Examples of PSE

The only difference from the previous example is that impact of "marketing" starts at the sixth working hour of the next day $i$. Let us regard PSE as a special sort of SE and define its scale as

$$s_i=\frac {Z_{p(i)}}{Z_{p(i-1)}}.$$ (134)

Here $p(i)$ is the subscript of the most recent previous week when the "marketing" starts on Tuesday at the sixth working hour. $p(i-1)$ is the subscript of the most recent previous Monday with no marketing.

Another way is to regard the impact of PSE is by decreasing the marketing scale $s_i$ in proportion to the duration of the impact

$$s^{6}_i=1/4 \ s_i .$$ (135)

Here

$$s_i=\frac {Z_{p(i)} }{Zz_{p(i-1)}},$$ (136)

where $p(i)$ is the subscript of the most recent previous week when the "marketing" starts at the sixth hour on Tuesday and $p(i-1)$ is the subsript of the most recent previous Monday with no marketing.

Expression (2.74) is an example of empirical approach when a PSE is regarded as a different special event. Expression (2.75) needs less data but is based on an expert assumption that scales are proportional to the impact duration.