Editing Forecasting (section)

=== Deterministic approach ===
A deterministic approach is when there is no stochastic variable involved and the forecasts depend on the selected functions and parameters.<ref name=":1">{{Cite journal |last1=Stoop |first1=Ruedi |last2=Orlando |first2=Giuseppe |last3=Bufalo |first3=Michele |last4=Della Rossa |first4=Fabio |date=2022-11-18 |title=Exploiting deterministic features in apparently stochastic data |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=19843 |doi=10.1038/s41598-022-23212-x |issn=2045-2322|doi-access=free |pmid=36400910 |pmc=9674651 |bibcode=2022NatSR..1219843S |hdl=11311/1233353 |hdl-access=free }}</ref><ref>{{Cite journal |last1=Orlando |first1=Giuseppe |last2=Bufalo |first2=Michele |last3=Stoop |first3=Ruedi |date=2022-02-01 |title=Financial markets' deterministic aspects modeled by a low-dimensional equation |journal=Scientific Reports |language=en |volume=12 |issue=1 |pages=1693 |doi=10.1038/s41598-022-05765-z |issn=2045-2322|doi-access=free |pmid=35105929 |pmc=8807815 |bibcode=2022NatSR..12.1693O |hdl=20.500.11850/531723 |hdl-access=free }}</ref> For example, given the function    

:<math>\begin{aligned} f_n(x_t) = \dfrac{1}{(1+x_t^n)} \, , \qquad n \in {\mathbb {N}},\;x\in {\mathbb {R}}. \end{aligned} </math>


The  short term behaviour <math>x_t</math>  and the is the medium-long term trend <math>y_t</math> are 
:<math>
\begin{aligned} {\left\{ \begin{array}{ll} x_{t+1} = \alpha f_n(x_t) + \gamma \, y_t + \delta \\ y_{t+1} = \beta \, y_t - \mu \, x_{t} + \eta  \end{array}\right. } \end{aligned}
</math>

where <math> \alpha, \gamma, \beta, \mu, \eta </math> are some parameters.

This approach has been proposed to simulate bursts of seemingly stochastic activity, interrupted by quieter periods. The assumption is that the presence of a strong deterministic ingredient is hidden by noise. The deterministic approach is noteworthy as it can reveal the underlying dynamical systems structure, which can be exploited for steering the dynamics into a desired regime.<ref name=":1" />