Abstract
Difference stationary time series may always be decomposed into, typically unobserved, trend and noise components and doing so leads to the class of unobserved component (UC) models. There are many ways of making such a decomposition and several are considered in this chapter, notably the Muth and Beveridge-Nelson decompositions. It is often important to estimate the unobserved trend and this may be done either by the general technique of signal extraction on assuming a specific ARIMA form for the trend, or by using an “ad hoc” trend filter, such as the Hodrick-Prescott or band-pass filters. The links between these two approaches are established and their relative merits are considered.
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