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I am new to time series analysis. I have hourly electricity demand data for five years (having multiple seasonalities at intra-daily, intra-weekly, and annual periodicities) and I want to guess the number of AR and MA terms using ACF and PACF. Please advice me how to remove seasonalities and guess the AR and MA terms.

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Standard ARIMA can only deal with a single seasonality, by taking seasonal differences. You might be able to work with multiple seasonal differences at different lags, but

  1. I have never seen this approach used by serious forecasters, which predisposes me to think it's not a good idea
  2. I personally think it's not a good idea, because it turns into a mess
  3. I don't know of any software that implements multiple-seasonal ARIMA

I'd much rather recommend you look at BATS or TBATS models, which are based on exponential smoothing. The tag wiki for the tag contains pointers to literature. This earlier question and previous posts containing "BATS" may be useful.

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