Definition of Special Events

Suppose that call rate in the next period (see expression (2.52) will be the same as in the present one multiplied by the scale $s_i$ of Special Event (SE) which is expected to be active in the next period. The periods where no special events are active we consider as periods with "neutral" special events. The scale $s_i$ determines the impact of special event to the call rate $z_i$ of next period.

The scale $s_i$ reflecting the impact of special event is estimated using empirical data (see expressions (2.53), (2.56)) and/or expert opinion. The impact of some special events such as Saturdays, Sundays, holidays, Christmas week e.t.c.. is well defined and instant. We denote them as Instant Special Events (ISE).

The impact of some others such as marketing messages is delayed, because the call rate reacts to these events with some delay. We denote them as Delay Special Events (DSE). The starts and the durations of DSE are fixed. The delay times $d$ and the durations $\tau$ of DSE impacts are estimated using the observed data and expert knowledge.

In some periods several DSE may be active simultaneously. We call such cases as the Multiple Special Event (MSE).

The starts and the durations of ISE and their impacts are defined as the starts and durations of the corresponding periods. The starts and the durations of DSE impacts are not necessarily equal to the starts and durations of the periods. This way a special sort of DSE appear that we shall call as the Partial Special Event (PSE) in the sense that the impact of that SE is active only during some part of the corresponding period. The delay times $d$ and durations $\tau$ of the impacts of DSE as well the scales $s$ defining the impact of all the special events are estimated using the available data and the expert knowledge.