# ARMA model for Time Series about volumes? GARCH?

I am trying to do some analysis and forecasting about a Time Series which is about volumes (how many people call to a call center per hour). I have about 2000 observations, in hourly data. I am aware that there are some gaps between hours (i.e. 3am no one calls).

I'd like to model the level of volume but I am doubting with which model to use. From a preliminar analysis I've done, the ACF of the level has clearly some seasonality. I attach a picture of the level and another of the ACF.

I have been thinking quite hard which model can be appropriate but I'm doubting. I'd thought in a Multiplicative Error Model (MEM), some ARMA-type model or a GARCH-type model. However I am very doubtful which is an interesting approach.

I'd really appreciate any suggestion!

Call center traffic exhibits : certainly intra-daily (high traffic during the day, little at night; day traffic will have different patterns depending on whether the call center is a corporate helpdesk or consumer-oriented) and intra-weekly (the weekend will be different from the weekdays). Plus, there may be spikes after new product introductions, or driven by other external or calendar events, or yearly seasonality for other seasons.

ARIMA typically can cope with one type of seasonality, not multiple ones. Plus, it's better with short seasonal cycles. If you have hourly data, then one weekly cycle is 168 observations. ARIMA may have difficulties with this.

I'd rather recommend that you look into forecasting methods that were specifically designed to deal with multiple seasonalities. One good algorithm is implemented in tbats() in the forecast package for R.

Plus, we have quite a few earlier questions and answers on "call center forecasting". I'd recommend you look through them; they may be inspirational.