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M Tests with a New Normalization Matrix

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Author Info

  • Zhongjun Qu

    ()
    (Department of Economics, Boston University)

  • Yi-Ting Chen

    ()
    (Institute of Economics, Academia Sinica)

Abstract

This paper proposes a new family of M tests, building on the work of Kuan and Lee (2006) and Kiefer, Vogelsang and Bunzel (2000). The new test replaces the asymptotic covariance matrix in the conventional M test with an alternative normalization matrix, constructed using moment functions estimated from (K + 1) recursive subsamples. It is simple to implement, automatically accounts for the e¤ect of parameter estimation uncertainty, and allows for condi- tional heteroskedasticity and serial correlation of general forms. It converges to the central F distribution under the fixed-K asymptotics, and to the Chi-square distribution if K is allowed to approach in?nity. We illustrate its applicability using three simulation examples. They are: (1) specification testing for conditional heteroskedastic models, (2) nonnested testing with serially correlated errors, and (3) testing for serial correlation with unknown heteroskedasticity. The test exhibits good size properties and its power can be substantially higher than the test of Kuan and Lee (2006). Overall, the results suggest that, by integrating "self-normalization" and "fixed-bandwidth asymptotics" into the M-testing framework, we obtain an analytically simple yet widely applicable approach to misspeci?cation testing.

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Bibliographic Info

Paper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2010-050.

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Length: 36 pages
Date of creation: Jan 2010
Date of revision:
Handle: RePEc:bos:wpaper:wp2010-050

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  1. Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests," Working Papers 05-08, Cornell University, Center for Analytic Economics.
  2. Xiaofeng Shao, 2010. "A self-normalized approach to confidence interval construction in time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(3), pages 343-366.
  3. Lundbergh, Stefan & Teräsvirta, Timo, 1998. "Evaluating GARCH models," Working Paper Series in Economics and Finance 292, Stockholm School of Economics, revised 03 May 1999.
  4. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. " On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
  5. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
  6. Wooldridge, Jeffrey M., 1991. "On the application of robust, regression- based diagnostics to models of conditional means and conditional variances," Journal of Econometrics, Elsevier, vol. 47(1), pages 5-46, January.
  7. Durbin, J, 1970. "Testing for Serial Correlation in Least-Squares Regression When Some of the Regressors are Lagged Dependent Variables," Econometrica, Econometric Society, vol. 38(3), pages 410-21, May.
  8. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  9. Pagan, Adrian & Vella, Frank, 1989. "Diagnostic Tests for Models Based on Individual Data: A Survey," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(S), pages S29-59, Supplemen.
  10. Kiefer, Nicholas M. & Bunzel, Helle & Vogelsang, Timothy & Vogelsang, Timothy & Bunzel, Helle, 2000. "Simple Robust Testing of Regression Hypotheses," Staff General Research Papers 1832, Iowa State University, Department of Economics.
  11. Ben S. Bernanke & Henning Bohn & Peter C. Reiss, 1985. "Alternative Nonnested Specification Tests of Time Series Investment Models," NBER Technical Working Papers 0049, National Bureau of Economic Research, Inc.
  12. Choi, Hwan-Sik & Kiefer, Nicholas M., 2008. "Robust Nonnested Testing and the Demand for Money," Journal of Business & Economic Statistics, American Statistical Association, vol. 26, pages 9-17, January.
  13. Bunzel, Helle & Kiefer, Nicholas M. & Vogelsang, Timothy, 2001. "Simple Robust Testing of Hypothesis in Non-Linear Models," Staff General Research Papers 5214, Iowa State University, Department of Economics.
  14. Berkes, Istv n & Horv th, Lajos & Kokoszka, Piotr, 2003. "Asymptotics For Garch Squared Residual Correlations," Econometric Theory, Cambridge University Press, vol. 19(04), pages 515-540, August.
  15. Hansen, Bruce E, 1994. "Autoregressive Conditional Density Estimation," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 35(3), pages 705-30, August.
  16. Heung Wong & Shiqing Ling, 2005. "Mixed Portmanteau Tests for Time-Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 569-579, 07.
  17. Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
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