Three Equivalent Methods for Filtering Finite Nonstationary Time Series.

To estimate the components in an unobserved autoregressive integrated moving average components model, three different approaches can be used--Kalman filtering plus smoothing, Wiener-Kolmogorov filtering, and penalized least squares smoothing. It is shown, in the article, that the three approaches are equivalent. As an application, it is shown that any of the three approaches can be used to filter a series with the Hodrick-Prescott filter but that Wiener-Kolmogorov filtering should be recommended.