Vector autoregressive models describe statistical properties of vector time series. Vector autoregressive models generalize the models used in ordinary autoregression.
Consider a vector time series:
| V(1), V(2), … |
In general, vector autoregressive models assume the some functional relation between the current value V(i) and N previous values:
| V(i) = F(V(i–1), V(i–2), …, V(i–N)) + n(i), |
where F() is a vector function of N vector arguments, n(i) is a vector of additive noise. The integer N here is called the order of the autoregressive model.