iosr-Jm   Volume-18 ~ Issue-2 ~ Mar. – Apr. 2022

Abstract:This paper presents the power of some tests for detecting heteroscedasticity in Constant Elasticity of Substitution (CES) nonlinear model. The tests used include Breusch-Pagan, Glejser, White, Park and Goldfeld- Quandt. The CES production function was transformed to intrinsically linear model through Kmenta linearization approach. Using the parameter estimates of the model, the residual was computed and used as the dependent for the auxiliary regression. The error structure data was drawn from a normal distribution with mean, zero and variance, 2
 . The sample sizes for the simulation were 10 and 30, 50 and 100, 150 and 200 for small, medium and large sample sizes, respectively with 10,000 replications. The levels of heteroscedasticity
introduced were 0.1, 0.5 and 0.9 for mild, moderate and severe heteroscedasticity, respectively. The result indicates that the power of the test for Glejser and Park tests increases as the sample size increases at every level of heteroscedasticity both at 1% and 5% levels of significance......

Key words: Heteroscedasticity, CES, Power of the test, Production Function

[1]. Ameniya, Takeshi. (1994) "Introduction to Statistics and Econometrics", Cambridge, MA: Harvard University Press.
[2]. Anne Peguin-Feissolle., Birgit Strikholm and Timo Terasvita (2008) "Testing the Granger Noncausality Hypothesis in Stationary Nonlinear Models of Unknown Functional Form", CREATES Research Papers, 2008-19, Dept of Economics and Business Economics, Aarhus University.
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[4]. Ayoola, J. F., and Olubusoye, O. E (2012) "Estimation of Parameters of Linear Econometric Model and the Power of Test in the Presence of Heteroscedasticity", Journal of Mathematical Theory and Modelling", Vol. 2 (5), 27-43.
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Abstract: In the course of solving scientific problems, it is not uncommon for the same searchable quantity to have different numerical values and the difference between them to be more than the margin of error in obtaining them. This creates uncertainty in the estimation of its true value. The smallest separate values number of the searchable quantity, at which a deterministic estimate is still possible, is three. The two values of the three that have the greatest difference are mutually exclusive. When the definition is independent, the third, intermediate value plays a clarifying role, indicating the proximity of the searchable quantity to one of the two mutually exclusive values. This paper considers the general solution of equations for the searchable quantity true value and its three separate values......

Key Word: deterministic estimate, uncertainty, systematic error, scatter, clarifying, general solution, particular solution, averaging, arithmetic mean, Hubble constant

[1]. Natalie Wolchover. Cosmologists Debate How Fast the Universe Is Expanding // Quanta magazine: August 8, 2019. URL: http://www.quantamagazine.org/cosmologists-debate-how-fast-the-universe-is-expanding-20190808, accessed 06.04.2022

Abstract: Most time series analysis have used different technical and fundamental approach in modeling result varies base on the approach used or applied. In these view, the aim of this study is to investigate the all Share Index of the Nigeria Stock Exchange rate using Generalized Autoregressive Conditional Heteroscedasticity (GARCH) approach and to test the existing models and select the best model for the data.
An upwards trend was observed from the time plot of the original series from the quarters along the years. The autocorrelation function plot of the original data was plotted to confirm the presence of seasonal variation in the data, the ACF plot indicated that the.......

Key Word: Autocorrelation, AIC, Forecast, Heteroscedasticity, Time plot, Volatility

[1]. Adnan, R. M., Yuan, X., Kisis, O. and Anam, R. Improving accuracy of river flow forecasting using LSSVR with gravitational search algorithm. Advances in Meteorology. 2017; (3):1-23.
[2]. Agwuegbo, S. O. N., Adewole, A. P. and Maduegbuna, A. N. A random walk model for stock market prices. Journal of Mathematical and Statistics. 2010; 6(3):342-346.
[3]. Ali, S. M. Time series analysis of Baghdad rainfall using ARIMA method. Iraqi Journal of Science. 2013; 54(4):1136-1142.
[4]. Al-Shaib, M.The predictability of the Amman Stock Exchange Using Univariate Autoregressive Integrated Moving Average (ARIMA) Model. Journal of Economic and Administrative Sciences. 2006; 22(2):17-35.
[5]. Ayodele, A. A., Aderemi, O. A and Charles, K. A. Stock price prediction using the ARIMA model. UKSim-AMSS 16th International Conference on Computer modeling and Simulation. 2014.

Abstract: Results are the expected outcome of every experimental or empirical research. Mathematically, these results could be extracted through analytical evaluation, numerical analysis or simulation. The presentation and interpretation of these results are the information conveyed to the end users for implementation. Consequently, the importance and relevance of result presentation and interpretation cannot be overemphasized. This paper studies the graphical presentation of results extracted from the analysis of dynamical model, involving either ordinary or delay differential equations, using MATLAB application and derived a novel plotyn code through the concept of plotyy and ploty4. The code is useful for plotting the results from the numerical analysis or simulation of dynamical systems of n-equations..

Key Word: Mathematical modeling; Dynamical system; Epidemiology; Graphical results; Plotyy; Plotyn

[1]. F. Benyah. Epidemiological modelling and analysis. The 13th Edward A. Bouchet/Abdus Salam workshop, 2007. University of Ghana, Legon, Accra, South Africa.
[2]. G.O. Agaba. Modelling of the spread of rabies with pre-exposure vaccination of humans. Mathematical Theory and Modeling, 4:57-63, 2014.
[3]. G.O. Agaba and M.C. Soomiyol. Analysing the spread of covid-19 using delay epidemic model with awareness. IOSR Journal of Mathematics, 16(3):52-59, 2020.
[4]. A. d'Onofrio. Stability properties of pulse vaccination strategy in SEIR epidemic model. Mathematical Biosciences, 179:57-72, 2002.
[5]. J. Medlock. Mathematical modelling of epidemics. Applied Mathematics Department, 2002. University of Washington

Abstract: In Number theory , Ramanujan's sum, usually denoted cq(n), is a function of two positive integer variables q and n defined by the formula. where (a, q) = 1 means that a only takes on values coprime to q. Also a real or complex valued function defined on the set of all positive integers is called an arithmetic function and an arithmetic function is said to be completely multiplicative function if f is not identically zero and f(mn) = f(m)f(n) for all m,n. we know the reduced residue system modulo N is the set of all integers m with gcd (m,N) = 1 and 0 ≤ m ≤ N.......

Key Word: Ramanujan sum, Arithmetic function, Multiplicative function, reduced residue system modulo integer

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[4]. Eckford Cohen, Arithmetical Inversion Formulas, Canadian J. Math., 12 (1960), pp 399-409.
[5]. Eckford Cohen, An Extension of Ramanujan's Sum , Vol.16, (1949), pp 85-90.

Abstract: The need to entrench strong foundation for the study of mathematics, so as to create a mathematics literate society to stimulate the development of the society motivated the researchers to conduct this research study on appraising the curriculum content coverage (Topical content coverage) and Learning Activity Index (LAI) of the approved mathematics texbooks in use in the Ebonyi State Junior secondary schools. The study adopted evaluation design. The instrument for data collection was the Approved Mathematics Textbook Assessment Instrument (AMTAI). Simple Random Sampling (SAR)was used to sample the twelve approved mathematics texbooks, which formed the sample of the study........

Key Word: Curriculum content coverage, learning acivity index, mathematics textbooks, topical content coverage, chi-square.

[1]. Asika, N.C. (2006), Research Methodology in the Behavioural Science. Lagos. Longman Nigeria PLC.
[2]. Ebonyi SMoE (2019). Annual School Census Report Abakaliki, Ebonyi State Ministry of Education.
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[5]. Ebonyi State Ministry of Education (2019). Basic Education Certificate Examination (BECE). Result Abakaliki, Examination Development centre.

Abstract: The need to create a mathematics literate society motivated the researchers to carry out this study to evaluate Teachers' Perception Index (TPI) and the Readability Index (RI) of approved mathematics textbooks in-use in junior secondary schools in Ebonyi State Nigeria. The study adopted evaluation design. The Instruments for data collection were theFlesch readability ease formular; the Approved Mathematics Textbook Assessment Instrument (AMAI) and 8 – point quantitative evaluation model for sciences books.Simple Random Sampling Technique was used to select four (4) approved mathematics textbooks, 7 secondary schools and 63 mathematics teachers that formed the sample of the study........

[1]. Ebonyi SMOE (2009). Basic Education Certificate Examination Result. Abakaliki, Examination Development Centre (EDC).
[2]. Emereole H.U (2008) A Quantitative Evaluation Approach for Science Textbooks: An 8-point model.Department of Mathematics and Science Education. Unpublished Thesis University of Botswana.
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[4]. Federal Republic of Nigeria. (2013). NationalPolicy on Education: 6th Edition NERDC, 3, Jibowu street Yaba Lagos-Nigeria
[5]. Maliki, E.B.; Nghan, A. N; and Ibu, J.E (2009). Analysis of Students' Performance in Junior Secondary School Mathematics Examination in Bayelsa State of Nigeriat. Home comm..sci, 3(2):131-134 (2009).