Daily Vector Prediction

We predict the hourly call rates for the next day. The predicted call rate $z_{ij}$ of the hour $j$ of the next day $i$ is expressed this way

$$z_{ij}=z_{p(i)j}\ s_{i-1}.$$ (138)

Here $z_{p(i)j}$ is the call rate of the hour $j$ of the day preceding the next one and $s_{i-1}$ is a scale of the present day $i-1$. The scales $s_{i-1}$ may differ depending on the impact of SE felt at the day $i$: working day, Saturday, Sunday, Christmas day, marketing day e.t.c.

$$s_{i}=\frac {Z_{i-1} }{ Z_{p(i-1)}} .$$ (139)

We denote by $p(i-1)$ a subscript of the day preceding the present one. Meaning of the term "preceding" is illustrated by the following examples.