Tuesday, July 26, 2016

The Forecasting Performance of Models for Cointegrated Data

Here's an interesting practical question that arises when you're considering different forms of econometric models for forecasting time-series data:
"Which type of model will perform best when the data are non-stationary, and perhaps cointegrated?"
To answer this question we have to think about the alternative models that are available to us; and we also have to decide on what we mean by 'best'. In other words, we have to agree on some sort of loss function or performance criterion for measuring forecast quality.

Notice that the question I've posed above allows for the possibility that the data that we're using are integrated, and the various series we're working with may or may not be cointegrated. This scenario covers a wide range of commonly encountered situations in econometrics.

In an earlier post I discussed some of the basic "mechanics" of forecasting from an Error Correction Model. This type of model is used in the case where our data are non-stationary and cointegrated, and we want to focus on the short-run dynamics of the relationship that we're modelling. However, in that post I deliberately didn't take up the issue of whether or not such a model will out-perform other competing models when it comes to forecasting.

Let's look at that issue here.