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A Simple Cointegrating Rank Test Without Vector Autoregression

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  • Mototsugu Shintani

    (Department of Economics, Vanderbilt University)

Abstract

This paper proposes a fully nonparametric test for cointegrating rank which does not require estimation of a vector autoregressive model. The test exploits the fact that the degeneracy in the moment matrix of the variables with mixed integration order corresponds to the notion of cointegration. With an appropriate standardization, the test statistics are shown to have a nuisance parameter free limiting distribution and to be consistent under reasonable conditions. Monte Carlo experiments also suggest that the performance of the test is satisfactory with a moderate sample size. The proposed tests are applied to the stochastic growth model using the U.S. aggregate data.

Suggested Citation

  • Mototsugu Shintani, 2000. "A Simple Cointegrating Rank Test Without Vector Autoregression," Vanderbilt University Department of Economics Working Papers 0044, Vanderbilt University Department of Economics.
    • Handle: RePEc:van:wpaper:0044
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    Cited by:

    1. Nielsen, Morten Ørregaard, 2010. "Nonparametric cointegration analysis of fractional systems with unknown integration orders," Journal of Econometrics, Elsevier, vol. 155(2), pages 170-187, April.
    2. Hwang, Jungbin & Sun, Yixiao, 2018. "SIMPLE, ROBUST, AND ACCURATE F AND t TESTS IN COINTEGRATED SYSTEMS," Econometric Theory, Cambridge University Press, vol. 34(5), pages 949-984, October.
    3. Mototsugu Shintani, 2006. "A nonparametric measure of convergence towards purchasing power parity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 589-604.
    4. Karsten Reichold, 2022. "A Residuals-Based Nonparametric Variance Ratio Test for Cointegration," Papers 2211.06288, arXiv.org, revised Dec 2022.
    5. Jorg Breitung & Gianluca Cubadda, 2009. "Testing for cointegration in high-dimensional systems," CEIS Research Paper 148, Tor Vergata University, CEIS, revised 30 Sep 2009.
    6. Mototsugu Shintani, 2006. "A nonparametric measure of convergence towards purchasing power parity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(5), pages 589-604, July.
    7. Morten {O}rregaard Nielsen & Won-Ki Seo & Dakyung Seong, 2023. "Inference on common trends in functional time series," Papers 2312.00590, arXiv.org, revised May 2024.
    8. Qihui Chen & Zheng Fang, 2018. "Improved Inference on the Rank of a Matrix," Papers 1812.02337, arXiv.org, revised Mar 2019.
    9. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    10. Odaki, Mitsuhiro, 2015. "Cointegration rank tests based on vector autoregressive approximations under alternative hypotheses," Economics Letters, Elsevier, vol. 136(C), pages 187-189.
    11. Ye Cai & Mototsugu Shintani, 2005. "On the Long-Run Variance Ratio Test for a Unit Root," Vanderbilt University Department of Economics Working Papers 0506, Vanderbilt University Department of Economics.
    12. Richard Fu & Marco Pagani, 2012. "On the cointegration of international stock indices," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 36(2), pages 463-480, April.
    13. George Kapetanios, 2003. "A New Nonparametric Test of Cointegration Rank," Working Papers 482, Queen Mary University of London, School of Economics and Finance.
    14. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    15. Zhang, Rongmao & Robinson, Peter & Yao, Qiwei, 2019. "Identifying cointegration by eigenanalysis," LSE Research Online Documents on Economics 87431, London School of Economics and Political Science, LSE Library.

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    More about this item

    Keywords

    Cointegration; long-run variance; nonparametric spectrum estimation; unit roots; variance ratio;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

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