nonlinear_process, lag=1, phi=1, sigma=1)

2 nonlinearly dependent time series simulation.

\(X_t\) and \(Y_t\) are together a bivariate nonlinear process. Noise follows \(\mathcal{N}(0, \sigma)\). With lag (1), this is

\[\begin{split}\begin{bmatrix} X_t \\ Y_t \end{bmatrix} = \begin{bmatrix} \phi \epsilon_t Y_{t - 1} \\ \eta_t \end{bmatrix}\end{split}\]
  • n (int) -- The number of samples desired by the simulation (>= 3).

  • lag (float, default: 1) -- The maximum time lag considered between x and y.

  • phi (float, default: 1) -- The AR coefficient.

  • sigma (float, default: 1) -- The variance of the noise.


x,y (ndarray) -- Simulated data matrices. x and y have shape (n,) where n is the number of samples.

Examples using