Pusat Pengajian Sains Matematik - Tesis
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- PublicationDetection Of Outliers And Structural Breaks In Structural Time Series Model Using Indicator Saturation Approach(2023-03)Rose, Farid Zamani CheThe presence of structural changes, specifically outliers and structural breaks, adversely affects the estimation of economic and financial indicators in terms of the model accuracy and forecasting performance. Focusing on the detection of outliers and structural breaks, which has recently gained growing research interest, this study aimed to examine the performance of indicator saturation, as an extension of the general-to-specific (GETS) modelling, in detecting these structural changes in structural time series model framework. The proposed technique is capable to detect the location, duration, magnitude and number of structural changes in time series data. To date, prior studies only considered using Autometrics embodied in OxMetrics to apply this approach in static data generating process (DGP). Addressing this gap, this study used the gets package in R to examine the performance of indicator saturation in dynamic model viz state space model. Through Monte Carlo simulations, the performance of indicator saturation was evaluated in terms of potency and gauge. Based on the simulation results, the sequential selection algorithm outperformed the non-sequential selection approach in the automatic GETS model selection procedure. The results also suggested α = 1/T as the optimum level of significance level.
- PublicationDynamics Of Co-Infectious Childhood Respiratory Diseases: Pertussis And Pneumonia(2023-02)Yakubu, Aisha AliyuPertussis is a vaccine-preventable respiratory disease that affects humans of all age groups, yet there are reported cases of resurgence. The disease is highly contagious and has posed detrimental effects on the lives of infants globally. The impact of pertussis worsened with the presence of viral infections such as pneumonia. Therefore, it is imperative to study the behavior of these diseases and suggest control strategies using a mathematical modeling approach. The study area and literature of mathematical models on pertussis and pneumonia co-infection dynamics is rather scanty. Therefore, this study is aimed at obtaining model equations using a system of nonlinear ordinary differential equations for a better understanding of the transmission dynamics and control of these diseases in the infant population. Further, the models are used to evaluate the intervention strategies for disease control. The first model is the general model describing the transmission dynamics of pertussis which incorporates a maternally derived immunity compartment. The dynamical behavior of the basic model is analyzed analytically and numerically. Numerical simulations were carried out using mathematical software. The basic reproduction number of the model is obtained and its behavior is analyzed by varying parameters.
- PublicationEstimation Of Weibull Parameters Using Simulated Annealing As Applied In Financial Data(2023-03)Hamza, AbubakarAn accurate analysis of financial data is vital to justify sustainability for investment potential in a company. Weibull distributions can be used to examine investment behaviour due to their flexibility to be transformed into other types of distribution. However, the selection of the most suitable estimators is still a challenging task. The present study proposes a simulated annealing algorithm (SA) in estimating the parameters of Weibull distribution with application to modified internal rate of return data (MIRR).The objective is to examine the investment potential of the shari’ah compliance companies of the Malaysia property sector (MPS). The MIRR were computed based on the data extracted from the companies’ financial reports from 2010 to 2018. The performance of the SA algorithm has been explored in terms of accuracies and estimation errors. The finding reveals that the Weibull distribution is well-suited to describing the investment behaviour of the MPS based on the estimates via the SA algorithm. Therefore, purchasing shares in this sector is very attractive for a long-term investment period, but may have a high risk of committing it as a result of fluctuations in the mean and variance of the estimate. Additionally, the two-parameter Weibull distribution has been extended by incorporating additional parameters to capture the uncertainty behaviour in the financial data.
- PublicationBayesian Networks With Greedy Backward Elimination In Feature Selection For Data Classification(2019-03)Ang, Sau LoongNaive Bayes (NB) is an efficient Bayesian classifier with wide range of applications in data classification. Having the advantage with its simple structure. Naive Bayes gains attention among the researchers with its good accuracy in classification result. Nevertheless, the major drawback of Naive Bayes is the strong independence assumption among the features which is restrictive. This weakness causes not only confusion in the causal relationships among the features but also doubtful representation of the real structure of Bayesian Network for classification. Further development of Naive Bayes in augmenting extra links or dependent relationships between the features such as the Tree Augmented Naive Bayes (TAN) end up with slight improvement in accuracy of classification result where the main problems stated above remain unsolved.
- PublicationNumerical Solutions For Two Dimensional Time-Fractional Differential Sub-Diffusion Equation(2019-04)Ali, UmairIn the past several decades, fractional differential equations (differential equation involving arbitrary order derivatives) have acquired much popularity in the area of science and engineering. This is because such equations can better model certain problems of fluid mechanics, physics, biological science, chemistry, hydrology and finance, amongst others, due to the fact that it can better represent system with memory. However, most fractional differential equations cannot be solved by exact analytical techniques.