Forecasting times eries with different daily length

Hey everybody!

I’ve been tasked by my company to forecast the amount of phone calls on an hourly basis during the company’s opening hours.

That all went pretty well - until I realized, that my company’s opening hours for phone calls is 9am to 3pm (6 hours total) on Mondays and 9am to 12am (3 hours) the remaining weekdays. That implies that I’ve some sort of “unbalanced” timeseries, because of the three extra hours every Monday.

As I see it that completely destroys my chance of utilizing an ARIMA-model, since the AR and MA terms can’t handle the unbalances.

I’ve been searching for some time now, and I really need some sort of strategy for this problem. My currently “fallback” strategy is to use a normal regression with dummies for every hour. This is however maybe not the best way forward.

So what I’m asking is; maybe you guys have experience with a problem like this, that you would like to share, or maybe some literature on the problem.

I’m currently working in SAS with the timeseries module (SAS ETS), so if you know of any procedure, that would also be much appreciated.



TS Contributor
a dumb question: why not model Mondays separately from the rest of the days? Or, better, have a Monday model, a Friday model and a mid-week model, as I kindof assume Fridays will also he different from the other days even if the opening hours are the same.

Hey Rogojel.

First off - sorry for the mistype in the title. And thanks for the input. Really appreciate it. :)

The short answer; I didn’t really think of that. And I could be a potential solution. The actual situation is that I’m trying to estimate the number of phone calls (on an hourly basis) as a function off letters the company has sent to the customer (amount on a daily basis) in the period up to the given date. The general level of phone calls might be more correlated with the previous days than the previous day of the week.
I’m pretty emptyhanded right now, but I would at least like to give it a try. If the model doesn’t fit the data, then so be it.


TS Contributor
maybe you could first model the total number of calls per day? That would probably be easier. Then, as a second step, model the conditional distribution for a day given that the total number for the day is X and there are Y hours available for a call.