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A Class of Nonlinear ARCH Models


  • Higgins, Matthew L
  • Bera, Anil K


A class of nonlinear autoregressive conditional heteroskedasticity models is suggested. The proposed class encompasses several functional forms for autoregressive conditional heteroskedasticity which have been put forth in the literature. A Lagrange multiplier test is developed to test Engle's autoregressive conditional heteroskedasticity specification against the wider class of models. This test provides an easily computed disgnostic check of the adequacy of an autoregressive conditional heteroskedasticity model after it has been estimated. The theory is applied to a number of weekly exchange rate series and the authors find strong evidence of nonlinear autoregressive conditional heteroskedasticity. Copyright 1992 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.

Suggested Citation

  • Higgins, Matthew L & Bera, Anil K, 1992. "A Class of Nonlinear ARCH Models," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 137-158, February.
  • Handle: RePEc:ier:iecrev:v:33:y:1992:i:1:p:137-58

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    References listed on IDEAS

    1. Abel, Andrew B., 1985. "Dynamic behavior of capital accumulation in a cash-in-advance model," Journal of Monetary Economics, Elsevier, vol. 16(1), pages 55-71, July.
    2. Lucas, Robert Jr. & Stokey, Nancy L., 1983. "Optimal fiscal and monetary policy in an economy without capital," Journal of Monetary Economics, Elsevier, vol. 12(1), pages 55-93.
    3. King, Robert G. & Plosser, Charles I., 1986. "Money as the mechanism of exchange," Journal of Monetary Economics, Elsevier, vol. 17(1), pages 93-115, January.
    4. Stockman, Alan C., 1981. "Anticipated inflation and the capital stock in a cash in-advance economy," Journal of Monetary Economics, Elsevier, vol. 8(3), pages 387-393.
    5. Aschauer, David & Greenwood, Jeremy, 1983. "A Further Exploration in the Theory of Exchange Rate Regimes," Journal of Political Economy, University of Chicago Press, vol. 91(5), pages 868-875, October.
    6. Svensson, Lars E O, 1985. "Money and Asset Prices in a Cash-in-Advance Economy," Journal of Political Economy, University of Chicago Press, vol. 93(5), pages 919-944, October.
    7. Lucas, Robert E, Jr, 1980. "Equilibrium in a Pure Currency Economy," Economic Inquiry, Western Economic Association International, vol. 18(2), pages 203-220, April.
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