Data from the Vector Autoregressive Model (p = 1)
Format
A matrix with 1000 rows (time points) and k = 3 columns (variables) generated from the p = 1 vector autoregressive model given by $$ Y_{1_{t}} = 1 + 0.4 Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + 0.0 Y_{1_{t - 1}} + 0.5 Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + 0.0 Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + 0.6 Y_{3_{t - 1}} + \varepsilon_{3_{t}} $$ which simplifies to $$ Y_{1_{t}} = 1 + 0.4 Y_{1_{t - 1}} + \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + 0.5 Y_{2_{t - 1}} + \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + 0.6 Y_{3_{t - 1}} + \varepsilon_{3_{t}} . $$ The covariance matrix of process noise is an identity matrix.