention to this.. – IrishStat Nov 23 '18 at 18:02
  • @IrishStats: TBATS models should accommodate seasonality at multiple scales and could be a good starting point to consider. Can you be be more specific about what aspects of the temporal dynamics you think are not captured by these models? Also, what modelling tools would you recommend as an alternative for forecasting hourly (not daily) data? – Isabella Ghement Nov 23 '18 at 18:26
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    AUTOBOX a piece of software that i have helped to develop can identify the appropriate individual holiday dependence/association leading to a "better forecast " for daily values which can then be used to get a better forecast for hourly values which are often related to the daily activity/forecast.The reference you give doesn't account for pulses, level shifts, seasonal pulses or local time trends ...all of which are common . Take a look at https://autobox.com/cms/index.php/blog/entry/forecasting-at-an-hourly-level and perhaps you can contact me offline to actually go further on this topic – IrishStat Nov 23 '18 at 20:23
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    a concrete example https://stats.stackexchange.com/questions/66825/forecasting-hourly-time-series-with-daily-weekly-annual-periodicity/66853#66853 – IrishStat Nov 23 '18 at 20:44

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Hourly data is best handled by incorporating daily sums as a predictor series into an ARMAX model. See https://stats.stackexchange.com/search?q=user%3A3382+daily+data for some very powerful examples and interesting discussions

Simple ARIMA models get confused when weekends are different from weekdays and holidays/events have an effect what is often useful is a combined model containg both deterministic structure and memory i.e. exogenous and endogenous . The problem with simple ARIMA or SARIMA models for hourly/daily data is that the model structure is all endogenous (autoregressive).

IrishStat
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  • Thanks for the insight, I should of also mentioned that i need to predict for the next hour so I don't think using daily sums would work in this case – Shug Nov 23 '18 at 13:42
  • Not so .. as you would have a prediction for the next day based upon prior days totals in order to condition the hourly forecast – IrishStat Nov 23 '18 at 14:03
  • Different days of the week often have different hourly patterns ( think train riidership ) thus to make a forecast for a particular hour of the day it make sense to possibly adjust for the particular day ( think a day after a holiday or before a holiday on the holiday itself) . – IrishStat Nov 23 '18 at 17:58
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    It is a mistake to think that what occurred 24 hours is more important than a specific hour forecast being relates to the nature of the day ...i.e. monday vs sunday , a day before a holiday ....Pure memory (sarima) even with day-of-the week indicators may not pick up seasonal (weekly.monthly,quarterly) effects which need to be identified and incorporated as features.. – IrishStat Nov 23 '18 at 20:38
  • Why don't you accept my answer and close the question.,m if you are satisfied.? – IrishStat Nov 28 '18 at 22:11