Signal Extraction and the Formulation of Unobserved Components Models

This paper looks at unobserved components models and examines the implied weighting pat- terns for signal extraction. There are three main themes. The first is the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is how setting up models with t- distributed disturbances leads to weighting patterns which are robust to outliers and breaks. The third is a comparison of implied weighting patterns with kernels used in nonparametric trend estimation and equivalent kernels used in spline smoothing. We also examine how weighting patterns are affected by heteroscedasticity and irregular spacing and provide an illustrative example.