When Form 8655 Reduced 2024

Here we will talk about estimating and using vector autoregressive models. Let's first state a VAR(p) model. Now, P is generic, so we are just using the lag polynomial here, Phi(L). We also know that we can represent the same model as a vector moving average model, and that's achieved by pre-multiplying both sides with the inverse of that lag polynomial. Depending on what we want to do, we are using different representations. So when we are talking about the estimation of the model, what we will use is the vector autoregressive representation. Let us state a VAR(1) model for simplicity, but this will generalize, and we are using a dimension of k equals 2, so two variables. Here's our VAR(1) model: we have one lag of the variables and the error terms. Now, we can write this down as individual equations. So the equation for the first element is going to be y1(t) = α1 + Φ11L + Φ12L + ... + Φ1pL + ε1(t). And the same for y2(t), we're just multiplying out all these matrices. So we have these two individual models which together represent our VAR(1) model. Let's call them A and B. And turns out that A and B can be estimated by OLS if the process is stationary, and you will know about stationarity conditions. One question that arises is how do I know that a VAR(1), so the lag order of 1, is appropriate? Now, basically two ways to go about that. You could either check for the autocorrelation in the residuals. Okay, what you want is that the residual vectors are uncorrelated. If there's autocorrelation, then we increase the lag order iteratively. Or, in addition to that, you could also look at the information criterion. Information criteria formalize a trade-off between the...