# Irregular Seasonality in time series

I understand seasonality of a time series normally means a cyclic component with constant frequency. For example, the frequency is 24 for daily cyclic trend of hourly data. One of the basic models for a seasonal time series should be Seasonal ARIMA.

However, if the seasonality is somewhat irregular and the data about that irregularity is given, I think there is better model than Seasonal ARIMA. ARIMA model can not utilize that information about irregularity.

For example, if the business hour of a restaurant is regular (say 11am to 8pm), Seasonal ARIMA model might be able to forecast the hourly sales of the restaurant with ARIMA(p,d,q)(P,D,Q)_24.

However, if their business hour is irregular day by day (say 10:30am-9pm today and 12am-5pm tomorrow...) and the business hours for each day is given to the modeler, I guess some other model which can deal with those irregular business hours is more useful than ARIMA.

Are there some models which can deal with such kind of irregular seasonality?

• Irregular hours might be an indication that the underlying pattern is different on those days -- e.g. people don't get up early for breakfast on Sunday, so they don't open until noon. If the underlying patterns are different, you don't want to assume they are the same. One way to approach this would be to model Monday-Friday, Saturday, and Sunday as 3 different models (assuming you see three different patterns). – zbicyclist Dec 3 '15 at 13:04
• @zbicyclist Thank you, but there is not such a pattern you mentioned. The business hour is totally random. However, the business hours before tomorrow are given That's why the model dealing with the random seasonality seems suitable for this problem. – rkjt50r983 Dec 3 '15 at 13:16