Predictive Distributions

Compute out-of-sample predictive distributions for the observed variables. The distributions can be estimated from the initial parameter and posterior mode values, or from a sample from the prior or the posterior distribution of the parameters. The number of parameters used is in this case determined by the selected maximum number of posterior draws to use for prediction on the posterior sampling frame on the Options tab. The number of simulation paths per parameter value is determined in the forecasting frame on the Miscellaneous tab. Options in the forecasting frame also determine the maximum forecast horizon and if the paths should be adjusted such that their mean value equal the population mean.

Distributions can be estimated for unconditional and conditional predictions. Moreover, the observed variables can either be in their original form, using the annualization data in the data construction file, or using the observed variable transformation functions from the same file. Conditional forecasts are based on direct manipulation of certain structural shocks.

The conditioning information provided in the data construction file via the Z field (see Table 2 for an example) can be influenced by selecting a subset of the conditioning variables and shocks. The former can be achieved from the select conditioning variables function on the Actions menu, while the latter is handled via the select conditioning shocks function on the same menu.

In addition, YADA can calculate prediction events and marginal predictive densities from the predictive distributions. A prediction event is defined from a variable taking a value between an upper and a lower bound for a certain number of periods. YADA can also perform a risk analysis based on the upper and lower bounds for the prediction events, thereby allowing for an assessment of downside and upside risks, as well as the balance of risks; see, e.g., Kilian and Manganelli (2007). The marginal predictive densities are period-specific (e.g., 2001Q2) kernel density estimates of the marginal predictive distribution.

Furthermore, when the observed variables are forecasted in their original form using draws from the prior or posterior distribution, then YADA can perform a decomposition of the forecast error variances into state variable, measurement error, shock, and parameter uncertainty. The decomposition is displayed in terms of their shares of the forecast error variances for the different forecast horizons considered.

When conditional predictions are calculated for the original variables, then YADA will also compute modesty statistics and write the results to a text-file. These results can then be retrieved from the View menu.

Additional Information

•	A more detailed description about prediction using Bayesian techniques can also be found in Section 12 of the YADA Manual.

•	Unconditional predictive distributions for the DSGE model are described in Section 12.1.1, while conditional predictive distributions are discussed in Section 12.2.

•	A more detained description about modesty statistics for the DSGE model is provided in Section 12.3.

•	A more detailed description of prediction events and risk analysis is given in Section 12.5.

•	A more detailed discussion about transformations of the data is provided in Section 17.5.1.

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