Choosing the Right Error in Term Structure Models
We study the influence of measurement error specification on estimation results in the context of continuous-time models of the term structure of interest rates. For this purpose, we estimate a two-factor mean-reverting stochastic model of the recent evolution of the Spanish term structure. The model is estimated under a baseline specification where errors are independent both serially and cross-sectionally, and the factors are general (i.e. unobservable), and under various other specifications, where factors are assumed to be observable, or where errors have either serial correlation, cross-sectional correlation, or both. We find that error specification has an important impact on the value of estimated fundamental parameters, i.e. those that define the continuous-time theoretical model. We conclude that the choice of specification may depend on what is the purpose of estimation, whether fitting, prediction, or accurate estimation of significant economic parameters.
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