Mathematical Theory and Modeling
http://www.iiste.org/Journals/index.php/MTM
<p><span id="internal-source-marker_0.04939836589619517"><span id="internal-source-marker_0.04939836589619517">Mathematical Theory and Modeling </span>is a peer reviewed journal published by IISTE. The journal publishes original papers at the forefront of mathematical theories, modelings, and applications. The journal is published in both printed and online versions. The online version is free access and download.</span></p><p><span>IISTE is member of <a href="http://www.crossref.org/01company/17crossref_members.html">CrossRef</a>.<br /></span></p>en-USMathematical Theory and Modeling2224-5804Some Multiple and Simple Real Root Finding Methods
http://www.iiste.org/Journals/index.php/MTM/article/view/39432
<p>Solving nonlinear equations with root finding is very common in science and engineering models. In particular, one applies it in mathematics, physics, electrical engineering and mechanical engineering. It is a researchable area in numerical analysis. This present work focuses on some iterative methods of higher order for multiple roots. New and existing novel multiple and simple root finding techniques are discussed. Methods independent of a multiplicity m of a root r, which function very well for both simple and multiple roots, are also presented. Error-correction and variatonal technique with some function estimations are used for the constructions. For the analysis of orders of convergence, some basic theorems are applied. Ample test examples are provided (in C++) for test of efficiencies with suitable initial guesses. And convergence of some methods to a root is shown graphically using matlab applications.</p> <p><strong>Keywords</strong>:Iterative algorithms, error-correction, variational methods, multiple roots, applications</p> <p> </p>Tekle Gemechu7The Relationship Between Urbanization and Precipitation in Kisumu City: Co-Integration Analysis
http://www.iiste.org/Journals/index.php/MTM/article/view/39433
<p>The work done in this study thesis is by empirical analysis. If two series are integrated of the same order, then the two series are said to be co-integrated and this is shown in the two series where the population series being non stationary is made stationary by third differencing and the stationary rainfall series subjected to the same order of differencing to achieve the co-integration rule. The OLS method was used and then the model parameters tested for adequacy. A linear Error Correction Model was fitted and evidence that a short term relationship between the rainfall and population series is seen to exist. Also, a high threshold value is observed at the second lag. A high R squared value of 0.9881 is an indication that the model fits well to the data. A small p-value also indicates that the model is highly significant. Hence, it is recommended that a close analysis of population growth rates be analyzed to aid in the prediction of the rainfall rates movements.</p> <p><strong>Keywords: </strong>OLS, Co-integrated, differencing, Error Correction Model, p-value.<strong> </strong></p> <p><strong> </strong></p>Benard Ochieng SambaGeorge OrwaJoseph Mungatu7Modeling Volatility in Nigeria Foreign Exchange Market Using GARCH-type Models
http://www.iiste.org/Journals/index.php/MTM/article/view/39434
<p>In this study, the performance of GARCH-type model is considered in modelling Nigeria foreign exchange returns. The datasets consists of the foreign exchange of Nigeria naira for the periods before recession and during recession. It is observed that volatility is higher during recession than when there was no recession. Model selection criteria based on Hannan-Quinn Information Criterion (HQIC) shows that Gaussian process is least considered model to capture the variability in foreign exchange rate returns in Nigeria, but student’s and Generalized Error distribution are more suitable, therefore forecast performance was used to access each of the Asymmetric models. The empirical analysis shows that GARCH (1, 1) and gjrGARCH (1, 1) with Student’s error distribution and iGARCH(1, 1), sGARCH(1,1), and csGARCH (1,1) are the best fitted models. Fifty days out-of-sample forecast shows that csGARCH (1, 1) based on Generalized Error distribution is the best predictive model based on Mean Square Error (MSE), and sGARCH based on Mean Absolute Error (MAE) and Directional Absolute Error (DAE). The study recommends that future study should consider alternative error distributions with a view to realizing a more robust volatility forecasting model that could guarantee sound policy choices.</p> <p><strong>Keywords</strong>: Volatility, foreign exchange, GARCH-type models, Error Distributions</p>Adesina, O.SOyewole OAdekola, L.O7A Comparative Study on Bias Regression Methods in the Presence of Multicollinearity Based on Gamma and Chi Square Distributions
http://www.iiste.org/Journals/index.php/MTM/article/view/39435
<p>The aim of this study is to compare some regression methods in the presence of multicollinearity problem. This problem makes the estimated regression coefficients by least squares method to be conditional upon the correlated predictor variables in the model. It is also a condition in a set of regression data that have two or more regressors which are redundant and have the same information. Therefore, some regression methods that handle with multicollinearity such as partial least square regression (PLSR), ridge regression (RR) and lasso regression (LR) had reported. In this paper, the methods were compared using simulated data that follows gamma and chi square distributions with <em>P=</em>4 and 10, and <em>n</em>=60 and 90. All results were compared with each other through Mean Square Log Error (MSLE), Mean Absolute Error (MAE) and R<sup>2</sup> of their estimated values for different methods. The results show that when <em>P</em>=4 and n=60 RR is better methods with gamma distribution, but with chi square distribution PLRS is better methods. Also, when <em>P=</em>4 and n=90, RR shows better results with gamma distribution but with chi square distribution all methods have equal predictive ability. However, at <em>P</em>=10 and n=60 RR performed better with both gamma and chi square distributions while RR shows better results at both gamma and chi square distributions when <em>P</em>=10 and n=90.</p> <p><strong>Keywords:</strong> Multicollinearity, Partial Least Square Regression, Ridge Regression, Principal Component Regression</p>Usman, U.Yau, S.A.Zakari, Y.7