arXiv 27 Jan 2017 · Mathematics — Statistics Theory
arXiv:1701.08149 · PDF · DOI · OpenAlex · Extracted main text
We extend the Granger-Johansen representation theorems for I(1) and I(2) vector autoregressive processes to accommodate processes that take values in an arbitrary complex separable Hilbert space. This more general setting is of central relevance for statistical applications involving functional time series. We first obtain a range of necessary and sufficient conditions for a pole in the inverse of a holomorphic index-zero Fredholm operator pencil to be of first or second order. Those conditions form the basis for our development of I(1) and I(2) representations of autoregressive Hilbertian processes. Cointegrating and attractor subspaces are characterized in terms of the behavior of the autoregressive operator pencil in a neighborhood of one.
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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 | Beare, B.\ K., Seo, J.\ and Seo, W.\ -K (2017) Cointegrated linear processes in Hilbert space self | 1.000 | 8 | 4 | 100% |
| 2 | Franchi, M.\ and Paruolo, P (2018) Cointegration in functional autoregressive processes | 1.000 | 6 | 3 | 100% |
| 3 | Johansen, S (1992) A representation of vector autoregressive processes integrated of order 2 | 0.928 | 4 | 3 | 100% |
| 4 | Hu, B.\ and Park, J.\ -Y (2016) Econometric analysis of functional dynamics in the presence of persistence | 0.843 | 3 | 3 | 100% |
| 5 | Johansen, S (2009) Representation of cointegrated autoregressive processes with application to fractional processes | 0.737 | 3 | 2 | 100% |
| 6 | Johansen, S (1991) Estimation and hypothesis testing of cointegration vectors in Gaussian vector autoregressive models | 0.737 | 3 | 2 | 100% |
| 7 | Gohberg, I., Goldberg, S.\ and Kaashoek, M.\ A (1990) Classes of Linear Operators, Vol.\ 1 | 0.693 | 6 | 3 | 33% |
| 8 | Granger, C.\ W.\ J (1983) Cointegrated variables and error-correcting models | 0.644 | 4 | 1 | 100% |
| 9 | Bosq, D (2000) Linear Processes in Function Spaces | 0.644 | 2 | 2 | 100% |
| 10 | Chang, Y., Hu, B.\ and Park, J.\ -Y (2016) On the error correction model for functional time series with unit roots | 0.644 | 2 | 2 | 100% |
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