Long Memory Models to Generate Synthetic Hydrological Series

Table 1

Variables to negative sequence analysis.

Random variable	Description	Calculus
Sequence length	Corresponds to the length of the intervals (𝑡1−𝑡2) and (𝑡3−𝑡4)	𝐶=(𝑡2−𝑡1)
Sequence sum	Corresponds to the area below the limit during the sequence. In the previous figure, it is equivalent to the areas 𝐴1 and 𝐴2	𝑆=∑^𝑡2𝑖=𝑡1(𝑍𝑖−𝜇𝑖)
Sequence intensity	Corresponds to the average value below the limit, that is, to the sequence sum divided by the respective sequence length	𝑆𝐼=𝐶=∑^𝑡2𝑖=𝑡1(𝑍𝑖−𝜇𝑖)(𝑡2−𝑡1)

Source: [25].