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

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  • Lu, Zudi

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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  • Lu, Zudi, 1996. "A note on geometric ergodicity of autoregressive conditional heteroscedasticity (ARCH) model," Statistics & Probability Letters, Elsevier, vol. 30(4), pages 305-311, November.
    • Handle: RePEc:eee:stapro:v:30:y:1996:i:4:p:305-311
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    References listed on IDEAS

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    1. Engle, Robert F, 1983. "Estimates of the Variance of U.S. Inflation Based upon the ARCH Model," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 15(3), pages 286-301, August.
    2. 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.
    3. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    4. 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.
    5. Weiss, Andrew A, 1986. "ARCH and Bilinear Time Series Models: Comparison and Combination," Journal of Business & Economic Statistics, American Statistical Association, vol. 4(1), pages 59-70, January.
    6. Bera, Anil K & Higgins, Matthew L, 1993. "ARCH Models: Properties, Estimation and Testing," Journal of Economic Surveys, Wiley Blackwell, vol. 7(4), pages 305-366, December.
    7. A. K. Bera & M. L. Higgins, 1992. "A Test For Conditional Heteroskedasticity In Time Series Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(6), pages 501-519, November.
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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(5), pages 935-958, October.
    2. Cline, Daren B. H. & Pu, Huay-min H., 1999. "Stability of nonlinear AR(1) time series with delay," Stochastic Processes and their Applications, Elsevier, vol. 82(2), pages 307-333, August.
    3. Theis Lange, 2009. "First and second order non-linear cointegration models," CREATES Research Papers 2009-04, Department of Economics and Business Economics, Aarhus University.
    4. Lu, Zudi & Jiang, Zhenyu, 2001. "L1 geometric ergodicity of a multivariate nonlinear AR model with an ARCH term," Statistics & Probability Letters, Elsevier, vol. 51(2), pages 121-130, January.
    5. Li, Degui & Lu, Zudi & Linton, Oliver, 2010. "Loch linear fitting under near epoch dependence: uniform consistency with convergence rate," LSE Research Online Documents on Economics 58160, London School of Economics and Political Science, LSE Library.
    6. Lu, Zudi & Linton, Oliver, 2007. "Local Linear Fitting Under Near Epoch Dependence," Econometric Theory, Cambridge University Press, vol. 23(1), pages 37-70, February.
    7. Fanyu Meng & Wenwu Gong & Jun Liang & Xian Li & Yiping Zeng & Lili Yang, 2021. "Impact of different control policies for COVID-19 outbreak on the air transportation industry: A comparison between China, the U.S. and Singapore," PLOS ONE, Public Library of Science, vol. 16(3), pages 1-19, March.
    8. Carvalho, Alexandre & Skoulakis, Georgios, 2005. "Ergodicity and existence of moments for local mixtures of linear autoregressions," Statistics & Probability Letters, Elsevier, vol. 71(4), pages 313-322, March.

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