A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models

This paper conducts a computational analysis of several specifications of the affine term structure model (ATSM) to explore the tradeoff between estimation when parameter restrictions are imposed and computational burdens are simplified and estimation in the absence of parameter restrictions and the economic implications of the findings are able to be generalized. We measure the effects of this tradeoff using distance measures constructed from histograms containing data corresponding to important components of the state space model formulation for the ATSM generated from simulation analyses. In estimating each specification, we optimize the log-likelihood function for the underlying state space model using the Kalman filter (KF). We find that the introduction of parameter restrictions bolsters the variability in its computation by introducing complex parameter dependencies (e.g., higher order exponents, exponentiation, logarithms, logarithms of higher order exponents) that are difficult to interpret. For conditional moments, the introduction of parameter restrictions reduces the complexity of the parameter dependencies and this reduces the variability in its computation. Finally, we connect these insights obtained from the simulation analyses to the application of the KF using market data and perform consistency tests on each state space model to demonstrate the accuracy of the application of the KF. Suggestions for future research are provided.