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A well-documented property of the Beveridge–Nelson trend–cycle decomposition is the perfect negative correlation between trend and cycle innovations. We show how this may be consistent with a structural model where permanent innovations enter the cycle or transitory innovations enter the trend, and that identification restrictions are necessary to make this structural distinction. A reduced-form unrestricted version is compatible with either option, but cannot distinguish which is relevant. We discuss economic interpretations and implications using U.S. real GDP data.

We empirically analyze the trend characteristics of per capita CO 2 emissions in OECD countries from 1971 to 2009. We use a statistically robust procedure, which is valid regardless of whether per capita CO 2 emissions are trend stationary or contain a stochastic trend, to test for the presence of a deterministic trend and a structural break in the trend. Our results suggest that the trend in per capita CO 2 emissions shifts downward or is reversed for a number of OECD countries either after the 1970s oil shocks or during the early-to mid-2000s. JEL classication: C12, Q53

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits nonzero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

Economists typically use seasonally adjusted data in which the assumption is imposed that seasonality is uncorrelated with trend and cycle. The importance of this assumption has been highlighted by the Great Recession. The paper examines an unobserved components model that permits non-zero correlations between seasonal and nonseasonal shocks. Identification conditions for estimation of the parameters are discussed from the perspectives of both analytical and simulation results. Applications to UK household consumption expenditures and US employment reject the zero correlation restrictions and also show that the correlation assumptions imposed have important implications about the evolution of the trend and cycle in the post-Great Recession period.

This paper places the data revision model of Jacobs and van Norden (2011) within a class of trend-cycle decompositions relating directly to the Beveridge-Nelson decomposition. In both these approaches identifying restrictions on the covariance matrix under simple and realistic conditions may produce a smoothed estimate of the underlying series which is more volatile than the observed series.JEL classification: C22, C53, C82

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SummaryWe propose a state space modeling framework to evaluate a set of forecasts that target the same variable but are updated along the forecast horizon. The approach decomposes forecast errors into three distinct horizon-specific processes, namely, bias, rational error and implicit error, and attributes forecast revisions to corrections for these forecast errors. We derive the conditions under which forecasts that contain error that is irrelevant to the target can still present the second moment bounds of rational forecasts. By evaluating multi-horizon daily maximum temperature forecasts for Melbourne, Australia, we demonstrate how this modeling framework analyzes the dynamics of the forecast revision structure across horizons. Understanding forecast revisions is critical for weather forecast users to determine the optimal timing for their planning decision.JEL classification: C32; C53