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I have much the same problem as predict-the-next-24-hours, I have several years of hourly data of demand, and I would like to predict the next 24 hours.

Ignoring the multi-seasonality issues - is it reasonable to expect the classical methods (ARIMA and ETS), to be able to forecast this much ahead?

I understand that in business scenarios, the ARIMA order is very likely to be $p+q<6$, and ETS can be paralleled with ARIMA models with even smaller p and q.

So - is it true that these models make use of the dynamics of the very last (6 or so) items in the series, and expecting them to forecast the next 24th item amounts to pure speculation? Is it possible that in a scenario like this it's better to simply aggregate the seasonal (weekly/daily) mean demand and just use that and ignore the forecasting models?

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  • $\begingroup$ How much data do you have? How variable / chaotic is your series? $\endgroup$ – user2974951 Oct 3 at 6:46
  • $\begingroup$ @user2974951 - several years, not sure about variability - will check. But my question is in principle, not related to my specific data (does that make sense?) $\endgroup$ – ihadanny Oct 3 at 7:07
  • $\begingroup$ I asked those questions because it depends on the data. If the data is very periodic then you can predict 1000 years ahead (figuratively speaking), and also depends on how much data you have, the more the better because you can potentially learn important patterns. If you are trying to predict 24 hours ahead from only 6 hours of data, that will he hard. $\endgroup$ – user2974951 Oct 3 at 7:38
  • $\begingroup$ stats.stackexchange.com/… contains a number of my responses to hourly data. Some of them may be helpful to you. The problem with simple memory based models ( pure arima i.e.looking back models) is that there may be a fixed effect applicable to each hour. possibly dependent on the day-of-the-week and holidays and perhaps day-of-the-month ....and of course anomalies , changes in levels, changes in trends et al. $\endgroup$ – IrishStat Oct 4 at 15:04
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Yes, there is no problem with ARIMA/ETS with forecasting a full seasonal cycle of 24 data points ahead.

I think you may be misunderstanding the way that ARIMA and ETS deal with seasonality. ARIMA takes period-over-period differences (i.e., looking at the difference of the time series between point $t$ and point $t-24$), and then models this difference using ARIMA. Thus, we don't just look back 6 periods - we may be looking back 6 seasonal periods.

This is actually a very rough approximation to what is actually happening. See here for the actual details.

ETS or exponential smoothing does something similar. In the smoothing formulation, you would have a seasonal shape consisting of 24 (additive or multiplicative) indices, one for every hour of the day. And with every observation, you update only the entry corresponding to the current hour. And again, you can apply this to the separately smoothed level and trend components to get seasonal forecasts. Here is an explanation of seasonal smoothing.

If the daily seasonality is dominant in your series, I would expect SARIMA or ETS forecasts to be quite competitive with more complex approaches that model possible multiple seasonalities. In any case, I would use a seasonal forecast::auto.arima() and forecast::ets() forecast as benchmarks. They will certainly be faster in fitting than forecast::bats() or forecast::tbats().

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