Open Access Original Research Article

Evaluating Properties and Performance of Long Memory Models from an Emerging Foreign Markets Return Innovations

Deebom Zorle Dum, Isaac Didi Essi, Amos Emeka

Asian Journal of Probability and Statistics, Page 1-23
DOI: 10.9734/ajpas/2021/v11i430271

The study investigates evaluate properties and performance of long memory models from emerging foreign markets return innovations between 1991 - 2020. The purpose of the study includes; investigate the persistence of shocks in Nigerian international markets, model long-range dependence, test the efficient markets hypothesis using fractionally integrated volatility models, develop an appropriate long memory model for Nigerian international markets, compare the advantages between short and long memory models in modeling for the returns in Nigerian international Markets and Give forecast values for future occurrences. The design for the study was an ex post facto research design. The data used for this study were Nigerian crude oil prices (Dollar per Barrel), exchange rate, and Agricultural Commodity prices extracted from the website of the Central Bank of Nigeria (CBN) www.cbn.ng. The total data points were 1044 and it spanned from 1st January 1991 to 30th January 2020. The statistical software used for data analysis was STATA 15 and OX metrics version 7. In an attempt to achieve the aim of the study, parametric and non-parametric methods of detecting Long Memory were applied. The study applied short and long memory models in an attempt to spot out the deficiencies associated with the short memory models. The results confirmed the presence of long memory in sales and returns on prices in Nigerian international markets. The presence of long memory in both sales and returns on prices in Nigerian International markets disprove the efficient market hypothesis which says that the future returns and volatility values are unpredictable. Similarly, base on performance evaluation using the Akaike information criteria, ARFIMA(1,-0.021,1) model was found to be the best fit model to the data after checking the adequacy of the model selected. Sequel to the above, it was recommended that there is a need for a strong financial and economic reform policy to curb persistent shocks in Nigerian international markets. This is because a stable local financial currency builds confidence in an economy, especially when foreign investors intend to invest in the country’s economy. For example, exchange rate policies also trim down the desire for local investors to trade in the international market. Also, for empirical estimation of long memory sales and returns on prices in Nigeria international markets, ARFIMA(1,-0.021,1) model should be considered appropriate. Two years (January, 20 to Dec-22) step ahead forecast shows that the predicted value for Cocoa Bean Sale using the ARFIMA (1,-0.021,1) falls between the range of 1.907247 to 1.915947.

Open Access Original Research Article

Statistical Quality Control Charts Based on Hyper-Geometrically Distributed Data

John E. Usen, Okim I. Ikpan, Mfawa D. Santos, Anthony A. Isaac, George C. MacGeorge, Mmekutufon F. Ekpety

Asian Journal of Probability and Statistics, Page 24-34
DOI: 10.9734/ajpas/2021/v11i430272

In some production and administrative processes, the occurrence of certain events is best described by a hyper-geometric distribution, which in turn should be pictorially depicted by what should be called a “hyper-geometric chart (Hg-chart)” in the field of Statistical Quality Control (SQC). However, this has never been the practice, since the existence of such a chart is absent; as such, prompting administrators and process engineers to make use of already existing charts for approximately depicting hyper-geometric processes. In this article, an SQC chart for any hyper-geometric process has been developed for the total number of events in a fixed number of units. This chart has been referred to as the Hg-chart. The center line (CC), lower control limit (LCL) and the upper control limit (UCL) have been obtained for the proposed chart with a sketch of how the proposed chart should be if used for simulation. It has been recommended that simulation should be used to test the proposed chart as this could prove to be more efficient and appropriate for describing hyper-geometric data rather than using an inappropriate chart to be an approximation for solving the problem.

Open Access Original Research Article

Perfect Dominating Set of An Interval-Valued Fuzzy Graphs

Faisal M. AL-Ahmadi, Mahiuob M. Q. Shubatah

Asian Journal of Probability and Statistics, Page 35-46
DOI: 10.9734/ajpas/2021/v11i430273

Aims/ Objectives: Perfect domination is very much useful in network theory, Electrical stations and several fields of mathematics. In This paper, perfect domination in an intervalvalued fuzzy graphs is defined and studied. Some bounds on perfect domination number γp(G) are provided for several interval-valued fuzzy graphs, such as complete, wheel and star,.. etc. Furthermore, the relationship of γp(G): with some other known parameters in interval-valued fuzzy graphs investigated with some suitable examples.

Open Access Original Research Article

Finite Euclidean Geometry Approach for Constructing Balanced Incomplete Block Design (BIBD)

U. P. Akra, S. S. Akpan, T. A. Ugbe, O. E. Ntekim

Asian Journal of Probability and Statistics, Page 47-59
DOI: 10.9734/ajpas/2021/v11i430274

In block design, construction of Balanced Incomplete Block Design (BIBD) remained an unsolved problem in combinatorial design; also various construction techniques have been introduced to build the elements of BIBDs for specific parameters; no general method has been proposed to find a suitable structure for BIBDs. This paper aim at employing Finite Euclidean Geometry FEG (N,s) of N – dimensional space to construct balanced incomplete block design (BIBD). Also geometrical construction of FEG (2,2) BIBDs has been made. The results show that this technique proved a better method for constructing BIBD than other methods in terms of estimation of parameters to build the design structure.

Open Access Original Research Article

Multivariate-Based Technique for Solving Multi-Response Surface Optimization (MRSO) Problems: The Case of a Maximization Problem

John E. Usen, Stephen S. Akpan, Thomas A. Ugbe, Ikpang N. Ikpang, Joy O. Uket, Bright O. Obeten

Asian Journal of Probability and Statistics, Page 60-85
DOI: 10.9734/ajpas/2021/v11i430275

Multi-response surface optimization (MRSO) is a problem that is peculiar to an industrial setting, where the aim of a process engineer is to set his process at operating conditions that simultaneously optimize a set of process responses. In Statistics, several methods have been proffered for tackling problems of this nature. Some of such methods are that of: overlapping contour plots, constrained optimization problem, loss function approach, process capability approach, distance function approach, game theory approach, and the desirability function approach. These, methods are however, not without teething flaws as they are either too problem specific, or require very complex and inflexible routines; little wonder, the method of desirability function has gained popularity especially because it overcomes the latter limitation. In this article, we have proposed and implemented a multivariate-based technique for solving MRSO problems. The technique fused the ideas of response surface methodology (RSM), multivariate multiple regression and Pareto optimality. In our technique, RSM was implemented on an all-maximization problem as a case-study process; in which case, first-order models (FOMs) for the responses were fitted using 2k factorial designs until the FOMs proved to be inadequate, while uniform precision rotatable central composite design was used to obtain second-order models (SOMs) for the respective responses in the event of model inadequacy of the FOMs. With the implementation of the proposed technique to the case study, optimal operating conditions were obtained, with observations stemming thereof summarized as axioms. The first, second and third axioms respectively stated that: (1) the mid-point of all optimal operating conditions obtained via the proposed technique is Pareto optimal, (2) the mid-point of all optimal responses at the Pareto optimal operating condition is Pareto optimal, and (3) the region bounded by each of the optimal operating conditions from each second-order model (SOM) is a Pareto front.