The outstanding ability of Bayesian methods in forecasting has been known since the works of Litterman (1979) and Doan, Litterman, and Sims (1984), but only recently these methods have become widely used thanks to the improvement of computing power. This course aims at providing the basic tools to produce forecasts of financial and macroeconomic data using Bayesian methods.
The Bayesian approach offers three main advantages.
- Particularly well suited in handling very large cross-sections of data, even when the time series available are short.
- Offers a theoretically grounded way to impose judgmental information and a-priori beliefs in the forecasting model.
- Provide a natural environment to produce forecasts of the whole distribution of a time series, i.e. fan charts.
Day 1 – Introduction to Bayesian forecasting
- The Bayesian approach to econometrics – Comparison with the Classical approach
- Posterior simulators
- The univariate linear regression model, estimation via Gibbs sampling
- Forecasting with the classical linear regression model
- GAUSS example: Forecasting US and UK macroeconomic variables
- Density forecasting with the classical linear regression model
- GAUSS example: Fan charts for US and UK inflation
- Bayesian Model Selection
- GAUSS example: selecting a model to forecast UK inflation
Day 2 – Forecasting with large datasets
- Bayesian Vector Autoregressions (BVARs) – Specification and Estimation
- Model and lag selection via marginal likelihood
- Point forecasts with BVARs
- GAUSS example: Forecasting exchange rates using a large panel
- Density forecasting with BVARs
- GAUSS example: Density forecasts of the yield curve
- Priors from macroeconomic and finance theory for VARs
- Efficient programming in GAUSS: the multi-threading approach
- GAUSS example: How to implement multi-threading
Day 3 -Advanced topics
- Markov Chain Monte Carlo Methods
- The Random-Walk Metropolis algorithm
- GAUSS example: RW-Metropolis. Estimation and convergence
- The Independence Metropolis algorithm
- GAUSS example: Independence-Metropolis – Estimation and convergence
- Modelling drifts in volatility. Stochastic volatility models
- GAUSS example: Density forecasts of US and UK inflation
- Bayesian model averaging
- GAUSS example: Forecast averaging with US and UK macro variables