Fiducial predictive densities and econometric duration analysis - YANG, Zhenlin (Institutional Knowledge at Singapore Management University, 2003)
In this article, we propose using fiducial predictive density (FPD) as a density estimate, which leads naturally to estimators of survivor and hazard functions and provides a simple way of constructing shortest prediction intervals. This approach is studied in detail in the context of two flexible duration models proposed in this paper, namely the trans-normal and trans-exponential families, by presenting the FPDs, their basic properties, their Bayesian correspondence and their applications in econometric duration analysis. Empirical evidences show that the FPD method provides better estimates of survivor and hazard functions, particularly the latter, than does the usual maximum likelihood method. It provides shortest prediction intervals for a future duration, which can be much shorter than the regular equitailed prediction intervals. The trans-normal model has an easy extension to include exogenous variables, whereas the trans-exponential model allows for the analysis of censored data. Finally, when the transformation function is indexed by unknown parameter(s), the FPD method still provides asymptotically correct inference when the transformation parameter is replaced by its estimator.