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Portmanteau-type tests for unit-root and cointegration

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  • Zhang, Rongmao
  • Chan, Ngai Hang

Abstract

This paper proposes a new portmanteau-type statistic by combining several lags of the sample autocorrelations to test for the presence of a unit-root of an autoregressive model. The proposed method is nonparametric in nature, which is model free and easy to implement. It avoids modeling the fitted residuals and does not require estimation of nuisance parameters, as commonly done in the augmented Dickey–Fuller or Phillips–Perron procedure. Asymptotic properties of the test are established under general stationary conditions on the noises. Finite sample studies are also reported to illustrate the superior power of the proposed method. Applications to test for cointegration are also given.

Suggested Citation

  • Zhang, Rongmao & Chan, Ngai Hang, 2018. "Portmanteau-type tests for unit-root and cointegration," Journal of Econometrics, Elsevier, vol. 207(2), pages 307-324.
    • Handle: RePEc:eee:econom:v:207:y:2018:i:2:p:307-324
    DOI: 10.1016/j.jeconom.2018.08.004
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    1. Michael Jansson, 2008. "Semiparametric Power Envelopes for Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 76(5), pages 1103-1142, September.
    2. Sargan, John Denis & Bhargava, Alok, 1983. "Testing Residuals from Least Squares Regression for Being Generated by the Gaussian Random Walk," Econometrica, Econometric Society, vol. 51(1), pages 153-174, January.
    3. Bierens, Herman J., 1993. "Higher-order sample autocorrelations and the unit root hypothesis," Journal of Econometrics, Elsevier, vol. 57(1-3), pages 137-160.
    4. Cai, Ye & Shintani, Mototsugu, 2006. "On The Alternative Long-Run Variance Ratio Test For A Unit Root," Econometric Theory, Cambridge University Press, vol. 22(3), pages 347-372, June.
    5. Andrews, Donald W K, 1991. "Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation," Econometrica, Econometric Society, vol. 59(3), pages 817-858, May.
    6. Phillips, Peter C B, 1988. "Regression Theory for Near-Integrated Time Series," Econometrica, Econometric Society, vol. 56(5), pages 1021-1043, September.
    7. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    8. Elliott, Graham & Rothenberg, Thomas J & Stock, James H, 1996. "Efficient Tests for an Autoregressive Unit Root," Econometrica, Econometric Society, vol. 64(4), pages 813-836, July.
    9. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-856, July.
    10. Schwert, G. William, 1987. "Effects of model specification on tests for unit roots in macroeconomic data," Journal of Monetary Economics, Elsevier, vol. 20(1), pages 73-103, July.
    11. Fan, Yanqin & Gençay, Ramazan, 2010. "Unit Root Tests With Wavelets," Econometric Theory, Cambridge University Press, vol. 26(5), pages 1305-1331, October.
    12. Michael Jansson & Marcelo J. Moreira, 2006. "Optimal Inference in Regression Models with Nearly Integrated Regressors," Econometrica, Econometric Society, vol. 74(3), pages 681-714, May.
    13. Wu, Wei Biao, 2009. "An asymptotic theory for sample covariances of Bernoulli shifts," Stochastic Processes and their Applications, Elsevier, vol. 119(2), pages 453-467, February.
    14. 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.
    15. Engle, Robert & Granger, Clive, 2015. "Co-integration and error correction: Representation, estimation, and testing," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 39(3), pages 106-135.
    16. Serena Ng & Pierre Perron, 2001. "LAG Length Selection and the Construction of Unit Root Tests with Good Size and Power," Econometrica, Econometric Society, vol. 69(6), pages 1519-1554, November.
    17. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    18. Müller, Ulrich K. & Watson, Mark W., 2013. "Low-frequency robust cointegration testing," Journal of Econometrics, Elsevier, vol. 174(2), pages 66-81.
    19. Ulrich K. Müller & Mark W. Watson, 2008. "Testing Models of Low-Frequency Variability," Econometrica, Econometric Society, vol. 76(5), pages 979-1016, September.
    20. Johansen, Soren, 1991. "Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models," Econometrica, Econometric Society, vol. 59(6), pages 1551-1580, November.
    21. Bierens, Herman J., 1997. "Nonparametric cointegration analysis," Journal of Econometrics, Elsevier, vol. 77(2), pages 379-404, April.
    22. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    23. Andrews, Donald W.K., 1988. "Laws of Large Numbers for Dependent Non-Identically Distributed Random Variables," Econometric Theory, Cambridge University Press, vol. 4(3), pages 458-467, December.
    24. Breitung, Jorg, 2002. "Nonparametric tests for unit roots and cointegration," Journal of Econometrics, Elsevier, vol. 108(2), pages 343-363, June.
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    3. Dogo Armand Dago & Yu Pei, 2025. "Evaluating the Position of Côte d’Ivoire’s Cocoa Industry on the Global Production Chain and the Influencing Factors," Sustainability, MDPI, vol. 17(3), pages 1-33, January.

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    More about this item

    Keywords

    Autoregressive processes; Cointegration; Portmanteau test; Sample covariance; Unit-root;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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