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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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File URL: http://cowles.econ.yale.edu/P/cd/d10b/d1077.pdf
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Bibliographic Info

Paper provided by Cowles Foundation for Research in Economics, Yale University in its series Cowles Foundation Discussion Papers with number 1077.

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Length: 27 pages
Date of creation: Sep 1994
Date of revision:
Publication status: Published in Journal of the American Statistical Association (September 1996), 91(435): 1331-1342
Handle: RePEc:cwl:cwldpp:1077

Note: CFP 933.
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References

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  1. Andrews, Donald W.K., 1992. "Generic Uniform Convergence," Econometric Theory, Cambridge University Press, vol. 8(02), pages 241-257, June.
  2. 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.
  3. Andrews, Donald W K, 1993. "Tests for Parameter Instability and Structural Change with Unknown Change Point," Econometrica, Econometric Society, vol. 61(4), pages 821-56, July.
  4. Herman J. Bierens & Werner Ploberger, 1997. "Asymptotic Theory of Integrated Conditional Moment Tests," Econometrica, Econometric Society, vol. 65(5), pages 1129-1152, September.
  5. Hansen, B.E., 1991. "Inference when a Nuisance Parameter is Not Identified Under the Null Hypothesis," RCER Working Papers 296, University of Rochester - Center for Economic Research (RCER).
  6. B. Pötscher, 1985. "The behaviour of the Lagrangian multiplier test in testing the orders of an ARMA-model," Metrika, Springer, vol. 32(1), pages 129-150, December.
  7. 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.
  8. 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 284-98, December.
  9. 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.
  10. repec:cup:etheor:v:8:y:1992:i:2:p:241-57 is not listed on IDEAS
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Cited by:
  1. 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, 08.
  2. 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.
  3. 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.
  4. 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, vol. 147(1), pages 11-40, April.
  5. 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.
  6. 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.

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