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Asymptotics of Cointegration Tests for High-Dimensional VAR($k$)

Anna Bykhovskaya, Vadim Gorin

arXiv 15 Feb 2022 · Econometrics · publishedThe Review of Economics and Statistics (2024) · 3 citations (OpenAlex)

arXiv:2202.07150 · PDF · DOI · OpenAlex · Extracted main text

Abstract

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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48
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91
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Most heavily cited references

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.

ReferenceIntensityMentionsSectionsMain text
1A. Bykhovskaya and V. Gorin (2022) Cointegration in large vars1.0001811100%
2P. J. Forrester (2010) Log-gases and random matrices1.00084100%
3I. Johnstone (2008) Multivariate analysis and jacobi ensembles: largest eigenvalue, tracy-widom limits and rates of convergence0.73732100%
4R. J. Muirhead (2009) Aspects of multivariate statistical theory0.73732100%
5A. Bykhovskaya and V. Gorin (2023) High-dimensional canonical correlation analysis0.64441100%
6A. Onatski and C. Wang (2018) Alternative asymptotics for cointegration tests in large vars0.64441100%
7L. Erdos and H. T. Yau (2012) Universality of local spectral statistics of random matrices0.64422100%
8T. W. Anderson (2003) Introduction to multivariate statistical analysis, 3rd edition0.64422100%
9S. Johansen (1991) Estimation and hypothesis testing of cointegration vectors in gaussian vector autoregressive models0.58531100%
10E. Meckes and M. Meckes (2013) Spectral measures of powers of random matrices0.51121100%

Showing the top 10 of 48 scored citations.

Cited by, within the corpus

arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.

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11cm Inference on common trends in functional time series0.73732
2Canonical correlation analysis of stochastic trends via functional approximation0.652122
3A Residuals-Based Nonparametric Variance Ratio Test for Cointegration0.64422
4On LASSO for High Dimensional Predictive Regression0.40511