Non-Linear Kalman Filtering Techniques for Term-Structure Models

The state space form is a useful framework for estimating Markovian term-structure models with unobserved state variables. In this paper, we consider an econometric method which accommodates non-linearity in the measurement equation, for example when estimating exponential-a ne models using prices of coupon bonds. The ltering algorithm is known as the iterative, extended Kalman lter (IEKF), and the model parameters are estimated by quasi maximum likelihood (QML), based on predictions errors obtained from the IEKF recursions. While, in general, the QML estimator is inconsistent, a Monte Carlo study demonstrates that the biases are very small, and economically insigni cant, in sample con gurations that are representative of real-world data. The main contribution of the paper is a detailed account of an e cient computer implementation of the QML-IEKF technique. In this process, we calculate general expressions for the analytical derivatives of the log-likelihood function and the IEKF recursions, including the update step which is only de ned implicitly as the solution to a non-linear GLS problem.