Solving and analyzing DSGE models in the frequency domain

I solve multivariate linear rational expectations models in the frequency domain using the generalized Schur decomposition, providing a numerical implementation suitable for standard DSGE estimation and analysis procedures. This approach generalizes the time domain restriction of autoregressive-moving average exogenous driving forces to arbitrary covariance stationary processes. Applied to the standard New Keynesian model, I find that a Bayesian analysis favors a single parameter log harmonic function of the lag operator over the usual AR(1) assumption as it generates hump shaped autocorrelation patterns more consistent with the data.