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Tests for real and complex unit roots in vector autoregressive models

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  • Nyblom, Jukka
  • Suomala, Jaakko

Abstract

The article proposes new tests for the number of real and complex unit roots in vector autoregressive models. The tests are based on the eigenvalues of the sample companion matrix. The limiting distributions of the eigenvalues converging to the unit eigenvalues turn out to be of a non-standard form and expressible in terms of Brownian motions. The tests are defined such that the null distributions related to eigenvalues ±1 are the same. The tests for the unit eigenvalues with nonzero imaginary part are defined independently of the angular frequency. When the tests are adjusted for deterministic terms, the null distributions usually change. Critical values are tabulated via simulations. Also some simulation based finite sample properties are presented together with comparisons with corresponding likelihood ratio tests. The relation of the unit roots to cointegration is discussed. An empirical example is provided to show how to use the test with real data.

Suggested Citation

  • Nyblom, Jukka & Suomala, Jaakko, 2014. "Tests for real and complex unit roots in vector autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 224-239.
    • Handle: RePEc:eee:jmvana:v:130:y:2014:i:c:p:224-239
    DOI: 10.1016/j.jmva.2014.05.012
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    References listed on IDEAS

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    6. Johansen, Soren, 1995. "Likelihood-Based Inference in Cointegrated Vector Autoregressive Models," OUP Catalogue, Oxford University Press, number 9780198774501.
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