Open Access Original Research Article

Comparison of the Performance of the SANN, SARIMA and ARIMA Models for Forecasting Quarterly GDP of Nigeria

Chukwudike C. Nwokike, Emmanuel W. Okereke

Asian Research Journal of Mathematics, Page 1-20
DOI: 10.9734/arjom/2021/v17i330280

This research aimed at modelling and forecasting the quarterly GDP of Nigeria using the Seasonal Artificial Neural Network (SANN), SARIMA and Box-Jenkins models as well as comparing their predictive performance. The three models mentioned earlier were successfully fitted to the data set. Tentative architecture for the SANN was suggested by varying the number of neurons in the hidden layer while that of the input and output layer remained constant at 4. It was observed that the best architecture was when the hidden layer had 10 neurons and thus SANN (4-10-4) was chosen as the best. In fitting the ARIMA/SARIMA models, the Augmented Dickey Fuller (ADF) test was used to check for stationarity. Variance stabilization and Stationarity were achieved after logarithm transformation and first regular differencing. The ARIMA/SARIMA model with lowest AIC, BIC and HQIC values was chosen as the best amongst the competing models and fitted to the data. The adequacy of the fitted models was confirmed observing the correlogram of the residuals and the Ljung-Box Chi-Squared test result. The SANN model performed better than the SARIMA and ARIMA models as it had a Mean Squared Error value of 0.004 while SARIMA and ARIMA had mean squared errors of 0.527 and 0.705 respectively. It was concluded that the SANN which is a non-linear model be used in modelling the quarterly GDP of Nigeria. Hybrid models which combine the strength of individual models are recommended for further research.

Open Access Original Research Article

Estimation of the Residuals Entropy Function of Inverse Weibull Distribution Based on Generalized Type-II Hybrid Censored Samples

Moshera A. M. Ahmad

Asian Research Journal of Mathematics, Page 21-34
DOI: 10.9734/arjom/2021/v17i330281

Shannon’s entropy plays important role in the information theory. However, it can’t be applied to systems which have survived for some time. Therefore, the concept of residual entropy was developed. In this paper, the estimation of the entropy of a two-parameter inverse Weibull distribution based on the generalized type-II hybrid censored sample is considered. The Bayes estimator for the residual entropy of the Inverse Weibull distribution under the generalized type-II hybrid censored sample is given. Simulation experiments are conducted to see the effectiveness of the different estimators.

Open Access Original Research Article

Comparative Modelling of Price Volatility in Nigerian Crude Oil Markets Using Symmetric and Asymmetric GARCH Models

Deebom Zorle Dum, Mazi Yellow Dimkpa, Chims Benjamin Ele, Richard Igbudu Chinedu, George Laurretta Emugha

Asian Research Journal of Mathematics, Page 35-54
DOI: 10.9734/arjom/2021/v17i330282

The study aimed at developing an appropriate GARCH model for modelling in Nigerian Crude Oil Prices Markets using symmetric and Asymmetric GARCH models while the specific objectives of the study include to: build an appropriate Symmetric and asymmetric Generalized Autoregressive Conditional Heteroskedacity (GARCH) model for Nigerian Crude Oil Prices, compare the advantage of using Symmetric and Asymmetric GARCH.  The data for the study was extracted from the Central Bank of Nigeria online statistical database starting from January, 1982 to December, 2018. The software used in estimating the parameters of the model is Econometric view (Eview) software version ten (10). Two classes of models were used in the study; they are symmetric and Asymmetric GARCH models. The results of the estimated models revealed that Asymmetric GARCH model (EGARCH (1,1) in student’s-t error assumption gave a better fit than the first order Symmetric GARCH models. Also, Using EGARCH (1,1) models with their corresponding error distribution in estimating crude oil price was found that the larger the size of the estimated news components of the model, the higher the negative news associated with high impact of volatility. This means that conditional volatility estimated using EGARCH model has strong asymmetric characteristic which is prone to news sensitivity. Based on the above findings, recommendations were made in the study.

Open Access Original Research Article

Analytical Solution of a Non-isothermal Flow in Cylindrical Geometry

Chinedu Nwaigwe, Innocent Uchenna Amadi

Asian Research Journal of Mathematics, Page 55-76
DOI: 10.9734/arjom/2021/v17i330283

This study proposes analytical solution to the problem of transport in a Newtonian fluid within a cylindrical domain. The flow is assumed to be dominated along the channel axis, and is taken to be axi-symmetric. No-slip boundary condition is considered for velocity while the temperature and concentration have Dirichlet boundary values. The resulting problem is transformed into a set of non-trivial variable coefficient differential equations in a cylindrical geometry. By adopting the series solution method of Frobenius, the closed-form analytical solutions are derived for the flow variables. We conduct an analysis of the derived model, and showed that, indeed, the flow variables are axi-symmetric. We also state and prove another theorem to show that the derived concentration model is positivity preserving – meaning that it yields positive concentration - provided the boundary value is non-negative. Finally, we present graphical results for the flow variables and discuss the effect of the relevant flow parameters. The results showed that (i) an increase in the cooling parameter, reduces the fluid velocity, (ii) the temperature decreases as the cooling parameter increases   and (iii) an increase in the injection parameter, leads to increase in the concentration.

Open Access Original Research Article

A Study on Sum Formulas of Generalized Hexanacci Numbers: Closed Forms of the Sum Formulas ∑n k=0 xkWk and ∑nk=1 xkW−k

Yüksel Soykan

Asian Research Journal of Mathematics, Page 93-118
DOI: 10.9734/arjom/2021/v17i330285

In this paper, closed forms of the sum formulas ∑n =0 xkWk and ∑n k=1 xkW-k for generalized Hexanacci numbers are presented. As special cases, we give summation formulas of Hexanacci, Hexanacci-Lucas, and other sixth-order recurrence sequences.

Open Access Original Research Article

Generalized Weierstrass Integrability of a Class of Second-order Nonlinear Differential Equations

Xin Zhao, Yanxia Hu

Asian Research Journal of Mathematics, Page 119-133
DOI: 10.9734/arjom/2021/v17i330286

The generalized Weierstrass integrability of a class of second-order nonlinear differential equations is considered. The conditions of existence and the corresponding expressions of generalized Weierstrass inverse integrating factors of the second-order nonlinear differential equation are presented. The relationship between the generalized Weierstrass inverse integrating factors and the Weierstrass inverse integrating factors is given. Finally, as an application of the main results, a Kudryashov-Sinelshchikov equation for obtaining traveling wave solutions is considered.

Open Access Original Research Article

Connections on Valuated Binary Tree and Their Applications in Factoring Odd Integers

Xingbo Wang, Jinfeng Luo, Ying Tian, Li Ma

Asian Research Journal of Mathematics, Page 134-153
DOI: 10.9734/arjom/2021/v17i330287

This paper makes an investigation on geometric relationships among nodes of the valuated binary trees, including parallelism, connection and penetration. By defining central lines and distance from a node to a line, some intrinsic connections are discovered to connect nodes between different subtrees. It is proved that a node out of a subtree can penetrate into the subtree along a parallel connection. If the connection starts downward from a node that is a multiple of the subtree’s root, then all the nodes on the connection are multiples of the root. Accordingly composite odd integers on such connections can be easily factorized. The paper proves the new results with detail mathematical reasoning and demonstrates several numerical experiments made with Maple software to factorize rapidly a kind of big odd integers that are of the length from 59 to 99 decimal digits. It is once again shown that the valuated binary tree might be a key to unlock the lock of the integer factorization problem.

Open Access Review Article

Lattices and the Geometry of Numbers

Sourangshu Ghosh

Asian Research Journal of Mathematics, Page 77-92
DOI: 10.9734/arjom/2021/v17i330284

In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory.  This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to study the properties of algebraic numbers. It has application on various other fields of mathematics especially the study of Diophantine equations, analysis of functional analysis etc. This paper gives an elementary introduction to the field of geometry of numbers. In this paper we shall first give a broad overview of the concept of lattice and then discuss about the geometrical properties it has and its applications.