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A Note On Inequality Constraints In The Garch Model

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  • Tsai, Henghsiu
  • Chan, Kung-Sik

Abstract

We consider the parameter restrictions that need to be imposed to ensure that the conditional variance process of a GARCH(p,q) model remains nonnegative. Previously, Nelson and Cao (1992, Journal of Business ’ Economic Statistics 10, 229–235) provided a set of necessary and sufficient conditions for the aforementioned nonnegativity property for GARCH(p,q) models with p ≤ 2 and derived a sufficient condition for the general case of GARCH(p,q) models with p ≥ 3. In this paper, we show that the sufficient condition of Nelson and Cao (1992) for p ≥ 3 actually is also a necessary condition. In addition, we point out the linkage between the absolute monotonicity of the generalized autoregressive conditional heteroskedastic (GARCH) generating function and the nonnegativity of the GARCH kernel, and we use it to provide examples of sufficient conditions for this nonnegativity property to hold.

Suggested Citation

  • Tsai, Henghsiu & Chan, Kung-Sik, 2008. "A Note On Inequality Constraints In The Garch Model," Econometric Theory, Cambridge University Press, vol. 24(3), pages 823-828, June.
    • Handle: RePEc:cup:etheor:v:24:y:2008:i:03:p:823-828_08
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    Cited by:

    1. Christian Francq & Genaro Sucarrat, 2018. "An Exponential Chi-Squared QMLE for Log-GARCH Models Via the ARMA Representation," Journal of Financial Econometrics, Oxford University Press, vol. 16(1), pages 129-154.
    2. Karanasos, Menelaos & Xu, Yongdeng & Yfanti, Stavroula, 2017. "Constrained QML Estimation for Multivariate Asymmetric MEM with Spillovers: The Practicality of Matrix Inequalities," Cardiff Economics Working Papers E2017/14, Cardiff University, Cardiff Business School, Economics Section.
    3. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    4. Nakatani, Tomoaki & Teräsvirta, Timo, 2008. "Positivity constraints on the conditional variances in the family of conditional correlation GARCH models," Finance Research Letters, Elsevier, vol. 5(2), pages 88-95, June.
    5. Adnen Ben Nasr & Ahdi N. Ajmi & Rangan Gupta, 2013. "Modeling the Volatility of the Dow Jones Islamic Market World Index Using a Fractionally Integrated Time Varying GARCH (FITVGARCH) Model," Working Papers 201357, University of Pretoria, Department of Economics.
    6. Conrad, Christian & Karanasos, Menelaos, 2010. "Negative Volatility Spillovers In The Unrestricted Eccc-Garch Model," Econometric Theory, Cambridge University Press, vol. 26(3), pages 838-862, June.
    7. Abdeljalil Settar & Nadia Idrissi Fatmi & Mohammed Badaoui, 2021. "New Approach in Dealing with the Non-Negativity of the Conditional Variance in the Estimation of GARCH Model," Central European Journal of Economic Modelling and Econometrics, Central European Journal of Economic Modelling and Econometrics, vol. 13(1), pages 55-74, March.
    8. Pan, Qunxing & Li, Peng & Du, Xiuli, 2023. "An improved FIGARCH model with the fractional differencing operator (1-νL)d," Finance Research Letters, Elsevier, vol. 55(PB).
    9. Conrad, Christian & Weber, Enzo, 2013. "Measuring Persistence in Volatility Spillovers," VfS Annual Conference 2013 (Duesseldorf): Competition Policy and Regulation in a Global Economic Order 79850, Verein für Socialpolitik / German Economic Association.
    10. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    11. Martinez Oscar & Olmo Jose, 2012. "A Nonlinear Threshold Model for the Dependence of Extremes of Stationary Sequences," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 16(3), pages 1-39, September.
    12. Henghsiu Tsai & K. S. Chan, 2007. "A Note on Non‐Negative Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(3), pages 350-360, May.
    13. Menelaos Karanasos & Ning Zeng, 2013. "Conditional heteroskedasticity in macroeconomics data: UK inflation, output growth and their uncertainties," Chapters, in: Nigar Hashimzade & Michael A. Thornton (ed.), Handbook of Research Methods and Applications in Empirical Macroeconomics, chapter 12, pages 266-288, Edward Elgar Publishing.
    14. Adnen Ben Nasr & Mohamed Boutahar & Abdelwahed Trabelsi, 2010. "Fractionally integrated time varying GARCH model," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 19(3), pages 399-430, August.

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