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Predictive Distributions

 

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Compute out-of-sample predictive distributions for the observed variables. The distributions can be estimated from the initial parameter values, the DSGE posterior mode, the posterior mode values and the posterior darws. 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.

The predictive distributions depend on the assumption regarding updating of beliefs. By default, YADA does not update beliefs and therefore follows the prescription of the learning literature. It is possible to change this behavior by removing the check-mark on the option "Use fixed beliefs for projections" on the Learning 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.

It is also possible to focus on the calculation of the predictive likelihood for any subset of the observed variables and the choice between the marginal forecasts (T+h only) and the joint forecasts (T+1,T+2,...T+h) using the prior or the posterior draws. Furthermore, for the unconditional forecasts and the original data, it is also possible to compute the marginal predictive moments using the prior or the posterior draws. The probability integral transform (PIT) can be computed based on the marginal predictive moments conditional on the parameters using the posterior draws. Optionally, one can also compute these statestimation.istics based on the simulated paths from the unconditional forecasts.

The continuous ranked probability score (CRPS) for individual observed variables and the energy score (ES) for a joint set of variables can be estimated via simulated paths for the unconditional forecasts based on the prior or the posterior draws. These scores cover marginal forecast horizons and are both proper scoring rules. In contrast to the log predictive score, which uses the log predictive likelihood (predicted density evaluated at observed value) only, the CRPS and ES are not local scoring rules. For further details on scoring rules, see Gneiting and Raftery (2007).

The zero lower bound is supported for the adaptive learning case. The unconditional forecasts using the prior or the posterior draws can be estimated, as well as the predictive likelihood and the CRPS/ES statistics.

 

Additional Information

A more detailed description about prediction using Bayesian techniques can also be found in Section 12 of the YADA Manual.
Forecasting under adaptive learning is discussed in Section 17.11 of the YADA Manual.
The zero lower bound under adaptive learning is presented in Section 17.12 of the YADA Manual.

 

 


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