# Vector Autoregression (VAR)

## Vector Autoregression (VAR)

### Vector Autoregression (VAR)

We consider a vector of observables, not just one

Autoregressive (AR) model for a vector.

VAR(p) looks \(p\) back.

The AR(\(p\)) model is:

\(y_t=\alpha + \sum_{i=1}^p\beta y_{t-i}+\epsilon_t\)

VAR(\(p\)) generalises this to where \(y_t\) is a vector. We define VAR(\(p\)) as:

\(y_t\)

\(y_t=c + \sum_{i=1}^pA_i y_{t-i}+\epsilon_t\)

### VAR impulse response

### Bayesian VAR

## Structural models

### Autoregressive Distributed Lag (ARDL) model

Include lagged y and lagged x (and current x)