Examples of PSE

Suppose that the only difference from the previous example is that impact of "marketing" starts at the second working hour of the present Monday $i-1$. Let us regard PSE as a special sort of SE and define its scale as

$$s_{i-1}=\frac {z_{i-1} }{ z_{p(i-1)}} .$$ (144)

where $p(i-1)$ is the index of the day preceding the present one.

Another way is to regard the impact of PSE by decreasing the marketing impact $s_{i-1}$ in proportion to the duration of the impact

$$s^{2}_{i-1}=1/4 \ s_{i-1} .$$ (145)

Here

$$s_{i-1}=\frac {z_{p^3(i-1)} }{ z_{p(p^3(i-1))}} .$$ (146)

where $p^3(i-1)$ is the index of the preceding marketing Monday and $p(p^3(i-1))$ is the index of the day preceding $p^3(i-1)$.

The expression (2.85) needs less data but is based on the assumption that scales are proportional to the impact duration, what is obviously not true. The expression (2.85) involves expert opinion indirectly by assuming the proportionality of scales.

The expression (2.84) is an example of empirical approach when a PSE is regarded as a different special event.