Example processes

SNLST(n_steps, x₀, k)

Dynamically linear process transformed by a strongly nonlinear static transformation (SNLST)^[1].

Equations

The system is by the following map:

with the transformation $s(t) = x(t)^3$.

References

randomwalk(n_steps, x₀)

Linear random walk (AR(1) process with a unit root)^[1]. This is an example of a nonstationary linear process.

References

NSAR2(n_steps, x₀, x₁)

Cyclostationary AR(2) process^[1].

References

AR1(n_steps, x₀, k)

Simple AR(1) model with no static transformation^[1].

Equations

The system is given by the following map:

where $a(t)$ is a draw from a normal distribution with zero mean and unit variance. x₀ sets the initial condition and k is the tunable parameter in the map.

References