Bayesian Analysis of Combining Forecasts

Mean forecasts from professional surveys are often found to outperform most individual responses. However, much fewer studies relate the survey of expert forecasts with alternative weighting schemes. The first chapter estimates the Bayesian weighted average surveyed forecasts from the Survey of Professional Forecasters (SPF) across five target variables: Real Gross Domestic Product Growth (RGDP), Unemployment Rate (UNEMP), Consumer Price Index Inflation Rate (CPI), Three-month Treasury Bill Rate (TBILL) and Ten-year Treasury Bond Rate (TBOND). It introduces a posterior weighting scheme adopting the Bayesian inference method to linear regression. Performances of the Bayesian combined forecast are compared with those single forecasts derived from the standard equally-weighted average and performance-based approaches. The finding suggests that the Bayesian combined forecast produces a superior implication when combining multiple short-term interest rate predictions. The Bayesian forecast combination beats the simple average of multiple inflation, short-term and long-term interest rates forecast series. Given the role of prior knowledge in the Bayesian linear modeling, a forecaster may not neglect the standard combining approaches when estimating a combination of forecasts. Chapter two investigates panelists\u27 unique forecasts and forecast ability differences. The study evaluates differences in individual forecasts from the Bayesian point of view, employing the Bayes Factor (BF) forecast comparison. The mean forecast is a benchmark, where differences between an individual response and the mean forecast potentially tell us whether some forecasters are reliably better than others. The empirical analysis rests on the US SPF, where the samples are point estimates of five target variables: RGDP, UNEMP, CPI, TBILL, and TBOND. The BF indicates equal and unequal predictive ability relative probabilities between the mean and multiple individual forecasts. The statistical test suggests evidence in favor of the alternative hypothesis. Forecasting performances of experts in the survey differ from one another across target variables. Panelists\u27 unique forecasts and forecast ability differences are more often found in the set of CPI, TBILL, and TBOND individual forecasts than in the RGDP and UNEMP series. The ability differences confirm the non-dominant CPI, TBILL, and TBOND mean forecasts found in the first chapter. The third chapter estimates the relationship between mortgage restructures and borrowers\u27 family characteristics incorporating the standard binary response models using Probit, Logit, and Cauchit link functions together with the Gosset and the Pregibon link families. The finding suggests that the Gosset model outperforms Probit specification, while the Pregibon outperforms Logit specification. The restructuring probability increases with the number of children and family heads widowed, separated, or divorced. According to the sample, family heads looking for a job, relying on a workfare program, or with disabilities are also more likely to restructure the loan