The purpose of the project
The main scientific objective of the proposal is to evaluate the usefulness of modeling and forecasting macroeconomics phenomena with averaging characteristics of vector autoregressive (VAR) models. This approach concerns model selection, combining forecasts, and impulse response functions based on the whole model space. The additional specific aim of the project is to determine the effectiveness of the proposed method by implementing an automatic averaging approach to VAR models in open source program gretl.
We consider the following research hypothesis:
1. Model selection based on vector autoregressive model averaging is an effective method of identifying the most likely determinants of endogenous variables.
2. The forecasts obtained by the model averaging procedure are an effective approach for vector autoregressive models and generate more accurate predictions than models based on a single specification.
We also consider research problems, which can be described as the following specific hypotheses:
1. Forecasts obtained from the vector autoregressive model outperform when the distribution of the posterior model probabilities is flatter.
2. Impulse response function gives more reliable results when the pooling strategy is considered.
3. Model selection strategy based on posterior inclusion probabilities (for example, the median model) gives better results in terms of forecasting performance.
4. Vector autoregressive models obtained by averaging techniques are more robust than models obtained from a single specification.
The conception of averaging vector autoregressive models is an innovative approach, and there are no automatic procedures ensuring effective techniques dealing with the proposed solution. The innovation occurs in dealing with numerical calculations using automatic model selection techniques for vector autoregressive models. A very large number of variable combinations of competing models requires high computation effort. This will be ensured by using the Message Passing Interface (MPI) parallelization technique and implemented in the procedure of automatic model averaging for VAR models.
The proposal assumes research on a theoretical and numerical conception of averaging estimates of the vector autoregressive model. This approach will allow it to pool information from all potential models and combine information received from a large set of models based on starting specification, not only from one single model.
The used methodology of model averaging is known in the literature but has not been applied and verified to vector autoregressive models in such automatic performance. By using probabilistic methods and solutions, the explanatory calculation power is numerically stable and offers good results for proposed research. The generated forecasts will base on averaging (combining) predictions from all accepted models and weighted by their posterior probabilities. The comparison of forecast accuracy will be provided using classical measures of forecast errors like root mean square forecast error, mean absolute percentage error, Theil's inequality coefficient, and tests comparing competitive forecasts like the Diebold-Mariano test or Hansen's test for Superior Predictive Ability.