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Testing for ARCH in the presence of a possibly misspecified conditional mean

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  • Lumsdaine, Robin L.
  • Ng, Serena

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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Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 93 (1999)
Issue (Month): 2 (December)
Pages: 257-279

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Handle: RePEc:eee:econom:v:93:y:1999:i:2:p:257-279

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Web page: http://www.elsevier.com/locate/jeconom

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Citations

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Cited by:
  1. Ludwig, Alexander, 2013. "Sovereign risk contagion in the Eurozone: A time-varying coefficient approach," Dresden Discussion Paper Series in Economics 02/13, Dresden University of Technology, Faculty of Business and Economics, Department of Economics.
  2. Juan Carlos Escanciano, 2006. "Joint Diagnostic Tests for Conditional Mean and Variance Specifications," Faculty Working Papers 02/06, School of Economics and Business Administration, University of Navarra.
  3. Fatum, Rasmus & Yamamoto, Yohei, 2014. "Large versus small foreign exchange interventions," Journal of Banking & Finance, Elsevier, vol. 43(C), pages 114-123.
  4. Ewa Ratuszny, 2013. "Robust Estimation in VaR Modelling - Univariate Approaches using Bounded Innovation Propagation and Regression Quantiles Methodology," Central European Journal of Economic Modelling and Econometrics, CEJEME, vol. 5(1), pages 35-63, March.
  5. Elena Andreou & Bas J.M. Werker, 2014. "Residual-based Rank Specification Tests for AR-GARCH type models," University of Cyprus Working Papers in Economics 02-2014, University of Cyprus Department of Economics.
  6. 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.
  7. Arouri, Mohamed El Hedi & Hammoudeh, Shawkat & Lahiani, Amine & Nguyen, Duc Khuong, 2013. "On the short- and long-run efficiency of energy and precious metal markets," Energy Economics, Elsevier, vol. 40(C), pages 832-844.
  8. Carlos Escanciano, J., 2008. "Joint and marginal specification tests for conditional mean and variance models," Journal of Econometrics, Elsevier, vol. 143(1), pages 74-87, March.
  9. Lumsdaine, Robin L. & Prasad, Eswar, 2002. "Identifying the Common Component of International Economic Fluctuations: A New Approach," IZA Discussion Papers 487, Institute for the Study of Labor (IZA).
  10. Manfred M. Fischer & Wolfgang Koller, 2001. "Testing for Non-Linear Dependence in Univariate Time Series: An Empirical Investigation of the Austrian Unemployment Rate," ERSA conference papers ersa01p233, European Regional Science Association.
  11. Kyrtsou, Catherine, 2008. "Re-examining the sources of heteroskedasticity: The paradigm of noisy chaotic models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(27), pages 6785-6789.
  12. 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.
  13. Metiu Norbert, 2011. "Financial contagion in developed sovereign bond markets," Research Memorandum 004, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).
  14. Metiu, Norbert, 2012. "Sovereign risk contagion in the Eurozone," Economics Letters, Elsevier, vol. 117(1), pages 35-38.
  15. Bill Russell, 2013. "ARCH and structural breaks in United States inflation," Dundee Discussion Papers in Economics 277, Economic Studies, University of Dundee.
  16. Austin, Darran & Ward, Bert & Dalziel, Paul, 2007. "The demand for money in China 1987-2004: A non-linear modelling approach," China Economic Review, Elsevier, vol. 18(2), pages 190-204.
  17. Sitzia, Bruno & Iovino, Doriana, 2008. "Nonlinearities in Exchange rates: Double EGARCH Threshold Models for Forecasting Volatility," MPRA Paper 8661, University Library of Munich, Germany.
  18. 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.

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