Bayesian smoothing spline with dependency models

Abstract

The smoothing spline model is widely used for fitting a smooth curve because of its flexibility and smoothing properties. Our study is motivated by estimating the long-term trend of the U.S. unemployment level. In this dissertation, a class of Bayesian smoothing spline with dependency models is developed. The unemployment level and other labor-force time series, which are often used to analyze market and economic conditions, are strongly in uenced by seasonality, as well as irregular or short-term fluctuations. We apply the basic Bayesian smoothing spline model to obtain the smooth estimation of the trend from a time series, which captures the fundamental tendency of general economic expansions and contractions. We further generalize the basic Bayesian smoothing spline model with dependence structure. This generalization significantly improves the boundary performance and elevates the overall accuracy and precision by borrowing information from different cycles. Finally, we construct the multivariate Bayesian smoothing spline with dependency model, which enables us to estimate the trends of the unemployment and employment level simultaneously. The accuracy and precision are improved by the joint model.