Compute out-of-sample predictive distributions for the observed variables via a DSGE-VAR model The distributions can be estimated from the initial parameter, the marginal/joint/DSGE posterior mode values, or from a sample from the prior or the posterior distribution of the parameters. The number of parameters used for the posterior distribution case is 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. 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.
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 can be based on:
1. | direct manipulation of certain structural shocks; |
2. | by using the approach of Waggoner and Zha (1999) by restricting the moments of the structural shocks over the conditioning sample; or |
3. | a combination of these two approaches. |
The third method means that a subset of all the shocks, conditional on the remaining shocks, has a distribution such that the conditioning assumptions are satisfied, while the remaining shocks have their usual distribution.
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 (when using the direct manipulation approach). 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 DSGE-VAR menu item View. For the conditional predictions, YADA also allows the user to add a small number to the upper and subtract the same number from the lower bound. This solves an issue with the patch function for HG2 graphics in matlab (default graphics engine since version 2014b), where the case when the upper and lower bounds coincide may lead to erroneously plotted bounds.
In the case of unconditional forecasts, 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 (T+h forecasts only) and the joint (T+1,T+2,...T+h forecasts). The predictive likelihood can, for example, be used to select between models in an out-of-sample forecasting comparison. The user can choose between fixed parameter calculcations and Monte Carlo integration. In addition, the fixed parameters cases (initial parameter values and posterior mode values) can focus on a plug-in estimate of the predictive likelihood and a Laplace approximation esitimate. Monte Carlo integration is either based on the prior or the posterior parameter draws. The estimator of the predictive likelihood in these cases have an importance sampling interpretation.
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, as well as the stationary predictive variances and their decomposition into shock and parameter uncertainty. The stationary predictive variance is computed from the steady-state of the observed variables. This means that parameter uncertainty is constant over the full prediction horizon since the steady-state point forecast is the steady-state.
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-VAR model are described in Section 16.8. |
• | Conditional predictive distributions for the DSGE-VAR are discussed in Section 16.9. |
• | A more detailed description of prediction events and risk analysis is given in 12.5. |
• | Additional details on the predictive likelihood are provided in Sections 12.6 and 16.10. |
• | A more detailed discussion about transformations of the data is provided in Section 18.5.1. |
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