QMLE of periodic time-varying bilinear– GARCH models

References

• Aknouche, A., and A. Bibi. 2008. Quasi-maximum likelihood estimation of periodic GARCH and periodic ARMA-GARCH processes. Journal of Time Series Analysis 30 (1):19–46.
   Web of Science ®Google Scholar
• Aknouche, A., and H. Guerbyenne. 2009. Periodic stationarity of random coefficient periodic autoregressions. Statistics & Probability Letters 79 (7):990–6.
   Web of Science ®Google Scholar
• Bibi, A., and A. Ghezal. 2016. On periodic time-varying bilinear processes: Structure and asymptotic inference. Statistical Methods & Applications 25 (3):395–420.
   Web of Science ®Google Scholar
• Bibi, A., and A. Ghezal. 2018. Markov-switching BILINEAR-GARCH models: Structure and estimation. Communications in Statistics—Theory and Methods 47 (2):307–23.
   Web of Science ®Google Scholar
• Bibi, A., and I. Lescheb. 2010. Strong consistency and asymptotic normality of least squares estimators for PGARCH and PARMA-PGARCH. Statistics & Probability Letters 80 (19–20): 1532–42.
   Web of Science ®Google Scholar
• Bibi, A., and A. J. Oyet. 2004. Estimation of some bilinear time series models with time-varying coefficients. Stochastic Analysis & Applications 22 (2):355–76.
   Web of Science ®Google Scholar
• Black, F. 1976. Studies in stock price volatility changes. In: Proceedings of the 1976 Meeting of the Business and Economic Statistics Section, American Statistical Association, Washington, D.C., pp. 177–81.
   Google Scholar
• Bollerslev, T., and E. Ghysels. 1996. Periodic autoregressive conditional heteroskedasticity. Journal of Business and Economic Statistics 14 (2):139–51.
   Web of Science ®Google Scholar
• Bougerol, P., and N. Picard. 1992. Strict stationarity of generalized autoregressive processes. Annals of Probability 20 (4):1714–30.
   Web of Science ®Google Scholar
• Chan, N. H., and C. T. Ng. 2009. Statistical inference for non-stationary GARCH(p, q) models. Electronic Journal of Statistics 3:956–92.
   Web of Science ®Google Scholar
• Choi, M. S., J. A. Park, and S. Y. Hwang. 2012. Asymmetric GARCH processes featuring both threshold effect and bilinear structure. Statistics & Probability Letters 82 (3):419–26.
   Web of Science ®Google Scholar
• Francq, C., and J. M. Zakoïan. 2004. Maximum likelihood estimation of pure GARCH and ARMA-GARCH processes. Bernoulli 10 (4):605–37.
   Web of Science ®Google Scholar
• Franses, P. H., and R. Paap. 2000. Modelling day-of-the-week seasonality in the S&P 500 index. Applied Financial Economics 10 (5):483–8.
   Google Scholar
• Hamdi, F., and S. Souam. 2013. Mixture periodic GARCH models: Applications to exchange rate modeling. In: 5th international conference on modeling, simulation and applied optimization (ICMSAO), Hammamet, Tunisie IEEE xplore, 28–30 April 2013, pp. 1–6.
   Google Scholar
• Horst, U. 2001. The stochastic Eq. Yt+1=AtYt+Bt with non-stationary coefficients. Journal of Applied Probability 38 (1):80–94.
   Web of Science ®Google Scholar
• Jensen, S. T., and A. Rahbek. 2004. Asymptotic normality of the QML estimator of ARCH in the nonstationary case. Econometrica 72 (2):641–6.
   Web of Science ®Google Scholar
• Meitz, M., and P. Saikkonen. 2011. Parameter estimation in nonlinear AR-GARCH models. Economic Theory 27 (6):1236–78.
   Google Scholar
• Nelson, D. B., and C. Q. Cao. 1992. Inequality constraints in the univariate GARCH model. Journal of Business & Economic Statistics 10 (2):229–35.
   Web of Science ®Google Scholar
• Rajae, A., and G. Melard. 2006. Asymptotic properties of quasi-maximum likelihood estimators for ARMA models with time-dependent coefficients. Statistical Inference for Stochastic Processes 9 (3):279–330.
   Google Scholar
• Rodriguez, M., and E. Ruiz. 2012. Revisiting several popular GARCH models with leverage effect: Differences and similarities. Journal of Financial Econometrics 10 (4):637–68.
   Web of Science ®Google Scholar
• Storti, G., and C. Vitale. 2003. BL-GARCH models and asymmetries in volatility. Statistical Methods & Applications 12 (1):19–39.
   Google Scholar
• Storti, G., and C. Vitale. 2003. Likelihood inference in BL-GARCH models. Computational Statistics 18 (3):387–400.
   Web of Science ®Google Scholar
• Straumann, D., and T. Mikosch. 2006. Quasi-maximum likelihood estimation in conditionally heteroscedastic time series: A stochastic recurrence equation approach. The Annals of Statistics 34 (5):2449–95.
   Web of Science ®Google Scholar