M Tests with a New Normalization Matrix
AbstractThis 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Boston University - Department of Economics in its series Boston University - Department of Economics - Working Papers Series with number WP2010-050.
Length: 36 pages
Date of creation: Jan 2010
Date of revision:
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Stefan Lundbergh & Timo Teräsvirta, 1999.
"Evaluating GARCH Models,"
Tinbergen Institute Discussion Papers
99-008/4, Tinbergen Institute.
- 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.
- Lawrence R. Glosten & Ravi Jagannathan & David E. Runkle, 1993. "On the relation between the expected value and the volatility of the nominal excess return on stocks," Staff Report 157, Federal Reserve Bank of Minneapolis.
- 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.
- 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.
- 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.
- Qu, Zhongjun, 2008. "Testing for structural change in regression quantiles," Journal of Econometrics, Elsevier, vol. 146(1), pages 170-184, September.
- Hansen, B.E., 1992.
"Autoregressive Conditional Density Estimation,"
RCER Working Papers
322, University of Rochester - Center for Economic Research (RCER).
- 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.
- Bernanke, Ben & Bohn, Henning & Reiss, Peter C., 1988. "Alternative non-nested specification tests of time-series investment models," Journal of Econometrics, Elsevier, vol. 37(3), pages 293-326, March.
- 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.
- 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.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005.
"A New Asymptotic Theory for Heteroskedasticity-Autocorrelation Robust Tests,"
05-08, Cornell University, Center for Analytic Economics.
- Kiefer, Nicholas M. & Vogelsang, Timothy J., 2005. "A New Asymptotic Theory For Heteroskedasticity-Autocorrelation Robust Tests," Econometric Theory, Cambridge University Press, vol. 21(06), pages 1130-1164, December.
- Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
- 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.
- Bunzel H. & Kiefer N. M. & Vogelsang T. J., 2001.
"Simple Robust Testing of Hypotheses in Nonlinear Models,"
Journal of the American Statistical Association,
American Statistical Association, vol. 96, pages 1088-1096, September.
- 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.
- 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.
- 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.
- Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-70, March.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Courtney Sullivan).
If references are entirely missing, you can add them using this form.