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A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model

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  • Lu, Zudi
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    Abstract

    For the pth-order linear ARCH model, , where [alpha]0 > 0, [alpha]i [greater-or-equal, slanted] 0, I = 1, 2, ..., p, {[var epsilon]t} is an i.i.d. normal white noise with E[var epsilon]t = 0, E[var epsilon]t2 = 1, and [var epsilon]t is independent of {Xs, s

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    Bibliographic Info

    Article provided by Elsevier in its journal Statistics & Probability Letters.

    Volume (Year): 30 (1996)
    Issue (Month): 4 (November)
    Pages: 305-311

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    Handle: RePEc:eee:stapro:v:30:y:1996:i:4:p:305-311

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    Related research

    Keywords: Geometric ergodicity Conditional heteroscedasticity ARCH model Nonlinear time series Markov process;

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    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 347-70, March.
    2. 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.
    3. Weiss, Andrew A, 1986. "ARCH and Bilinear Time Series Models: Comparison and Combination," Journal of Business & Economic Statistics, American Statistical Association, American Statistical Association, vol. 4(1), pages 59-70, January.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, Econometric Society, vol. 50(4), pages 987-1007, July.
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    Cited by:
    1. Li, Degui & Lu, Zudi & Linton, Oliver, 2012. "Local Linear Fitting Under Near Epoch Dependence: Uniform Consistency With Convergence Rates," Econometric Theory, Cambridge University Press, vol. 28(05), pages 935-958, October.
    2. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(01), pages 37-70, February.
    3. Cline, Daren B. H. & Pu, Huay-min H., 1999. "Stability of nonlinear AR(1) time series with delay," Stochastic Processes and their Applications, Elsevier, Elsevier, vol. 82(2), pages 307-333, August.
    4. Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, School of Economics and Management, University of Aarhus.

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