Hierarchical Bayes methodology for improving estimation: Applications to demand forecasting and portfolio analysis

This dissertation focuses on resolving two practical problems using hierarchical Bayes methodologies. It presents the statistical issues raised from two business problems, develops frameworks and models to address these issues, followed by empirical results. The first part of the work (Chapters 2 & 3) focuses on the issue of demand forecasting in the seasonal apparel industry, where little information on consumer demand is available before the beginning of a sales season. In this industry, the key to reducing inventory costs due to markdowns and stockouts is the ability to adjust the order quantity based on newly arrived market information. The statistical problem addressed here is to update the forecast for demand by efficiently incorporating information from new market orders, macro-level aggregate demand and experts' beliefs. Several demand estimation approaches are discussed, and empirical results on their performances are presented. The second part of the work (Chapters 4 & 5) focuses on improving portfolio performance using Bayesian shrinkage estimation. The performance of a portfolio depends on the behavior of the underlying set of assets. Parameters describing the behavior of the portfolio include the expected returns of the set of assets and the covariance structure of the set of assets given that asset returns are normally distributed. The statistical problem addressed here is to reduce errors in the estimation of the expectation and covariance structure of asset returns. Portfolio strategies derived from improved parameter estimates lead to superior investment decisions. Several ways of estimating the parameters are discussed. The double-shrinkage methods that shrink both the mean and the covariance matrix, consistently yield superior performance over other estimation approaches. It also results in more stable and efficient portfolio allocations. In summary, we first identify two important practical problems where improving estimation accuracy is essential. Then, we develop theoretical frameworks to address the issues. Next, empirical results are provided to validate the proposed models. Lastly, hierarchical Bayes estimation is the key and also serves as the link between the two parts of this dissertation.