GMM estimation and asymptotic properties in periodic GARCH(1, 1) models

References

[1] A. Aknouche and A. Bibi, Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes, J. Time Series Anal. 30 (2009), no. 1, 19–46. 10.1111/j.1467-9892.2008.00598.xSearch in Google Scholar

[2] A. Bibi and A. Aknouche, On periodic GARCH processes: Stationarity, existence of moments and geometric ergodicity, Math. Methods Statist. 17 (2008), no. 4, 305–316. 10.3103/S1066530708040029Search in Google Scholar

[3] A. Bibi and I. Lescheb, Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH models, Statist. Probab. Lett. 80 (2010), no. 19–20, 1532–1542. 10.1016/j.spl.2010.06.007Search in Google Scholar

[4] A. Bibi and I. Lescheb, Estimation and asymptotic properties in periodic GARCH ⁢ ( 1 , 1 ) models, Comm. Statist. Theory Methods 42 (2013), no. 19, 3497–3513. 10.1080/03610926.2011.633201Search in Google Scholar

[5] P. Billingsley, Probability and Measure, 3rd ed., John Wiley & Sons, New York, 1995. Search in Google Scholar

[6] T. Bollerslev and E. Ghysels, Periodic autoregressive conditional heteroscedasticity, J. Business Econ. Statist. 14 (1996), 139–151. 10.1080/07350015.1996.10524640Search in Google Scholar

[7] P. Bougerol and N. Picard, Stationarity of GARCH processes and of some nonnegative time series, J. Econometrics 52 (1992), no. 1–2, 115–127. 10.1016/0304-4076(92)90067-2Search in Google Scholar

[8] A. Brandt, The stochastic equation Y n + 1 = A n ⁢ Y n + B n with stationary coefficients, Adv. Appl. Probab. 18 (1986), no. 1, 211–220. 10.1017/S0001867800015639Search in Google Scholar

[9] C. Francq and J.-M. Zakoïan, The L 2 -structures of standard and switching-regime GARCH models, Stochastic Process. Appl. 115 (2005), no. 9, 1557–1582. 10.1016/j.spa.2005.04.005Search in Google Scholar

[10] L. P. Hansen, Large sample properties of generalized method of moments estimators, Econometrica 50 (1982), no. 4, 1029–1054. 10.2307/1912775Search in Google Scholar

[11] I. Lescheb, Asymptotic inference for periodic ARCH processes, Random Oper. Stoch. Equ. 19 (2011), no. 3, 283–294. 10.1515/ROSE.2011.015Search in Google Scholar

[12] I. Lescheb, On stationarity of the periodic AGARCH processes, Random Oper. Stoch. Equ. 23 (2015), no. 1, 31–37. 10.1515/rose-2014-0027Search in Google Scholar

[13] I. Lescheb and W. Slimani, On the stationarity and existence of moments of the periodic EGARCH process, Monte Carlo Methods Appl. 29 (2023), no. 4, 333–350. 10.1515/mcma-2023-2011Search in Google Scholar