Data from the Vector Autoregressive Model with Exogenous Variables (p = 2)

Data from the Vector Autoregressive Model with Exogenous Variables (p = 2)

Usage

dat_p2_exo

Format

A matrix with 1000 rows (time points) and k = 3 (autoregressive variables) plus m = 3 columns (exogenous variables) generated from the p = 2 vector autoregressive model given by $$ Y_{1_{t}} = 1 + 0.4 Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + 0.1 Y_{1_{t - 2}} + 0.0 Y_{2_{t - 2}} + 0.0 Y_{3_{t - 2}} + 0.5 X_{1} + 0.0 X_{2} + 0.0 X_{3} \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + 0.0 Y_{1_{t - 1}} + 0.5 Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + 0.0 Y_{1_{t - 2}} + 0.2 Y_{2_{t - 2}} + 0.0 Y_{3_{t - 2}} + 0.0 X_{1} + 0.5 X_{2} + 0.0 X_{3} \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + 0.0 Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + 0.6 Y_{3_{t - 1}} + 0.0 Y_{1_{t - 2}} + 0.0 Y_{2_{t - 2}} + 0.3 Y_{3_{t - 2}} + 0.0 X_{1} + 0.0 X_{2} + 0.5 X_{3} \varepsilon_{3_{t}} $$ which simplifies to $$ Y_{1_{t}} = 1 + 0.4 Y_{1_{t - 1}} + 0.1 Y_{1_{t - 2}} + 0.5 X_{1} \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + 0.5 Y_{2_{t - 1}} + 0.2 Y_{2_{t - 2}} + 0.5 X_{2} \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + 0.6 Y_{3_{t - 1}} + 0.3 Y_{3_{t - 2}} + 0.5 X_{3} \varepsilon_{3_{t}} . $$ The covariance matrix of process noise is an identity matrix.