Estimating VAR models under non-stationarity and cointegration: alternative approaches for forecasting cattle prices

Multivariate VAR models estimated with non-stationary data raise difficult econometric questions because differencing to achieve stationary can introduced distortions into multivariate models. Three approaches have been suggested for estimating such models:(1) Vector error correction (VEC) models difference the data to achieve stationary and use an error correction term to replace the long-run information lost through differencing; (2) VAR models can be estimated with raw data in levels if the non-stationary data is also cointegrated because recent theoretical work proves that estimation with such data will yield consistent parameter estimates; (3) Bayesian parameter estimates are not affected by non-stationarity, although some analysts argue that Bayesian analysis is not appropriate for data that is also cointegrated. A multivariate cattle price model provides a good framework for comparing these approaches because the major variables are both non-stationary and cointegrated, and because the model's optimal lag structure includes long lags. Forecast results for a 58-month horizon indicate that the VAR model generated the lowest mean square errors (MSE), and both the VAR and VEC models outperformed the Bayesian forecasting models. We conclude that the comparison between VAR and VEC depends on the lengths of lags included in the forecasting model, and that Bayesian analysis is not appropriate for cointegrated data.