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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.

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    $\begingroup$ 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). $\endgroup$ – Isabella Ghement Nov 23 '18 at 0:56
  • $\begingroup$ Yes there is other seasonality as well. $\endgroup$ – Shug Nov 23 '18 at 13:48
  • $\begingroup$ 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: robjhyndman.com/hyndsight/seasonal-periods. $\endgroup$ – Isabella Ghement Nov 23 '18 at 16:28
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    $\begingroup$ 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 autobox.com/cms/index.php/blog/entry/… and perhaps you can contact me offline to actually go further on this topic $\endgroup$ – IrishStat Nov 23 '18 at 20:23
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    $\begingroup$ a concrete example stats.stackexchange.com/questions/66825/… $\endgroup$ – 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).

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  • $\begingroup$ 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 $\endgroup$ – Shug Nov 23 '18 at 13:42
  • $\begingroup$ Not so .. as you would have a prediction for the next day based upon prior days totals in order to condition the hourly forecast $\endgroup$ – IrishStat Nov 23 '18 at 14:03
  • $\begingroup$ 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) . $\endgroup$ – IrishStat Nov 23 '18 at 17:58
  • $\begingroup$ 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.. $\endgroup$ – IrishStat Nov 23 '18 at 20:38
  • $\begingroup$ Why don't you accept my answer and close the question.,m if you are satisfied.? $\endgroup$ – IrishStat Nov 28 '18 at 22:11

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