# RDP 2013-07: An Empirical BVAR-DSGE Model of the Australian Economy 4. Forecasting

## 4.1 Methodology

The forecasting process for the BVECMX and the Minnesota VAR is as follows. In each case we draw from the joint posterior of the parameters and the variance-covariance matrix of the shocks. Using these simulated parameter values, a vector of shocks is drawn and a realisation of yt+1 is found. We then iterate forward, using the same parameters and repeatedly draw new shocks. To create a forecast density this process is repeated 1,000 times, from which we calculate a mean forecast. As we have demeaned the variables prior to estimation, we add back the mean of the data to obtain the final forecasts.

The BVECMX model requires forecasts of the exogenous variables, namely those of the large economy. As discussed above, in practice these might be sourced from international organisations, such as the IMF, although here we simply generate them using the large economy Minnesota VAR. For simplicity, we use the posterior mean of the VAR parameters, rather than taking into account parameter uncertainty.[26]

## 4.2 Evaluation

To evaluate the forecast performance of the various models we recursively construct out-of-sample forecasts for the period 2006:Q1–2011:Q2, that is, for each quarter, we re-estimate the models before forecasting. The mean of the data over the estimation period is added back into the forecasts, and this may vary over time because of the recursive estimation. This process does not fully recreate the real-time problem faced by forecasters given that we use final, rather than real-time data. We focus on the quarterly forecasts one and two quarters ahead, as well as the year-ended forecasts one and two years ahead, for all variables except the interest rate.[27] We compare the forecasting performance across models primarily by their RMSE and their bias.

## Footnotes

Kadiyala and Karlsson (1997) describe this as the ‘customary’ approach. [26]

Consequently we obtain 22 and 19 one-quarter- and one-year-ahead forecasts. [27]