What are the Differences in Trend Cycle Decompositions by Beveridge and Nelson and by Unobserved Component Models?
建立了一个统一框架，将多种趋势-周期分解方法视为特例，并从频域角度比较了BN分解和UC模型等方法的差异，发现仅凭统计标准难以从备选单变量模型中选出最优。
When a certain procedure is applied to extract two component processes from a single observed process, it is necessary to impose a set of restrictions that defines two components. One popular restriction is the assumption that the shocks to the trend and cycle are orthogonal. Another is the assumption that the trend is a pure random walk process. The unobserved components (UC) model (Harvey, 1985 Harvey , A. C. ( 1985 ). Trends and cycles in macroeconomic time series . Journal of Business and Economic Statistics 3 : 216 – 227 .[Taylor & Francis Online], [Web of Science ®] , [Google Scholar]) assumes both of the above, whereas the BN decomposition (Beveridge and Nelson, 1981 Beveridge , S. , Nelson , C. R. ( 1981 ). A new approach to decomposition of economic time series into permanent and transitory components with particular attention to measurement of the Business Cycle . Journal of Monetary Economics 7 : 151 – 174 .[Crossref], [Web of Science ®] , [Google Scholar]) assumes only the latter. Quah (1992 Quah , D. ( 1992 ). The relative importance of permanent and transitory components: Identification and some theoretical bounds . Econometrica 60 : 107 – 118 .[Crossref], [Web of Science ®] , [Google Scholar]) investigates a broad class of decompositions by making the former assumption only. This paper develops a convenient general framework in which alternative trend-cycle decompositions are regarded as special cases, and examines alternative decomposition schemes from the perspective of the frequency domain. We find that, although the conventional UC model is not necessarily a misspecification for describing the postwar U.S. GDP, choosing a univariate model among alternatives on the purely statistical grounds is difficult.