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Testing for ARCH in the Presence of a Possibly Misspecified Conditional Mean

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Author Info
Robin L. Lumsdaine (Princeton University)
Serena Ng () (Boston College)

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Abstract

Ever since the development of the Autoregressive Conditional Heteroskedasticity (ARCH) model (Engle [1982]), testing for the presence of ARCH has become a routine diagnostic. One popular method of testing for ARCH is T times the R^2 from a regression of squared residuals on p of its lags. This test has been shown to have a Lagrange multiplier interpretation and is asymptotically distributed as a Chi^2(p) random variable. Underlying this test is the assumption of a correctly specified conditional mean. In this paper, we consider the properties of the ARCH test when there is a possibly misspecified conditional mean. Examples of misspecification include omitted variables, structural change, and parameter instability. We show that misspecification will lead to overrejection of the null of conditional homoskedasticity. We demonstrate the use of recursive residuals to improve the fit of a first stage conditional mean regression. We illustrate these results via Monte Carlo simulation and consider two empirical examples.

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Publisher Info
Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 370.

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Length: 24 pages
Date of creation: 27 Aug 1998
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Handle: RePEc:boc:bocoec:370

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Related research
Keywords: ARCH; model misspecification; recursive residuals; Lagrange Multiplier test;

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Find related papers by JEL classification:
C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions
C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation and Testing

References listed on IDEAS
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  1. Lee, Byung-Joo, 1992. "A Heteroskedasticity Test Robust to Conditional Mean Misspecification," Econometrica, Econometric Society, vol. 60(1), pages 159-71, January. [Downloadable!] (restricted)
  2. Lamoureux, Christopher G & Lastrapes, William D, 1990. "Persistence in Variance, Structural Change, and the GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 8(2), pages 225-34, April.
  3. Perron, Pierre, 1989. "The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis," Econometrica, Econometric Society, vol. 57(6), pages 1361-1401, November. [Downloadable!] (restricted)
    Other versions:
  4. Zivot, Eric & Andrews, Donald W K, 1992. "Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(3), pages 251-70, July.
    Other versions:
  5. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July. [Downloadable!] (restricted)
  6. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January. [Downloadable!] (restricted)
  7. Diebold, Francis X & Nerlove, Marc, 1989. "The Dynamics of Exchange Rate Volatility: A Multivariate Latent Factor Arch Model," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 4(1), pages 1-21, Jan.-Mar.. [Downloadable!] (restricted)
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  8. Serena Ng & Timothy J. Vogelsang, 1997. "Analysis of Vector Autoregressions in the Presence of Shifts in Mean," Boston College Working Papers in Economics 379, Boston College Department of Economics. [Downloadable!]
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  9. Paul Rilstone, 1992. "A simple bera-jarque normality test for nonparametric residuals," Econometric Reviews, Taylor and Francis Journals, vol. 11(3), pages 355-365. [Downloadable!] (restricted)
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Cited by:
(explanations, 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.)

  1. Rituparna Kar & Nityananda Sarkar, 2006. "Mean and volatility dynamics of Indian rupee/US dollar exchange rate series: an empirical investigation," Asia-Pacific Financial Markets, Springer, vol. 13(1), pages 41-69, March. [Downloadable!] (restricted)
  2. E Andreou & A Pelloni & M Sensier, 2003. "The effect of nominal shock uncertainty on output growth," Centre for Growth and Business Cycle Research Discussion Paper Series 40, Economics, The Univeristy of Manchester. [Downloadable!]
  3. E. Ruiz & M.A. Carnero & D. Pereira, 2004. "Effects of Level Outliers on the Identification and Estimation of GARCH Models," Econometric Society 2004 Australasian Meetings 21, Econometric Society. [Downloadable!]
  4. Robin L. Lumsdaine & Eswar S. Prasad, 2003. "Identifying the Common Component of International Economic Fluctuations: A New Approach," Economic Journal, Royal Economic Society, vol. 113(484), pages 101-127, January. [Downloadable!] (restricted)
    Other versions:
  5. M. Angeles Carnero & Daniel Peña & Esther Ruiz, 2001. "Outliers And Conditional Autoregressive Heteroscedasticity In Time Series," Statistics and Econometrics Working Papers ws010704, Universidad Carlos III, Departamento de Estadística y Econometría. [Downloadable!]
  6. Sitzia, Bruno & Iovino, Doriana, 2008. "Nonlinearities in Exchange rates: Double EGARCH Threshold Models for Forecasting Volatility," MPRA Paper 8661, University Library of Munich, Germany. [Downloadable!]
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