Tobias Hartl, Rolf Tschernig, Enzo Weber
arXiv 11 May 2020 · Econometrics · 1 citations (OpenAlex)
arXiv:2005.05266 · PDF · DOI · OpenAlex · Extracted main text
We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a fractional lag operator into the autoregressive polynomial of the cyclical component. The model allows for an endogenous estimation of the integration order jointly with the other model parameters and, therefore, no prior specification tests with respect to persistence are required. We relate the model to the Beveridge-Nelson decomposition and derive a modified Kalman filter estimator for the fractional components. Identification, consistency, and asymptotic normality of the maximum likelihood estimator are shown. For US macroeconomic data we demonstrate that, unlike $I(1)$ correlated unobserved components models, the new model estimates a smooth trend together with a cycle hitting all NBER recessions. While $I(1)$ unobserved components models yield an upward-biased signal-to-noise ratio whenever the integration order of the data-generating mechanism is greater than one, the fractionally integrated model attributes less variation to the long-run shocks due to the fractional trend specification and a higher variation to the cycle shocks due to the fractional lag operator, leading to more persistent cycles and smooth trend estimates that reflect macroeconomic common sense.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Morley, Nelson \ Zivot (2003) Why are the Beveridge-Nelson and unobserved-components decompositions of GDP so different?, The Review of Economics and Statisti… | 1.000 | 11 | 4 | 100% |
| 2 | Weber (2011) Analyzing U.S. output and the Great Moderation by simultaneous unobserved components, Journal of Money, Credit and Banking 43(8)… self | 1.000 | 9 | 3 | 100% |
| 3 | Johansen (2008) A representation theory for a class of vector autoregressive models for fractional processes, Econometric Theory 24(3): 651–676 | 0.874 | 6 | 2 | 100% |
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| 6 | Hartl \ Weigand (2019) Approximate state space modelling of unobserved fractional components, arXiv:1812.09142, arXiv.org | 0.811 | 4 | 2 | 100% |
| 7 | Hualde \ Robinson (2011) Gaussian pseudo-maximum likelihood estimation of fractional time series models, The Annals of Statistics 39(6): 3152–3181 | 0.811 | 4 | 2 | 100% |
| 8 | Nielsen (2015) Asymptotics for the conditional-sum-of-squares estimator in multivariate fractional time-series models, Journal of Time Series A… | 0.811 | 4 | 2 | 100% |
| 9 | Perron \ Wada (2009) Let's take a break: Trends and cycles in US real GDP, Journal of Monetary Economics 56(6): 749–765 | 0.811 | 4 | 2 | 100% |
| 10 | Harvey \ Trimbur (2003) General model-based filters for extracting cycles and trends in economic time series, The Review of Economics and Statistics 85(… | 0.737 | 3 | 2 | 100% |
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