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Mr. Francis Vitek
This paper considers the problem of jointly decomposing a set of time series variables into cyclical and trend components, subject to sets of stochastic linear restrictions among these cyclical and trend components. We derive a closed form solution to an ordinary problem featuring homogeneous penalty term difference orders and static restrictions, as well as to a generalized problem featuring heterogeneous penalty term difference orders and dynamic restrictions. We use our Generalized Multivariate Linear Filter to jointly estimate potential output, the natural rate of unemployment and the natural rate of interest, conditional on selected equilibrium conditions from a calibrated New Keynesian model.
Mr. Francis Vitek and Ulric Eriksson von Allmen

corresponding univariate filters are 0.918 for the inflation gap, 0.950 for the output gap, 0.972 for the unemployment rate gap, and 0.970 for the interest rate gap. Focusing on material reductions in linear association, sensitivity analysis with respect to the smoothing parameters reveals that adjusting the smoothness of trend inflation only affects the inflation gap estimates, of potential output affects all of the gap estimates, of the natural rate of unemployment only affects the unemployment rate gap estimates, and of the natural rate of interest only affects the