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Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series

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  • Choi, In

Abstract

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and cumulative distribution functions are obtained, and the exact limiting cumulative distribution functions are tabulated. Finite sample performance of the proposed tests is studied by simulation. The tests display stable size when the lag truncation number for the long-run variance estimation is chosen appropriately. But the power of the tests is generally not high at selected sample sizes. The test for the null of trend-stationarity is applied to the U.S. macroeconomic time series along with the Phillips-Perron Z (null) test. For some monthly and annual series, the two tests provide consistent inferential results. But for most series, the two contradictory nulls of trend-stationarity and a unit root cannot be rejected at the conventional significance levels.

Suggested Citation

  • Choi, In, 1994. "Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series," Econometric Theory, Cambridge University Press, vol. 10(3-4), pages 720-746, August.
  • Handle: RePEc:cup:etheor:v:10:y:1994:i:3-4:p:720-746_00
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    Cited by:

    1. Kurozumi, Eiji, 2009. "Construction of Stationarity Tests with Less Size Distortions," Hitotsubashi Journal of Economics, Hitotsubashi University, vol. 50(1), pages 87-105, June.
    2. Gulasekaran Rajaguru & Tilak Abeysinghe, 2009. "A Gaussian Test for Cointegration," SCAPE Policy Research Working Paper Series 0905, National University of Singapore, Department of Economics, SCAPE.
    3. Choi, In, 2001. "Unit root tests for panel data," Journal of International Money and Finance, Elsevier, vol. 20(2), pages 249-272, April.
    4. Cho, Cheol-Keun & Amsler, Christine & Schmidt, Peter, 2015. "A test of the null of integer integration against the alternative of fractional integration," Journal of Econometrics, Elsevier, vol. 187(1), pages 217-237.
    5. Arvid Raknerud & Bjørn Helge Vatne, 2012. "The relation between banks' funding costs, retail rates and loan volumes: An analysis of Norwegian bank micro data," Working Paper 2012/17, Norges Bank.
    6. Arvid Raknerud & Bjørn Helge Vatne & Ketil Rakkestad, 2011. "How do banks' funding costs affect interest margins?," Discussion Papers 665, Statistics Norway, Research Department.
    7. Amsler Christine & Schmidt Peter, 2012. "A Comparison of the Robustness of Several Tests of Short Memory to Autocorrelated Errors," Journal of Econometric Methods, De Gruyter, vol. 1(1), pages 56-66, August.
    8. Nunzio Cappuccio & Diego Lubian, 2007. "Asymptotic Null Distributions of Stationarity and Nonstationarity Tests Under Local-to-finite Variance Errors," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 59(3), pages 403-423, September.
    9. Kirstin Hubrich & Helmut Lutkepohl & Pentti Saikkonen, 2001. "A Review Of Systems Cointegration Tests," Econometric Reviews, Taylor & Francis Journals, vol. 20(3), pages 247-318.
    10. L.A. Gil-Alana, 2003. "Testing the Power of a Generalization of the KPSS-Tests against Fractionally Integrated Hypotheses," Computational Economics, Springer;Society for Computational Economics, vol. 22(1), pages 23-38, August.
    11. Choi, In & Chul Ahn, Byung, 1998. "Testing the null of stationarity for multiple time series," Journal of Econometrics, Elsevier, vol. 88(1), pages 41-77, November.
    12. P. S. Sephton, 2010. "Unit roots and purchasing power parity: another kick at the can," Applied Economics, Taylor & Francis Journals, vol. 42(27), pages 3439-3453.
    13. Amsler Christine & Schmidt Peter & Vogelsang Timothy J, 2009. "The KPSS Test Using Fixed-b Critical Values: Size and Power in Highly Autocorrelated Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-44, December.
    14. S Shahnawaz, 2004. "Market Power and Unites States Sectoral Textile Imports," Economic Issues Journal Articles, Economic Issues, vol. 9(2), pages 69-84, September.
    15. Caner, M. & Kilian, L., 2001. "Size distortions of tests of the null hypothesis of stationarity: evidence and implications for the PPP debate," Journal of International Money and Finance, Elsevier, vol. 20(5), pages 639-657, October.
    16. Muller, Ulrich K., 2005. "Size and power of tests of stationarity in highly autocorrelated time series," Journal of Econometrics, Elsevier, vol. 128(2), pages 195-213, October.
    17. Jansson, Michael, 2004. "Stationarity Testing With Covariates," Econometric Theory, Cambridge University Press, vol. 20(01), pages 56-94, February.
    18. Ahn & Byung Chul, 1994. "Testing the null of stationarity in the presence of structural breaks for multiple time series," Econometrics 9411001, EconWPA, revised 08 Nov 1994.
    19. Choi, In, 1999. "Testing the Random Walk Hypothesis for Real Exchange Rates," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 14(3), pages 293-308, May-June.

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