Data from the Multilevel Vector Autoregressive Model (p = 2)
Source:R/fitAutoReg-dat-ml-p2.R
dat_ml_p2.RdData from the Multilevel Vector Autoregressive Model (p = 2)
Format
A list of length n = 100 consisting of matrices with 1000 rows (time points) and k = 3 columns (variables) generated from the p = 2 multilevel vector autoregressive model given by $$ Y_{1_{t}} = 1 + \mathcal{N} \left( \mu = 0.4, \sigma^2 = 0.01 \right) Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + \mathcal{N} \left( \mu = 0.1, \sigma^2 = 0.01 \right) Y_{1_{t - 2}} + 0.0 Y_{2_{t - 2}} + 0.0 Y_{3_{t - 2}} + \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + 0.0 Y_{1_{t - 1}} + \mathcal{N} \left( \mu = 0.5, \sigma^2 = 0.01 \right) Y_{2_{t - 1}} + 0.0 Y_{3_{t - 1}} + 0.0 Y_{1_{t - 2}} + \mathcal{N} \left( \mu = 0.2, \sigma^2 = 0.01 \right) Y_{2_{t - 2}} + 0.0 Y_{3_{t - 2}} + \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + 0.0 Y_{1_{t - 1}} + 0.0 Y_{2_{t - 1}} + \mathcal{N} \left( \mu = 0.6, \sigma^2 = 0.01 \right) Y_{3_{t - 1}} + 0.0 Y_{1_{t - 2}} + 0.0 Y_{2_{t - 2}} + \mathcal{N} \left( \mu = 0.3, \sigma^2 = 0.01 \right) Y_{3_{t - 2}} + \varepsilon_{3_{t}} $$ which simplifies to $$ Y_{1_{t}} = 1 + \mathcal{N} \left( \mu = 0.4, \sigma^2 = 0.01 \right) Y_{1_{t - 1}} + \mathcal{N} \left( \mu = 0.1, \sigma^2 = 0.01 \right) Y_{1_{t - 2}} + \varepsilon_{1_{t}} , $$ $$ Y_{2_{t}} = 1 + \mathcal{N} \left( \mu = 0.5, \sigma^2 = 0.01 \right) Y_{2_{t - 1}} + \mathcal{N} \left( \mu = 0.2, \sigma^2 = 0.01 \right) Y_{2_{t - 2}} + \varepsilon_{2_{t}} , $$ and $$ Y_{3_{t}} = 1 + \mathcal{N} \left( \mu = 0.6, \sigma^2 = 0.01 \right) Y_{3_{t - 1}} + \mathcal{N} \left( \mu = 0.3, \sigma^2 = 0.01 \right) Y_{3_{t - 2}} + \varepsilon_{3_{t}} . $$ The covariance matrix of process noise is an identity matrix.