Signal extraction and the formulation of unobserved components models

This paper looks at unobserved components models and examines the implied weighting patterns for signal extraction. There are four main themes. The first concerns the implications of correlated disturbances driving the components, especially those cases in which the correlation is perfect. The second is about the way in which ARIMA-based methods for trend extraction relate to those based on unobserved components. The third explores the impact of heteroscedasticity and irregular spacing and shows how setting up models with t -distributed disturbances leads to weighting patterns which are robust to outliers and breaks. Finally, a comparison is made between implied weighting patterns with kernels used in non-parametric trend estimation and equivalent kernels used in spline smoothing. It is demonstrated that with irregularly spaced data, the weighting used by conventional spline smoothing techniques is not the same as that obtained from the time series model based approach.