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New tests for unit roots in autoregressive processes with possibly infinite variance errors

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  • Shin, Dong Wan
  • So, Beong Soo
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    Abstract

    For autoregressive processes with possibly infinite variance innovations, tests for unit roots are constructed. The limiting null distributions of the test statistics are standard normal both for finite variance innovations and for infinite variance innovations. The test statistics are the pivotal statistics of modified M-estimators in which the signs of regressors rather than the regressors themselves are used as instrumental variables in estimating unit roots. A Monte-Carlo experiment compares the proposed tests favorably with tests based on the OLSE and tests based on the M-estimators for several innovations.

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 44 (1999)
    Issue (Month): 4 (October)
    Pages: 387-397

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    Handle: RePEc:eee:stapro:v:44:y:1999:i:4:p:387-397

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    Keywords: Infinite variance error M-estimation Unit root test;

    References

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    1. Davis, Richard A. & Knight, Keith & Liu, Jian, 1992. "M-estimation for autoregressions with infinite variance," Stochastic Processes and their Applications, Elsevier, vol. 40(1), pages 145-180, February.
    2. Franses, Philip Hans & Haldrup, Niels, 1994. "The Effects of Additive Outliers on Tests for Unit Roots and Cointegration," Journal of Business & Economic Statistics, American Statistical Association, vol. 12(4), pages 471-78, October.
    3. Herce, Miguel A., 1996. "Asymptotic Theory of LAD Estimation in a Unit Root Process with Finite Variance Errors," Econometric Theory, Cambridge University Press, vol. 12(01), pages 129-153, March.
    4. M. N. Hasan & R. W. Koenker, 1997. "Robust Rank Tests of the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 65(1), pages 133-162, January.
    5. Lucas, Andre, 1995. "An outlier robust unit root test with an application to the extended Nelson-Plosser data," Journal of Econometrics, Elsevier, vol. 66(1-2), pages 153-173.
    6. Phillips, P.C.B., 1990. "Time Series Regression With a Unit Root and Infinite-Variance Errors," Econometric Theory, Cambridge University Press, vol. 6(01), pages 44-62, March.
    7. Shin, Dong Wan & Sarkar, Sahadeb & Lee, Jong Hyup, 1996. "Unit root tests for time series with outliers," Statistics & Probability Letters, Elsevier, vol. 30(3), pages 189-197, October.
    8. Lucas, André, 1995. "Unit Root Tests Based on M Estimators," Econometric Theory, Cambridge University Press, vol. 11(02), pages 331-346, February.
    9. Shin, Dong Wan & So, Beong Soo, 1999. "Unit Root Tests Based On Adaptive Maximum Likelihood Estimation," Econometric Theory, Cambridge University Press, vol. 15(01), pages 1-23, February.
    10. Chan, Ngai Hang & Tran, Lanh Tat, 1989. "On the First-Order Autoregressive Process with Infinite Variance," Econometric Theory, Cambridge University Press, vol. 5(03), pages 354-362, December.
    11. Hansen, Bruce E., 1992. "Convergence to Stochastic Integrals for Dependent Heterogeneous Processes," Econometric Theory, Cambridge University Press, vol. 8(04), pages 489-500, December.
    12. So, Beong Soo & Shin, Dong Wan, 1999. "Cauchy Estimators For Autoregressive Processes With Applications To Unit Root Tests And Confidence Intervals," Econometric Theory, Cambridge University Press, vol. 15(02), pages 165-176, April.
    13. So, Beong Soo & Shin, Dong Wan, 1999. "Recursive mean adjustment in time-series inferences," Statistics & Probability Letters, Elsevier, vol. 43(1), pages 65-73, May.
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    Cited by:
    1. Shin, Dong Wan & Park, Soo Jung & Oh, Man-Suk, 2009. "A robust sign test for panel unit roots under cross sectional dependence," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 1312-1327, February.
    2. Wan Shin, Dong & Lee, Oesook, 2003. "An instrumental variable approach for tests of unit roots and seasonal unit roots in asymmetric time series models," Journal of Econometrics, Elsevier, vol. 115(1), pages 29-52, July.

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