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

$$z_{ij}=z_{i-1,j}\ s_{i}.$$ (128)

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

$$s_{i}=\frac {Z_{p(i)} }{ Z_{p(i-1)}} .$$ (129)

We denote by $p(i)$ the subscript of the nearest previous day similar to the next one. By $p(i-1)$ we denote the subscript of the nearest previous day similar to the present one. The meaning of "the nearest previous day similar to" is illustrated by following examples.