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Testing for Serial Correlation Against an ARMA(1,1) Process

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Abstract

This paper is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against ARMA(1,1) alternatives is considered. Sup Lagrange multiplier (LM) and exponential average LM tests are introduced and are shown to be asymptotically admissible for ARMA(1,1) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white noise alternatives. Simulation results compare the tests to several tests in the literature. These results show that the Exp-LM_{infinity} test has very good all-around power properties.

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  • Donald W.K. Andrews & Werner Ploberger, 1994. "Testing for Serial Correlation Against an ARMA(1,1) Process," Cowles Foundation Discussion Papers 1077, Cowles Foundation for Research in Economics, Yale University.
  • Handle: RePEc:cwl:cwldpp:1077 Note: CFP 933.
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    References listed on IDEAS

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    1. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
    2. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
    3. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
    4. 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.
    5. Rahman, Shahidur & King, Maxwell L, 1993. "Testing for ARMA (1, 1) Disturbances in the Linear Regression Model," Australian Economic Papers, Wiley Blackwell, vol. 32(61), pages 284-298, December.
    6. Hansen, Bruce E, 1996. "Inference When a Nuisance Parameter Is Not Identified under the Null Hypothesis," Econometrica, Econometric Society, vol. 64(2), pages 413-430, March.
    7. B. Pötscher, 1985. "The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 32(1), pages 129-150, December.
    8. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    9. Andrews, Donald W K & Ploberger, Werner, 1994. "Optimal Tests When a Nuisance Parameter Is Present Only under the Alternative," Econometrica, Econometric Society, vol. 62(6), pages 1383-1414, November.
    10. Donald W.K. Andrews & Werner Ploberger, 1993. "Admissibility of the Likelihood Ratio Test When a Nuisance Parameter Is Present OnlyUnder the Alternative," Cowles Foundation Discussion Papers 1058, Cowles Foundation for Research in Economics, Yale University.
    11. Robert B. Davies, 2002. "Hypothesis testing when a nuisance parameter is present only under the alternative: Linear model case," Biometrika, Biometrika Trust, vol. 89(2), pages 484-489, June.
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    Cited by:

    1. Donald W.K. Andrews & Liu, Xuemei Liu & Werner Ploberger, 1996. "Tests of Seasonal and Non-Seasonal Serial Correlation," Cowles Foundation Discussion Papers 1124, Cowles Foundation for Research in Economics, Yale University.
    2. Hansen, Bruce E., 2000. "Testing for structural change in conditional models," Journal of Econometrics, Elsevier, vol. 97(1), pages 93-115, July.
    3. Ravi Bansal & Amir Yaron, 2004. "Risks for the Long Run: A Potential Resolution of Asset Pricing Puzzles," Journal of Finance, American Finance Association, vol. 59(4), pages 1481-1509, August.
    4. Ai Deng Author-X-Name-First: Ai, 2006. "Local Power of Andrews and Ploberger Tests Against Nearly Integrated, Nearly White Noise Process," Boston University - Department of Economics - Working Papers Series WP2006-027, Boston University - Department of Economics.
    5. Joscha Beckmann & Ansgar Belke & Michael Kühl, 2011. "The dollar-euro exchange rate and macroeconomic fundamentals: a time-varying coefficient approach," Review of World Economics (Weltwirtschaftliches Archiv), Springer;Institut für Weltwirtschaft (Kiel Institute for the World Economy), vol. 147(1), pages 11-40, April.
    6. 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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