IDEAS home Printed from https://ideas.repec.org/a/eee/econom/v234y2023isp25-37.html
   My bibliography  Save this article

Reprint of: Generalized Autoregressive Conditional Heteroskedasticity

Author

Listed:
  • Bollerslev, Tim

Abstract

A natural generalization of the ARCH (Autoregressive Conditional Heteroskedastic) process introduced in Engle (1982) to allow for past conditional variances in the current conditional variance equation is proposed. Stationarity conditions and autocorrelation structure for this new class of parametric models are derived. Maximum likelihood estimation and testing are also considered. Finally an empirical example relating to the uncertainty of the inflation rate is presented.

Suggested Citation

  • Bollerslev, Tim, 2023. "Reprint of: Generalized Autoregressive Conditional Heteroskedasticity," Journal of Econometrics, Elsevier, vol. 234(S), pages 25-37.
    • Handle: RePEc:eee:econom:v:234:y:2023:i:s:p:25-37
    DOI: 10.1016/j.jeconom.2023.02.001
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304407623000477
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jeconom.2023.02.001?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Domowitz, Ian & Hakkio, Craig S., 1985. "Conditional variance and the risk premium in the foreign exchange market," Journal of International Economics, Elsevier, vol. 19(1-2), pages 47-66, August.
    2. Andrew A. Weiss, 1984. "Arma Models With Arch Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 5(2), pages 129-143, March.
    3. A. I. McLeod & W. K. Li, 1983. "Diagnostic Checking Arma Time Series Models Using Squared‐Residual Autocorrelations," Journal of Time Series Analysis, Wiley Blackwell, vol. 4(4), pages 269-273, July.
    4. Ernst R. Berndt & Bronwyn H. Hall & Robert E. Hall & Jerry A. Hausman, 1974. "Estimation and Inference in Nonlinear Structural Models," NBER Chapters, in: Annals of Economic and Social Measurement, Volume 3, number 4, pages 653-665, National Bureau of Economic Research, Inc.
    5. Godfrey, L G, 1981. "On the Invariance of the Lagrange Multiplier Test with Respect to Certain Changes in the Alternative Hypothesis," Econometrica, Econometric Society, vol. 49(6), pages 1443-1455, November.
    6. 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.
    7. Coulson, N. Edward & Robins, Russell P., 1985. "Aggregate economic activity and the variance of inflation : Another look," Economics Letters, Elsevier, vol. 17(1-2), pages 71-75.
    8. 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.
    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. Bollerslev, Tim, 1990. "Modelling the Coherence in Short-run Nominal Exchange Rates: A Multivariate Generalized ARCH Model," The Review of Economics and Statistics, MIT Press, vol. 72(3), pages 498-505, August.
    2. Adrian C. Darnell, 1994. "A Dictionary Of Econometrics," Books, Edward Elgar Publishing, number 118.
    3. McCurdy, Thomas H & Morgan, Ieuan G, 1988. "Testing the Martingale Hypothesis in Deutsche Mark Futures with Models Specifying the Form of Heteroscedasticity," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 3(3), pages 187-202, July-Sept.
    4. Jin Lee, 2000. "One-Sided Testing for ARCH Effect Using Wavelets," Econometric Society World Congress 2000 Contributed Papers 1214, Econometric Society.
    5. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    6. Li, Dong & Ling, Shiqing & Zakoïan, Jean-Michel, 2015. "Asymptotic inference in multiple-threshold double autoregressive models," Journal of Econometrics, Elsevier, vol. 189(2), pages 415-427.
    7. Hira Aftab & A. B. M. Rabiul Alam Beg, 2021. "Does Time Varying Risk Premia Exist in the International Bond Market? An Empirical Evidence from Australian and French Bond Market," IJFS, MDPI, vol. 9(1), pages 1-13, January.
    8. Christophe Belhomme, 1992. "Prime de risque et effet ARCH," Revue Économique, Programme National Persée, vol. 43(1), pages 55-70.
    9. 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.
    10. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521779654, January.
    11. Lei, Li-Fen, 1992. "Using futures and option contracts to manage price and quantity risk: A case of corn farmers in central Iowa," ISU General Staff Papers 1992010108000011326, Iowa State University, Department of Economics.
    12. Dennis W. Jansen, 1989. "Does inflation uncertainty affect output growth? Further evidence," Review, Federal Reserve Bank of St. Louis, issue Jul, pages 43-54.
    13. Luisa Nieto & Mª Dolores Robles Fernández & Ángeles Fernández, 2002. "Linear and Nonlinear Intraday Dynamics between the Eurostoxx-50," Documentos de Trabajo del ICAE 0208, Universidad Complutense de Madrid, Facultad de Ciencias Económicas y Empresariales, Instituto Complutense de Análisis Económico.
    14. 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.
    15. Huantian Xie & Dingfang Li & Lihua Xiong, 2016. "Exploring the Regional Variance using ARMA-GARCH Models," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(10), pages 3507-3518, August.
    16. Bentes, Sónia R., 2022. "On the stylized facts of precious metals’ volatility: A comparative analysis of pre- and during COVID-19 crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 600(C).
    17. Malliaropulos, Dimitrios, 1997. "A multivariate GARCH model of risk premia in foreign exchange markets," Economic Modelling, Elsevier, vol. 14(1), pages 61-79, January.
    18. Chionis, Dionysios & MacDonald, Ronald, 1997. "Some tests of market microstructure hypotheses in the foreign exchange market," Journal of Multinational Financial Management, Elsevier, vol. 7(3), pages 203-229, October.
    19. Davidson, Russell & MacKinnon, James G, 1988. "Double Length Artificial Regressions," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 50(2), pages 203-217, May.
    20. A. DAVID McDONALD & JON D. KENDALL & TIM LA. RIDLEY, 1993. "GARCH‐M Estimates of Variable Risk Premia for 180‐day Australian Bank Bills," The Economic Record, The Economic Society of Australia, vol. 69(1), pages 10-19, March.

    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:eee:econom:v:234:y:2023:i:s:p:25-37. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/jeconom .

    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.