James A. Duffy, Jerome R. Simons
arXiv 19 Feb 2020 · Econometrics · 1 citations (OpenAlex)
arXiv:2002.08092 · PDF · DOI · OpenAlex · Extracted main text
It has been known since Elliott (1998) that standard methods of inference on cointegrating relationships break down entirely when autoregressive roots are near but not exactly equal to unity. We consider this problem within the framework of a structural VAR, arguing this it is as much a problem of identification failure as it is of inference. We develop a characterisation of cointegration based on the impulse response function, which allows long-run equilibrium relationships to remain identified even in the absence of exact unit roots. Our approach also provides a framework in which the structural shocks driving the common persistent components continue to be identified via long-run restrictions, just as in an SVAR with exact unit roots. We show that inference on the cointegrating relationships is affected by nuisance parameters, in a manner familiar from predictive regression; indeed the two problems are asymptotically equivalent. By adapting the approach of Elliott, M\"uller and Watson (2015) to our setting, we develop tests that robustly control size while sacrificing little power (relative to tests that are efficient in the presence of exact unit roots).
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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 | Lütkepohl, H (2007) New Introduction to Multiple Time Series Analysis | 0.644 | 3 | 2 | 67% |
| 2 | Johansen, S (1995) Likelihood-based Inference in Cointegrated Vector Autoregressive Models | 0.511 | 2 | 2 | 50% |
| 3 | Stewart, G. W. and J.-g. Sun (1990) Matrix Perturbation Theory | 0.511 | 2 | 1 | 100% |
| 4 | Gohberg, I., S. Lancaster, and L. Rodman (1982) Matrix Polynomials | 0.405 | 1 | 1 | 100% |
| 5 | Hall, P. and C. C. Heyde (1980) Martingale Limit Theory and Its Application | 0.405 | 1 | 1 | 100% |
| 6 | Lang, S (1993) Real and Functional Analysis | 0.405 | 1 | 1 | 100% |
| 7 | Phillips, P. C. B (1988) Regression theory for near-integrated time series | 0.405 | 1 | 1 | 100% |
| 8 | Horn, R. A. and C. R. Johnson (2013) Matrix Analysis | 0.000 | 2 | 1 | 0% |
| 9 | Elliott, G., U. K. Müller, and M. W. Watson (2015) Nearly optimal test when a nuisance parameter is present under the null hypothesis | 0.000 | 1 | 1 | 0% |
Showing the top 9 of 9 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Uniform Inference For Cointegrated Vector Autoregressive Processes | 0.511 | 2 | 1 |
| 2 | Hypothesis testing on invariant subspaces of non-diagonalizable matrices with applications to network statistics | 0.000 | 2 | 2 |