Dimensionality Reduction and State Space Systems: Forecasting the US Treasury Yields Using Frequentist and Bayesian VARs

Abstract

Using a state-space system, I forecasted the US Treasury yields by employing frequentist and Bayesian methods after first decomposing the yields of varying maturities into its unobserved term structure factors. Then, I exploited the structure of the state-space model to forecast the Treasury yields, and compared the forecast performance of each model using the metric - mean squared forecast error, as the loss function. Among the frequentist methods, I applied the two-step Diebold-Li, two-step principal components, and one-step Kalman filter approaches. Likewise, I imposed the five different priors in Bayesian VARs -Diffuse, Minnesota, natural conjugate, independent normal inverse-Wishart, and the stochastic search variable selection priors. After forecasting the Treasury yields for 9 different forecast horizons, I found that the BVAR with Minnesota prior generally minimizes the loss function. I augmented the above BVARs by including macroeconomic variables and constructed impulse response functions with a recursive ordering identification scheme. Finally, I fitted a sign-restricted BVAR with dummy observations.