indep_ar¶
- hyppo.tools.indep_ar(n, lag=1, phi=0.5, sigma=1)¶
2 independent, stationary, autoregressive time series simulation.
\(X_t\) and \(Y_t\) are univarite AR(
1ag
) with \(\phi = 0.5\) for both series. Noise follows \(\mathcal{N}(0, \sigma)\). With lag (1), this is\[\begin{split}\begin{bmatrix} X_t \\ Y_t \end{bmatrix} = \begin{bmatrix} \phi & 0 \\ 0 & \phi \end{bmatrix} \begin{bmatrix} X_{t - 1} \\ Y_{t - 1} \end{bmatrix} + \begin{bmatrix} \epsilon_t \\ \eta_t \end{bmatrix}\end{split}\]