1. Adaptive Variable Selection
Model performance for selection, comparison, and combination should be evaluated with respect to specific forecasting goals
In sequential analysis, limitations of Bayesian model probabilities are clear
Marginal model likelihood is product of 1-step forecast densities
Model probabilities eventually degenerate (in practice) to the “wrong” model
Adaptive Variable Selection is a strategy to find sets of ‘useful’ models
Synthetic Gibbs Probabilities based on a model score for a specific objective
Local search strategy over model space to dynamically explore alternatives
Communication with a single representative model

2. Synthetic Example: k-step Forecast Score
Posterior Modal Model: AVS
Posterior Modal Model : BMA
𝜽 𝟏 has a varying effect, while 𝜽 𝟐 is stable

3. Economic Example

4. Economic Example: 12-month Forecast Score
Dominates BMA in 12-month predictive density
Advantage in long-term forecasting over multiple horizons

5. Economic Example: Path Forecasting Score
Maintains short-term predictive performance, improves long-term predictions
Produces realistic forecasts across multiple horizons