Brendan K. Beare, Massimo Franchi, Phil Howlett
arXiv 3 Feb 2024 · Econometrics · publishedQuantitative Economics (2026)
arXiv:2402.01966 · PDF · DOI · OpenAlex · Extracted main text
We provide a complete description of the set of all solutions to an autoregressive law of motion in a finite-dimensional complex vector space. Every solution is shown to be the sum of three parts, each corresponding to a directed flow of time. One part flows forward from the arbitrarily distant past; one flows backward from the arbitrarily distant future; and one flows outward from time zero. The three parts are obtained by applying three complementary spectral projections to the solution, these corresponding to a separation of the eigenvalues of the autoregressive operator according to whether they are inside, outside or on the unit circle. We provide a finite-dimensional parametrization of the set of all solutions.
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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 | Gregoir, Stéphane (1999) Multivariate time series with various hidden unit roots, part I: Integral operator algebra and representation theory | 0.874 | 6 | 2 | 100% |
| 2 | Banerjee, Sudipto, and Anindya Roy (2014) Linear Algebra and Matrix Analysis for Statistics | 0.737 | 3 | 2 | 100% |
| 3 | Gouriéroux, Christian, and Jean-Michel Zakoïan (2017) Local explosion modelling by non-causal process | 0.737 | 3 | 2 | 100% |
| 4 | Hamilton, James D.\ (1994) Time Series Analysis | 0.737 | 3 | 2 | 100% |
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| 6 | Hansen, Peter R.\ (2005) Granger's representation theorem: A closed form expression for $I(1)$ processes | 0.693 | 6 | 1 | 100% |
| 7 | Hansen, Bruce E.\ (2022) Econometrics | 0.693 | 6 | 1 | 100% |
| 8 | Axler, Sheldon (2024) Linear Algebra Done Right | 0.644 | 2 | 2 | 100% |
| 9 | Eddington, Arthur S.\ (1929) The Nature of the Physical World | 0.644 | 2 | 2 | 100% |
| 10 | Franchi, Massimo, and Paolo Paruolo (2019) A general inversion theorem for cointegration self | 0.644 | 2 | 2 | 100% |
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