arXiv 25 Jun 2020 · Econometrics · publishedThe Annals of Statistics (2022)
arXiv:2006.14179 · PDF · DOI · OpenAlex · Extracted main text
The paper analyses cointegration in vector autoregressive processes (VARs) for the cases when both the number of coordinates, $N$, and the number of time periods, $T$, are large and of the same order. We propose a way to examine a VAR of order $1$ for the presence of cointegration based on a modification of the Johansen likelihood ratio test. The advantage of our procedure over the original Johansen test and its finite sample corrections is that our test does not suffer from over-rejection. This is achieved through novel asymptotic theorems for eigenvalues of matrices in the test statistic in the regime of proportionally growing $N$ and $T$. Our theoretical findings are supported by Monte Carlo simulations and an empirical illustration. Moreover, we find a surprising connection with multivariate analysis of variance (MANOVA) and explain why it emerges.
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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 | Onatski and Wang (2018) Alternative asymptotics for cointegration tests in large vars | 1.000 | 6 | 3 | 100% |
| 2 | Johansen (1988) Statistical Analysis of Cointegrating Vectors | 1.000 | 5 | 4 | 100% |
| 3 | Johansen (1991) Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models | 1.000 | 5 | 4 | 100% |
| 4 | Onatski and Wang (2019) Extreme canonical correlations and high-dimensional cointegration analysis | 1.000 | 5 | 4 | 100% |
| 5 | Gonzalo and Pitarakis (1999) Dimensionality effect in cointegration analysis | 0.811 | 4 | 2 | 100% |
| 6 | Erdos and Yau (2012) Universality of local spectral statistics of random matrices | 0.737 | 4 | 3 | 50% |
| 7 | Bai and Silverstein (2010) | 0.737 | 3 | 3 | 67% |
| 8 | Tao and Vu (2012) Random matrices: the universality phenomenon for Wigner ensembles | 0.737 | 3 | 3 | 67% |
| 9 | Engle and Granger (1987) Co-integration and error correction: representation, estimation, and testing | 0.737 | 3 | 2 | 100% |
| 10 | Johnstone (2008) Multivariate analysis and Jacobi ensembles: largest eigenvalue, Tracy-Widom limits and rates of convergence | 0.659 | 7 | 3 | 29% |
Showing the top 10 of 62 scored citations.
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| 1 | 1cm Inference on common trends in functional time series | 0.811 | 4 | 2 |
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