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Reprint of: Generalized Autoregressive Conditional Heteroskedasticity

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  • 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.

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  • 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
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    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.
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    1. Khreshna Syuhada & Rizka Puspitasari & I Kadek Darma Arnawa & Lailatul Mufaridho & Elonasari Elonasari & Miftahul Jannah & Aniq Rohmawati, 2024. "Enhancing Value-at-Risk with Credible Expected Risk Models," IJFS, MDPI, vol. 12(3), pages 1-15, August.

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