# Utility systems

`TimeseriesSurrogates.SNLST`

— Function`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:

\[x(t) = k x(t-1) + a(t)\]

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

**References**

`TimeseriesSurrogates.randomwalk`

— Function`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**

`TimeseriesSurrogates.NSAR2`

— Function`NSAR2(n_steps, x₀, x₁)`

Cyclostationary AR(2) process^{[1]}.

**References**

`TimeseriesSurrogates.AR1`

— Function`AR1(; n_steps, x₀, k, rng)`

Simple AR(1) model given by the following map:

\[x(t+1) = k x(t) + a(t),\]

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. `rng`

is a random number generator

`TimeseriesSurrogates.random_cycles`

— Function`random_cycles(; periods=10 dt=π/20, σ = 0.05, frange = (0.8, 2.0))`

Make a timeseries that is composed of `period`

full sine wave periods, each with a random frequency in the range given by `frange`

, and added noise with std `σ`

. The sampling time is `dt`

.

- 1Lucio et al., Phys. Rev. E
*85*, 056202 (2012). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.056202 - 1Lucio et al., Phys. Rev. E
*85*, 056202 (2012). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.056202 - 1Lucio et al., Phys. Rev. E
*85*, 056202 (2012). https://journals.aps.org/pre/abstract/10.1103/PhysRevE.85.056202