Prediction Formulas for Continuous Time Linear Rational Expectations Models
نویسنده
چکیده
l1li' 11' In this note we derive optimal prediction formulas to be used in solving continuous time rational expectations models. In these derivations we employ Laplace transforms in a manner analogous to the use of z transforms for solving discrete time optimal prediction problems in Hansen and Sargent (1980a, Appendix A). The formulas are intended to play the same role for continuous time models that the discrete time formulas for optimal predictions of-geometric distributed leads did in Hansen and Sargent (1980a). 1. Convolutions and Prediction J,et L1 and L2 denote the spaces of all real-valued Borel measurable functions 4>on R that are absolutely integrable and square integrable, respectively. Let W denote a random measure defined on R with increments that are orthogonal and second-moment stationary. In other words,
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