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Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary

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  • Pantula, Sastry G

Abstract

Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies the asymptotic null distribution of the test statistics for testing "rho" = 1 in the model Y(" subscript" t) = "rho" Y("subscript" t-1) + e(" subscript" t) - "theta"e(" subscript" t-1) as "theta" approaches 1. It is shown that the test statistics differ from one another in their asymptotic properties depending on the rate at which "theta" converges to 1.

Suggested Citation

  • Pantula, Sastry G, 1991. "Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary," Journal of Business & Economic Statistics, American Statistical Association, vol. 9(1), pages 63-71, January.
  • Handle: RePEc:bes:jnlbes:v:9:y:1991:i:1:p:63-71
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    Cited by:

    1. Bhattacharyya, B.B. & Richardson, G.D. & Flores, P.V., 2006. "Unit roots: Periodogram ordinate," Statistics & Probability Letters, Elsevier, vol. 76(6), pages 641-651, March.
    2. Perron, Pierre, 1996. "The adequacy of asymptotic approximations in the near-integrated autoregressive model with dependent errors," Journal of Econometrics, Elsevier, vol. 70(2), pages 317-350, February.
    3. Yabe, Ryota, 2017. "Asymptotic distribution of the conditional-sum-of-squares estimator under moderate deviation from a unit root in MA(1)," Statistics & Probability Letters, Elsevier, vol. 125(C), pages 220-226.
    4. Artur Silva Lopes, 2006. "Deterministic seasonality in Dickey–Fuller tests: should we care?," Empirical Economics, Springer, vol. 31(1), pages 165-182, March.
    5. Perron, Pierre, 1992. "Racines unitaires en macroéconomie : le cas d’une variable," L'Actualité Economique, Société Canadienne de Science Economique, vol. 68(1), pages 325-356, mars et j.
    6. T. Berger & G. Everaert, 2006. "Re-examining the Structural and the Persistence Approach to Unemployment," Working Papers of Faculty of Economics and Business Administration, Ghent University, Belgium 06/383, Ghent University, Faculty of Economics and Business Administration.
    7. Kellard, Neil & Mark E Wohar, 2003. "Trends and Persistence in Primary Commodity Prices," Royal Economic Society Annual Conference 2003 118, Royal Economic Society.
    8. James H. Stock & Mark W. Watson, 1996. "Asymptotically Median Unbiased Estimation of Coefficient Variance in a Time Varying Parameter Model," NBER Technical Working Papers 0201, National Bureau of Economic Research, Inc.
    9. Jushan Bai & Serena Ng, 2004. "A PANIC Attack on Unit Roots and Cointegration," Econometrica, Econometric Society, vol. 72(4), pages 1127-1177, July.
    10. Chaudourne, Jeremy & Fève, Patrick & Guay, Alain, 2014. "Understanding the effect of technology shocks in SVARs with long-run restrictions," Journal of Economic Dynamics and Control, Elsevier, vol. 41(C), pages 154-172.
    11. Maarten Dossche & Gerdie Everaert, 2005. "Measuring inflation persistence: a structural time series approach," Working Paper Research 70, National Bank of Belgium.
    12. Samarjit Das & Kaushik Bhattacharya, 2008. "Price convergence across regions in India," Empirical Economics, Springer, vol. 34(2), pages 299-313, March.
    13. Valkanov, Rossen, 1999. "Equity Premium and Dividend Yield regressions: A lot of noise, little information, confusing results," University of California at Los Angeles, Anderson Graduate School of Management qt955135m1, Anderson Graduate School of Management, UCLA.
    14. YABE, Ryota, 2014. "Asymptotic Distribution of the Conditional Sum of Squares Estimator Under Moderate Deviation From a Unit Root in MA(1)," Discussion Papers 2014-19, Graduate School of Economics, Hitotsubashi University.
    15. Patrick Marsh, "undated". "Saddlepoint Approximations for Optimal Unit Root Tests," Discussion Papers 09/31, Department of Economics, University of York.
    16. YABE, Ryota, 2014. "Empirical Likelihood Confidence Intervals for Nonparametric Nonlinear Nonstationary Regression Models," Discussion Papers 2014-20, Graduate School of Economics, Hitotsubashi University.
    17. Slade, Margaret E., 2001. "Valuing Managerial Flexibility: An Application of Real-Option Theory to Mining Investments," Journal of Environmental Economics and Management, Elsevier, vol. 41(2), pages 193-233, March.
    18. 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.
    19. Österholm, Pär, 2003. "The Taylor Rule: A Spurious Regression?," Working Paper Series 2003:20, Uppsala University, Department of Economics.

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