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An improved FIGARCH model with the fractional differencing operator (1-νL)d

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  • Pan, Qunxing
  • Li, Peng
  • Du, Xiuli

Abstract

In this study, we propose a new volatility model called the product memory GARCH model by replacing (1 − L)d in the FIGARCH model of Baillie et al. (1996) with (1 − νL)d for 0 ≤ ν ≤ 1, where the impulse response function in its ARCH(∞) process has a decay rate in the form of the product of a geometric memory rate and a hyperbolic memory rate when the lags increase. Under the ARCH(∞) framework, the non-negativity constraints, the existence of the second, fourth, sixth, and eighth moments, and the memory length are investigated, and the Gaussian quasi-maximum likelihood estimation is also discussed. This improved model is of considerable significance in the evolution of GARCH-type models and financial econometrics.

Suggested Citation

  • 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).
    • Handle: RePEc:eee:finlet:v:55:y:2023:i:pb:s1544612323003471
    DOI: 10.1016/j.frl.2023.103975
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    References listed on IDEAS

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    1. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    2. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
    3. Kazakevicius, Vytautas & Leipus, Remigijus & Viano, Marie-Claude, 2004. "Stability of random coefficient ARCH models and aggregation schemes," Journal of Econometrics, Elsevier, vol. 120(1), pages 139-158, May.
    4. Whitney K. Newey & Douglas G. Steigerwald, 1997. "Asymptotic Bias for Quasi-Maximum-Likelihood Estimators in Conditional Heteroskedasticity Models," Econometrica, Econometric Society, vol. 65(3), pages 587-600, May.
    5. 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.
    6. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    7. Robinson, P. M., 1991. "Testing for strong serial correlation and dynamic conditional heteroskedasticity in multiple regression," Journal of Econometrics, Elsevier, vol. 47(1), pages 67-84, January.
    8. Marc Henry, 2001. "Averaged Periodogram Spectral Estimation with Long‐memory Conditional Heteroscedasticity," Journal of Time Series Analysis, Wiley Blackwell, vol. 22(4), pages 431-459, July.
    9. Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(1), pages 3-22, February.
    10. Kwan, Wilson & Li, Wai Keung & Li, Guodong, 2012. "On the estimation and diagnostic checking of the ARFIMA–HYGARCH model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3632-3644.
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    13. Nelson, Daniel B & Cao, Charles Q, 1992. "Inequality Constraints in the Univariate GARCH Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 10(2), pages 229-235, April.
    14. Ding, Zhuanxin & Granger, Clive W. J., 1996. "Modeling volatility persistence of speculative returns: A new approach," Journal of Econometrics, Elsevier, vol. 73(1), pages 185-215, July.
    15. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, 2004. "On the Autocorrelation Properties of Long‐Memory GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 265-282, March.
    16. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    17. 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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    More about this item

    Keywords

    ARCH(∞) process; FIGARCH model; Product memory GARCH model; Financial time series;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions

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