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Nonstationary Nonlinear Heteroskedasticity: An Alternative to ARCH

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Author Info
Joon Y. Park (Seoul National Univerisity and University of Tokyo)
Abstract

In this paper, we consider time series with the conditional heteroskedasticities that are given by nonlinear functions of integrated processes. Such time series are said to have nonlinear nonstationary heteroskedasticity (NNH), and the functions generating conditional heterogeneity are called heterogeneity generating functions (HGF's). Various statistical properties of time series with NNH are investigated for a wide class of HGF's. For NNH models with a variety of HGF's, volatility clustering and leptokurticity, which are common features of ARCH type models, are manifest. In particular, it is shown that the sample autocorrelations of their squared processes vanish only very slowly, or do not even vanish at all, in the limit. Volatility clustering is therefore well expected. The NNH models with certain types of HGF's indeed have sample characteristics that are very similar to those of ARCH type models. Moreover, the sample kurtosis of the NNH model either diverges or has a stable limiting distribution with support truncated on the left by the kurtosis of the innovations. This would well explain the presence of leptokurticity in many observed time series data. To illustrate the empirical relevancy of our model, we analyze the spreads between the forward and spot rates of USD/DM exchange rates. It is found that the conditional variances of the spreads can be well modeled as a nonlinear function of the levels of the spot rates.

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Paper provided by CIRJE, Faculty of Economics, University of Tokyo in its series CIRJE F-Series with number CIRJE-F-86.

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Length: 36 pages
Date of creation: Jul 2000
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Handle: RePEc:tky:fseres:2000cf86

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  1. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38. [Downloadable!] (restricted)
  2. Lothian, James R., 1997. "Multi-country evidence on the behavior of purchasing power parity under the current float," Journal of International Money and Finance, Elsevier, vol. 16(1), pages 19-35, February. [Downloadable!] (restricted)
  3. Park, Joon Y. & Phillips, Peter C.B., 1999. "Asymptotics For Nonlinear Transformations Of Integrated Time Series," Econometric Theory, Cambridge University Press, vol. 15(03), pages 269-298, June. [Downloadable!]
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  4. Tim Bollerslev & Robert F. Engle & Daniel B. Nelson, 1993. "ARCH Models," University of California at San Diego, Economics Working Paper Series 93-49, Department of Economics, UC San Diego. [Downloadable!]
    Other versions:
    • 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. [Downloadable!] (restricted)
  5. Hansen, Bruce E, 1995. "Regression with Nonstationary Volatility," Econometrica, Econometric Society, vol. 63(5), pages 1113-32, September. [Downloadable!] (restricted)
  6. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April. [Downloadable!] (restricted)
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