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I'm currently trying out several ARIMA models for time series data with seasonality.

The data consists of daily demand for two years. The data has strong weekly seasonality since Fridays and Saturdays have much higher values than remaining days.

The data presents also other types of seasonality since summer and Christmas have always higher values.

So, my data shows two types of seasonality. Is it possible to cope with both patterns in the same model?

$$ ARIMA(p,d,q)(p,d,q)_7(p,d,q)_{30} $$

Does the model above makes sense?

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    $\begingroup$ I'm not sure if seasonality of 12 makes sense unless you believe current day can be predicted based on data from 12 days before which is rather unusual. If you want to factor in monthly seasonality, you can simply dummy code the month of the year and pass it on as a regressors. $\endgroup$ – forecaster Nov 29 '15 at 21:02
  • $\begingroup$ Can be done, in principle, but I do not know of canned software which implements it! You must do your own programming. $\endgroup$ – kjetil b halvorsen Nov 29 '15 at 21:04
  • $\begingroup$ @forecaster - thanks for noticing. I've should have written 30 days lag and not 12 months lag. I will edit my post. $\endgroup$ – Eduardo Nov 29 '15 at 21:08
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    $\begingroup$ Ok, 30 days will also be a problem because you have 28 days and 31 days in a month, you could use day of the month and month of the year dummies as a regression variables and capture seasonality. $\endgroup$ – forecaster Nov 29 '15 at 21:37
  • $\begingroup$ @forecaster, using month of the year may not work since the OP says he only has two years of data. Thus he effectively has only two observations of the seasonal effect for each month. Eduardo, Rob J. Hyndman has several useful blog posts about modelling seasonality. His blog is here, you may search for "seasonality" and "TBATS". $\endgroup$ – Richard Hardy Nov 30 '15 at 19:58
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Even with two years of data it is often possible to detect dominant monthly effects ... not by any stepdown method ( often failing due to over-parameterization but by a prospective method requiring tentative model formulation . Incorporating waiting-to-be-discovered effects as Simple method of forecasting number of guests given current and historical data can lead to a useful hybrid model.

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