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Predictive Distributions

 

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Compute out-of-sample predictive distributions for the endogenous variables. The distributions can be estimated from the posterior mode values, or from a sample from 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 endogenous variables can either be in their original form or using the annualization data in the data construction file. Conditional forecasts are based on the approach of Waggoner and Zha (1999) by restricting the moments of the shocks over the conditioning sample.

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.

When conditional predictions are calculated for the original variables, then YADA will also compute modesty statistics and write these to text-file.

 

Additional Information

A detailed description about unconditional and conditional predictive distributions for the Bayesian VAR model can be found in Sections 14.5 and 14.6 of the YADA Manual, respectively.
A more detailed description of prediction events and risk analysis is given in Section 12.5.

 

 


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