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Testing Covariance Stationarity

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  • Zhijie Xiao
  • Luiz Renato Lima

Abstract

In this paper, we show that the widely used stationarity tests such as the Kwiatkowski Phillips, Schmidt, and Shin (KPSS) test have power close to size in the presence of time-varying unconditional variance. We propose a new test as a complement of the existing tests. Monte Carlo experiments show that the proposed test possesses the following characteristics: (i) in the presence of unit root or a structural change in the mean, the proposed test is as powerful as the KPSS and other tests; (ii) in the presence of a changing variance, the traditional tests perform badly whereas the proposed test has high power comparing to the existing tests; (iii) the proposed test has the same size as traditional stationarity tests under the null hypothesis of stationarity. An application to daily observations of return on U.S. Dollar/Euro exchange rate reveals the existence of instability in the unconditional variance when the entire sample is considered, but stability is found in subsamples.

Suggested Citation

  • Zhijie Xiao & Luiz Renato Lima, 2007. "Testing Covariance Stationarity," Econometric Reviews, Taylor & Francis Journals, vol. 26(6), pages 643-667.
    • Handle: RePEc:taf:emetrv:v:26:y:2007:i:6:p:643-667
    DOI: 10.1080/07474930701639080
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    Cited by:

    1. Lee, Sangyeol & Meintanis, Simos G. & Pretorius, Charl, 2022. "Monitoring procedures for strict stationarity based on the multivariate characteristic function," Journal of Multivariate Analysis, Elsevier, vol. 189(C).
    2. Aviral Kumar Tiwari & Aruna Kumar Dash & Subhendu Dutta, 2015. "Testing the mean reversion in prices of agricultural commodities in India," Economics Bulletin, AccessEcon, vol. 35(3), pages 1928-1940.
    3. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.
    4. Kapetanios, George, 2009. "Testing for strict stationarity in financial variables," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2346-2362, December.
    5. James E Payne & Junsoo Lee, 2024. "Global perspective on the permanent or transitory nature of shocks to tourist arrivals: Evidence from new unit root tests with structural breaks and factors," Tourism Economics, , vol. 30(1), pages 67-103, February.
    6. George Kapetanios, 2007. "Testing for Strict Stationarity," Working Papers 602, Queen Mary University of London, School of Economics and Finance.

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