arXiv 15 Feb 2022 · Econometrics · publishedThe Review of Economics and Statistics (2024) · 3 citations (OpenAlex)
arXiv:2202.07150 · PDF · DOI · OpenAlex · Extracted main text
The paper studies nonstationary high-dimensional vector autoregressions of order $k$, VAR($k$). Additional deterministic terms such as trend or seasonality are allowed. The number of time periods, $T$, and the number of coordinates, $N$, are assumed to be large and of the same order. Under this regime the first-order asymptotics of the Johansen likelihood ratio (LR), Pillai-Bartlett, and Hotelling-Lawley tests for cointegration are derived: the test statistics converge to nonrandom integrals. For more refined analysis, the paper proposes and analyzes a modification of the Johansen test. The new test for the absence of cointegration converges to the partial sum of the Airy$_1$ point process. Supporting Monte Carlo simulations indicate that the same behavior persists universally in many situations beyond those considered in our theorems. The paper presents empirical implementations of the approach for the analysis of S$&$P$100$ stocks and of cryptocurrencies. The latter example has a strong presence of multiple cointegrating relationships, while the results for the former are consistent with the null of no cointegration.
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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 | A. Bykhovskaya and V. Gorin (2022) Cointegration in large vars | 1.000 | 18 | 11 | 100% |
| 2 | P. J. Forrester (2010) Log-gases and random matrices | 1.000 | 8 | 4 | 100% |
| 3 | I. Johnstone (2008) Multivariate analysis and jacobi ensembles: largest eigenvalue, tracy-widom limits and rates of convergence | 0.737 | 3 | 2 | 100% |
| 4 | R. J. Muirhead (2009) Aspects of multivariate statistical theory | 0.737 | 3 | 2 | 100% |
| 5 | A. Bykhovskaya and V. Gorin (2023) High-dimensional canonical correlation analysis | 0.644 | 4 | 1 | 100% |
| 6 | A. Onatski and C. Wang (2018) Alternative asymptotics for cointegration tests in large vars | 0.644 | 4 | 1 | 100% |
| 7 | L. Erdos and H. T. Yau (2012) Universality of local spectral statistics of random matrices | 0.644 | 2 | 2 | 100% |
| 8 | T. W. Anderson (2003) Introduction to multivariate statistical analysis, 3rd edition | 0.644 | 2 | 2 | 100% |
| 9 | S. Johansen (1991) Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models | 0.585 | 3 | 1 | 100% |
| 10 | E. Meckes and M. Meckes (2013) Spectral measures of powers of random matrices | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 48 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | 1cm Inference on common trends in functional time series | 0.737 | 3 | 2 |
| 2 | Canonical correlation analysis of stochastic trends via functional approximation | 0.652 | 12 | 2 |
| 3 | A Residuals-Based Nonparametric Variance Ratio Test for Cointegration | 0.644 | 2 | 2 |
| 4 | On LASSO for High Dimensional Predictive Regression | 0.405 | 1 | 1 |