Three equivalent methods for filtering finite nonstationary time series

To estimate the components in an unobserved autoregressive integrated movin g average components model, three different approaches can be used-Kalman f iltering plus smoothing, Wiener-Kolmogorov filtering, and penalized least s quares 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 W iener-Kolmogorov filtering should be recommended.