Discrete-time implementation of continuous-time filters with application to regime-switching dynamics estimation

This paper details the implementation in discrete time of filters for a mean-reverting model formulated under a continuous-time framework, whereby a hidden Markov chain governs the model's parameters. Parameter estimates are determined via adaptive filters designed to extract hidden information from an observable time series. An application involving the dynamic behaviour of spot interest rates is considered. More specifically, we present an empirical study aimed at capturing accurately, on the basis of some benchmarks and statistical validation, the evolution of three country-specific rates in the European zone. Our analysis reveals some similar yield-rate and risk characteristics as well as independent market behaviours of the three EU sovereign states.