IDEAS home Printed from https://ideas.repec.org/a/cup/etheor/v2y1986i01p107-131_01.html
   My bibliography  Save this article

Asymptotic Theory for ARCH Models: Estimation and Testing

Author

Listed:
  • Weiss, Andrew A.

Abstract

In the context of a linear dynamic model with moving average errors, we consider a heteroscedastic model which represents an extension of the ARCH model introduced by Engle [4]. We discuss the properties of maximum likelihood and least squares estimates of the parameters of both the regression and ARCH equations, and also the properties of various tests of the model that are available. We do not assume that the errors are normally distributed.

Suggested Citation

  • Weiss, Andrew A., 1986. "Asymptotic Theory for ARCH Models: Estimation and Testing," Econometric Theory, Cambridge University Press, vol. 2(1), pages 107-131, April.
    • Handle: RePEc:cup:etheor:v:2:y:1986:i:01:p:107-131_01
    as

    Download full text from publisher

    File URL: https://www.cambridge.org/core/product/identifier/S0266466600011397/type/journal_article
    File Function: link to article abstract page
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. A. R. Pagan & A. D. Hall & P. K. Trivedi, 1983. "Assessing the Variability of Inflation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 50(4), pages 585-596.
    2. White, Halbert, 1982. "Maximum Likelihood Estimation of Misspecified Models," Econometrica, Econometric Society, vol. 50(1), pages 1-25, January.
    3. Z. Lomnicki, 1961. "Tests for departure from normality in the case of linear stochastic processes," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 4(1), pages 37-62, December.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Dhrymes, Phoebus J & Taylor, John B, 1976. "On an Efficient Two-Step Estimator for Dynamic Simultaneous Equations Models with Autoregressive Errors," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 17(2), pages 362-376, June.
    6. White, Halbert & Domowitz, Ian, 1984. "Nonlinear Regression with Dependent Observations," Econometrica, Econometric Society, vol. 52(1), pages 143-161, January.
    7. Godfrey, Leslie G, 1978. "Testing against General Autoregressive and Moving Average Error Models When the Regressors Include Lagged Dependent Variables," Econometrica, Econometric Society, vol. 46(6), pages 1293-1301, November.
    8. Gourieroux, Christian & Holly, Alberto & Monfort, Alain, 1982. "Likelihood Ratio Test, Wald Test, and Kuhn-Tucker Test in Linear Models with Inequality Constraints on the Regression Parameters," Econometrica, Econometric Society, vol. 50(1), pages 63-80, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Lijuan Huo & Jin Seo Cho, 2021. "Testing for the sandwich-form covariance matrix of the quasi-maximum likelihood estimator," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(2), pages 293-317, June.
    2. Lijuan Huo & Jin Seo Cho, 2019. "Testing for the Sandwich-Form Covariance Matrix Applied to Quasi-Maximum Likelihood Estimation Using Economic and Energy Price Growth Rates," Working papers 2019rwp-152, Yonsei University, Yonsei Economics Research Institute.
    3. Francq, Christian & Zakoïan, Jean-Michel, 2009. "Testing the Nullity of GARCH Coefficients: Correction of the Standard Tests and Relative Efficiency Comparisons," Journal of the American Statistical Association, American Statistical Association, vol. 104(485), pages 313-324.
    4. Tim Bollerslev & Ray Y. Chou & Narayanan Jayaraman & Kenneth F. Kroner - L, 1991. "es modéles ARCH en finance : un point sur la théorie et les résultats empiriques," Annals of Economics and Statistics, GENES, issue 24, pages 1-59.
    5. Jeffrey M. Woodridge, 1988. "A Unified Approach to Robust, Regression-Based Specification Tests," Working papers 480, Massachusetts Institute of Technology (MIT), Department of Economics.
    6. Demos, Antonis & Sentana, Enrique, 1998. "Testing for GARCH effects: a one-sided approach," Journal of Econometrics, Elsevier, vol. 86(1), pages 97-127, June.
    7. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521520911, November.
    8. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    9. Wooldridge, Jeffrey M., 1990. "A Unified Approach to Robust, Regression-Based Specification Tests," Econometric Theory, Cambridge University Press, vol. 6(1), pages 17-43, March.
    10. repec:bla:scandj:v:93:y:1991:i:2:p:189-211 is not listed on IDEAS
    11. Dennis W. Jansen, 1989. "Does inflation uncertainty affect output growth? Further evidence," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 43-54.
    12. Conrad, Christian & Hartmann, Matthias, 2014. "Cross-sectional evidence on the relation between monetary policy, macroeconomic conditions and low-frequency inflation uncertainty," Working Papers 0574, University of Heidelberg, Department of Economics.
    13. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    14. Zia-Ur- Rahman, 2019. "Influence of Excessive Expenditure of the Government in Perspective of Interest Rate and Money Circulation Which in Turn Affects the Growing Process in Pakistan," Asian Journal of Economics and Empirical Research, Asian Online Journal Publishing Group, vol. 6(2), pages 120-129.
    15. Bel, K. & Paap, R., 2013. "Modeling the impact of forecast-based regime switches on macroeconomic time series," Econometric Institute Research Papers EI 2013-25, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. repec:wyi:journl:002087 is not listed on IDEAS
    17. Gregory, Allan W. & McCurdy, Thomas H., 1986. "The unbiasedness hypothesis in the forward foreign exchange market: A specification analysis with application to France, Italy, Japan, the United Kingdom and West Germany," European Economic Review, Elsevier, vol. 30(2), pages 365-381, April.
    18. David F. Hendry, 2013. "Econometric Modelling: The ‘Consumption Function’ In Retrospect," Scottish Journal of Political Economy, Scottish Economic Society, vol. 60(5), pages 495-522, November.
    19. Marc Lavoie & Gabriel Rodriguez & Mario Seccareccia, 2004. "Similitudes and Discrepancies in Post-Keynesian and Marxist Theories of Investment: A Theoretical and Empirical Investigation," International Review of Applied Economics, Taylor & Francis Journals, vol. 18(2), pages 127-149.
    20. Matthias Hartmann & Helmut Herwartz & Yabibal M. Walle, 2012. "Where enterprise leads, finance follows. In-sample and out-of-sample evidence on the causal relation between finance and growth," Economics Bulletin, AccessEcon, vol. 32(1), pages 871-882.
    21. Jeffrey M. Wooldridge, 2002. "Inverse probability weighted M-estimators for sample selection, attrition, and stratification," Portuguese Economic Journal, Springer;Instituto Superior de Economia e Gestao, vol. 1(2), pages 117-139, August.
    22. Ericsson, Neil R & Hendry, David F & Mizon, Grayham E, 1998. "Exogeneity, Cointegration, and Economic Policy Analysis," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(4), pages 370-387, October.

    More about this item

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:cup:etheor:v:2:y:1986:i:01:p:107-131_01. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Kirk Stebbing (email available below). General contact details of provider: https://www.cambridge.org/ect .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.