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- ItemOpen AccessA Comparison of Mann and Ishikawa iterations of quasi-contraction operators(World Congress on Engineering, 2007) Olaleru, J.OIt is generally conjectured that the Mann iteration converges faster than the Ishikawa iteration for any operator defined on an arbitrary closed convex subset of a Banach space. The recent result of Babu et al  shows that this conjecture can be proved for a class of quasi-contractive operators called the Zamfirescu operators. In this paper it is shown that the proof can indeed be generalised to that of quasi-contraction maps.
- ItemOpen AccessEstimation Methods of the Markov Switching GARCH Models for Forecasting Exchange Rate Volatility(2019-09-13) Nkemnole, E.B; Ebomese, A.P.The Markov switching GARCH model offers rich dynamics to modelling financial data. Estimating this path dependence model is a challenging task because exact computation of the likelihood is impracticable in real life. This has led to so many numerical computational methods to obtain the maximum likelihood. Just as so many numerical methods have been adopted to estimate the likelihood function, others have also adopted other methods of estimation to model this path dependence model. In this research work, the method of maximum likelihood (ML) and the Bayesian method (BM) of estimation were used in estimating the parameters of the Markov-switching GARCH model for single regime, two regime and three regime and was applied to exchange rate data. It was discovered that the three regime switching GARCH model outperformed the other regime switching model for the method of ML based on their information criteria and the two regime switching performed better based on the deviance information criteria for the BM of estimation. Furthermore, the ML performed better than the BM based on their information criteria.