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Item Open Access Pre-emptive Integer Programming As a Method Achieving Priotization for Decision Making(Department of Statistics, Nasarawa State University Keffi., 2019-02-23) Maijamaa, Bilkisu; Muhammad, Engku NazriWith limited availability of resources, an approach to moderate both financial and quality output with transparency to allocate the available budget for better decision making is of great importance. Budget allocation on strategies is needed, Preemptive Integer programming model is proposed in this research paper to optimize the budget allocated by organizational management. In the model, marginal analysis is estimated in the form of rating by each strategy with respect to the amount of money spent on the strategy for previous year was used as a base, calculated and used as either the parameter for the respective variable in the objective function or the constraints in the models. The optimal results obtained were discussed and compared. This preemptive integer programming as a method achieving Priotization for decision making proves useful and suitable for organisations with strategies used as oriented programs to improve organizational output with limited availability of resourcesItem Open Access On the Effects of COVID-19 outbreak on the Nigerian Stock Exchange performance: Evidence from GARCH Models(Department of Statistics, Nasarawa State University Keffi., 2020-04-24) Adenonmon, Monday Osagie; Maijamaa, Bilkisu; Owoicholofu, DanielCOVID-19 was first identified in Wuhan, China in December 2019 and has caused huge death and has spread to almost all the parts of the world. There are speculation that most of the world economy and financial markets would be affected due to lockdown and social distancing. The first case of COVID-19 was first identified in Nigeria on 27th February 2020 and this study examines the effect of COVID-19 outbreak on the performance of the Nigeria stock exchange using historical data covering 2nd March 2015 to 16th April, 2020 sourced from a secondary source. This study considered the COVID-19 period from 2nd January 2020 to 16th April 2020, the results revealed a loss in stock returns and high volatility in stock returns under the COVID-19 period in Nigeria as against the normal period under study. In addition, Quadratic GARCH (QGARCH) and Exponential GARCH (EGARCH) models with dummy variable were applied to the stock returns shows that the COVID-19 has had negative effect on the stock returns in Nigeria. The study recommended that political and economic policy such as stable political environment, incentive to indigenous companies, diversification of the economy, flexible exchange rate regime be implemented so as to improve the financial market and to attract more and new investors to the Nigerian Stock Exchange.Item Open Access Program-Budget Marginal-Analysis for University Strategies concept of Planning and Execution(Department of Statistics, Nasarawa State University Keffi., 2018-06-22) Maijamaa, Bilkisu; Muhammad, Engku NazriResearch addressing budgeting allocation planning on budget allocation and execution planning on Priotization of strategies are scanty in literature. This study presents program-budget marginal-analysis for university budget planning and execution aimed at priotizing budget allocation on strategies used for improving university rating. The research will illustrate the program-budget marginal-analysis with little adjustment to suit the university strategic budget allocations. This paper proposes a conceptional frame work for budget planning execution on university strategies. The framework for implementing PBMA will identify the total amount of available resources or funding allocated to priorities, examination of the current allocation activity, evaluation of benefit of cost of expansion with regards to both existing and new introduced strategies, in any of the existing services in use, which is effective with fewer resources allocation. Alternatives to be allocated fewer resources with greater effectiveness included in the priotized list. The budget allocation has the potential to maximize efficiency of each strategic allocation for improving the university rating.Item Open Access On Survival of Hiv Patients Using Share Frailty Model(Department of Statistics, Nasarawa State University Keffi., 2016-04-19) Maijamaa, Bilkisu; Chaku, Shammah Emmanuel; Adehi, Mary Unekwu; Modu, BabaganaIn a situation of terminal event of death happening during follow-up period to preclude further occurrence for recurrent event, the shared frailty model is used considering proportional hazard model for the recurrent and terminal process. Covariates effect taken into account are the ART status of entry, number of medication taken and CD4PepBase of the HIV patient and dependence modeled by the shared frailty model on survival. Human immunodeficiency virus has now reduced from a fatal disease to a chronic disease due to a high rate of antiretroviral treatment ART. ART helps in reducing the viral load and hence bringing mortality due to HIV/AIDS to the lowest minimum. Factors associated with mortality in HIV has significantly studied in the most literature, less attention given to the stages of HIV at which the ART began about the survival time. The awareness and risk factors for mortality at each stage of HIV on when the ART starts for a subject considered in this paper. The research aimed at constructing appropriate measures on stages at which the ART is started to the survival time is evaluated using a shared frailty model to account for heterogeneity within groups of stages of HIV subject.Item Open Access COMPARISON OF ESTIMATORS EFFICIENCY FOR LINEAR REGRESSIONS WITH JOINT PRESENCE OF AUTOCORRELATION AND MULTICOLLINEARITY(Department of Statistics, Nasarawa Sate University Keffi., 2021-08-06) Anono, Zuabir Mohammed; Adenomon, Monday OsagieThis paper proposes a new estimator called Two stage K-L estimator by combining these two estimators previously proposed by Prais Winsten (1958) and Kibra with Lukman (2020) for autocorrelation and multicollinearity respectively and to derived the necessary and sufficient condition for its superiority over other competing estimators. Simulation study was used to ascertain the dominance of this new estimator using the finite sample properties of estimators in terms of the estimated mean squared error. The study findings shows that under severe autocorrelation and collinearity condition, the proposed Two stage K-L estimator appears to be having a similar performance with RMLE and MLE. Also, under severe autocorrelation and moderate collinearity condition, regardless of the sample size, the proposed Two stage K-L estimator is seen to outperform all other estimators and lastly, the Two stage K-L estimator appears to have an improved performance as the large sample sizes. The study recommends that when autocorrelation and multicollinearity level is at moderate to severe, the proposed Two stage K-L estimator will perform better regardless of the size of the data, and the degree of autocorrelation and multicollinearity should be considered while estimating parameters and thus applying an efficient estimator to avoid erroneous inferences.Item Open Access Studying the Impacts of Inflation, Import and Export on Gross Domestic Product using Markov Switching Vector Autoregressive Model(Department of Statistics, Nasarawa Sate University Keffi., 2022-03-05) Micheal, V.A.; Adenomon, Monday Osagieome macroeconomic variables have been studied based on their impacts and contribution to the economic growth especially in Nigeria. The study focuses on the im- pacts of inflation, import and export on the gross domestic product using Markov switch- ing vector autoregressive(MS-VAR) model which is designed for econometric modeling of univariate and multiple time series subject to shifts in regime. The data spanned through 1980 to 2020 from National Bureau of Statistics and Central Bank of Nigeria respectively. The result of ADF test and Philip Perron test showed that the variables are stationary at first difference I(1) at 5% critical value. The Zivot-Andrew unit root with structural break showed that the variables are also integrated of order 1. The respective dates correspond to transition of government in 1983, structural adjustment programme in 1986, election in 1993 and a coup in 1995. Inflation is statistically significant using Lee-Strazicich test for two structural breaks. The results of cointegration test indicated that there is no long run relationship among the variables of interest without and with structural breaks. MS-VAR result showed that the probability of staying in regime 1 (that is a period of expansion) in Nigeria economy is higher than in regime 2 (that is a period or state of recession) in the nation’s economy which suggests that regime 1 is more persistent than regime 2 and the period of growth in regime 1 is about 16 years while it lasted 11 years in regime 2. This implies that Nigeria economy is more stable in regime 1(expansion period) compared to that of regime 2.Item Open Access Robustness Test of the Two Stage K-L Estimator in Models with Multicollinear Regressors and Autocorrelated Error Term(Department of Statistics, Nasarawa Sate University Keffi., 2021-08-26) Anono, Zuabir Mohammed; Adenomon, Monday OsagieIn a classical multiple linear regression analysis, multicollinearity and autocorrelation are two main basic assumption violation problems. When multicollinearity exists, biased estimation techniques such as Maximum Likelihood, Restricted Maximum Likelihood and most recent the K-L estimator by Kibria and Lukman [1] are preferable to Ordinary Least Square. On the other hand, when autocorrelation exist in the data, robust estimators like Cochran Orcutt and Prais-Winsten [2] estimators are preferred. To handle these two problems jointly, the study combines the K-L with the Prais-Winsten’s two-stage estimator producing the Two-Stage K-L estimator proposed by Zubair & Adenomon [3]. The Mean Square Error (MSE) and Root Mean Square Error (RMSE) criterion was used to compare the performance of the estimators. Application of the estimators to two (2) real life data set with multicollinearity and autocorrelation problems reveals that the Two Stage K-L estimator is generally the most efficient.Item Open Access APPLICATION OF MARKOV-SWITCHING VECTOR AUTOREGRESSIVE MODEL TO GDP AND INFLATION IN NIGERIA(Department of Statistics, Nasarawa Sate University Keffi., 2022-09-03) Micheal, Vincent Abiodun; Adenomon, Monday Osagiehis study investigates the gross domestic products and inflation in Nigeria using a time series data from 1960 – 2019 with the aid of Markov switching vector autoregressive model. Markov switching vector autoregressive (MSVAR) model is used to determine the structure of inflation in Nigeria. The result from this study concludes that the MSVAR model is a high-degree flexible model having captured regime shifts in the mean, variance and parameters of the vector autoregressive process. Also, it is observed that inflation in this regard is well fitted by the MSVAR model and the filtered probabilities can be deduced. This gave reasons by the estimated parameters and the filtered probability plots of regime 1 and 2.The result shows that they have high transition probabilities of 0.99 and 0.97 respectively with expected durations that corresponds to the probability in a regime are 69 and 35 showing that inflation on the economic growth will stay in the origin state almost two time before movement to the second state. Therefore, this study concludes that there is regime switch in the data under study. Hence, it is recommended that the economic policy makers in Nigeria be cautious in decision making due to unstable inflation in Nigeria economy.Item Open Access Curbing the trend of covid-19 in Nigeria using non- pharmaceutical Interventions and Mathematical Models(Department of Statistics, Nasarawa Sate University Keffi., 2020-11-11) Adenomon, Monday Osagie; John, D.O.Item Open Access On Share Frailty Cure Model: An Application On Cervical Cancer(Department of Statistics, Nasarawa State University Keffi., 2016-03-11) Maijamaa, Bilkisu; Muhammad, Engku NazriSurvival analyses are greatly used in medical research especially frailty models which are mostly used to account for heterogeneity in time-to-event. Over the years treatment of cancer has progressed with some patients being cured from different type of cancer. Survival analysis is more focused on subjects that are less at risk of recurrences, metastasis or death after the first treatment as these set of subjects are regarded as being cured. The general assumption of standard frailty model is that all subjects have the same frailty. These assumptions ignore the heterogeneity of such frailties and will lead to incorrect results and conclusions. To address the identified deficiencies in previous studies, this research will propose a shared frailty cure model. Shared frailty assumes that within a cluster the value of frailty term is improved with constant and common frailty to all subjects in the same group clusters by measuring the correlation between event times within the cluster, hence representing changes over time in clusters or population heterogeneity. These structures can be achieved by introducing covariates that are rank specific by the process Shared frailty model, addressing the weakness of the cure frailty model by considering the homogeneity in groups or clusters were failure can be similar by having the same frailty.Item Open Access On the volatility of daily stock returns of Total Nigeria Plc: evidence from GARCH models, value-at-risk and backtesting(Department of Statistics, Nasarawa Sate University Keffi., 2020-08-06) Emenogu, N.G.; Adenomon, Monday Osagie; Nweze, N.O.This study investigates the volatility in daily stock returns for Total Nigeria Plc using nine variants of GARCH models: sGARCH, girGARCH, eGARCH, iGARCH, aGARCH, TGARCH, NGARCH, NAGARCH, and AVGARCH along with value at risk estimation and backtesting. We use daily data for Total Nigeria Plc returns for the period January 2, 2001 to May 8, 2017, and conclude that eGARCH and sGARCH perform better for normal innovations while NGARCH performs better for student t innovations. This investigation of the volatility, VaR, and backtesting of the daily stock price of Total Nigeria Plc is important as most previous studies covering the Nigerian stock market have not paid much attention to the application of backtesting as a primary approach. We found from the results of the estimations that the persistence of the GARCH models are stable except for few cases for which iGARCH and eGARCH were unstable. Additionally, for student t innovation, the sGARCH and girGARCH models failed to converge; the mean reverting number of days for returns differed from model to model. From the analysis of VaR and its backtesting, this study recommends shareholders and investors continue their business with Total Nigeria Plc because possible losses may be overcome in the future by improvements in stock prices. Furthermore, risk was reflected by significant up and down movement in the stock price at a 99% confidence level, suggesting that high risk brings a high return.Item Open Access Predicting αααα-amylase yield and malt quality of some sprouting cereals using 2nd order polynomial model(Department of Statistics, Nasarawa Sate University Keffi., 2009-07-07) Evans, Egwim C.; Adenomon, Monday OsagieAlpha amylase yield in sprouting Maize, Acha, Rice and Sorghum were studied for 180 h. The result was analyzed using 2nd order polynomial model. The result showed that the rate of - amylase secretion with growth period is significantly high (p < 0.05) and the R2 for each ranged from 67 - 90%, while the R2 for sprouting vigour ranged within 99% for all the cereals studied. The prediction for amylase activity from sprouting vigour was significant (p < 0.05) for all the cereals studied, the R2 for all the cereals ranged between 63 - 91%. The results conclude that αααα-amylase and malt quality can be predicted in sprouting cereals from the growth vigour.Item Open Access Modelling The Dynamic Relationship Between Rainfall and Temperature Time Series Data In Niger State, Nigeria.(Department of Statistics, Nasarawa Sate University Keffi., 2013-03-05) Adenomon, Monday Osagie; Ojehomon, V.E.T.; Oyejola, B.A.Vector Autoregression (VAR) has some very attractive features and has provided a valuable tool for analysing dynamics among time series processes. This paper examined the dynamic relationship between rainfall and temperature time series data in Niger State, Nigeria, collected from the Meteorological station, NCRI, Badeggi, Niger State, Nigeria which spanned from January 1981 to December 2010. The VAR model favoured VAR at lag 8 which indicated bi- directional causation from rainfall to temperature and from temperature to rainfall. The Impulse Response Functions and the Forecast Error Variance Decomposition were further used to interpret the VAR model. We concluded that modelling rainfall and temperature together in Niger State will further improved the forecast of rainfall and temperature respectively.Item Open Access Statistical Investigation on the Hydrolysis and Fermentation Processes of Cassava Peels in the Production of Bioethanol(Department of Statistics, Nasarawa Sate University Keffi., 2017-10-31) Adenomon, Monday Osagie; Evans, Patience O.; Nma, Tela MusaThere are several types of experiments which require statistical investigation. These are characterized by the nature of treatments under investigation and also the nature of comparison required among them so as to meet the objectives of the experiment. To achieve this, cassava peels was collected from Kasuwa Gwari market Minna, Niger state dried and taken for hydrolysis and fermentation processes. Temperature, acid concentration, cassava biomass ratio, ph and time were varied to get the optimum yield of reducing sugar. Curve fitting and a two-way analysis of variance were used in analyzing the data. Most of the results from the experiment follows quadratic model. Furthermore, time and temperature were very significant in both hydrolysis and fermentation processes. We therefore concluded that for hydrolysis process yield is optimum at 110°C and 30mins, while for fermentation process yield is optimum at 35°C and at 6 days and 7 days respectively.Item Open Access Fitting a Poisson Regression Model to Reported Deaths from HIV/AIDS in Nigeria(Department of Statistics, Nasarawa Sate University Keffi., 2017-10-31) Adenomon, Monday Osagie; Adebukola, Adenomon Clarahe Human Immunodeficiency Virus (HIV)/Acquired Immunodeficiency syndrome (AIDS) epidemic has become one of the greatest challenges to public health among adults in Sub-Saharan African. In Nigeria, HIV/AIDS epidemic remain one of the major causes of death in the general population, particularly among young adult. In this paper, we will use Poisson regression model to study the linear trend of annual deaths resulting from HIV/AIDS in Nigeria for the period of 1996 to 2004. The result from the Poisson regression revealed an increase in rate of death resulting from HIV/AIDS in Nigeria. Therefore, there should be increase in the level of awareness of HIV/AIDS and other precautionary measures should also be observed in other to reduce the menace.Item Open Access On the Performances of Classical VAR and Sims-Zha Bayesian VAR Models in the Presence of Collinearity and Autocorrelated Error Terms(Department of Statistics, Nasarawa Sate University Keffi., 2016-02-25) Adenomon, Monday Osagie; Evans, Patience O.In time series literature, many authors have found out that multicollinearity and autocorrelation usually afflict time series data. In this paper, we compare the performances of classical VAR and Sims-Zha Bayesian VAR models with quadratic decay on bivariate time series data jointly influ- enced by collinearity and autocorrelation. We simulate bivariate time series data for different col- linearity levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) and autocorrelation levels (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) for time series length of 8, 16, 32, 64, 128, 256 respectively. The results from 10,000 simulations reveal that the models performance varies with the collinearity and autocorrelation levels, and with the time series lengths. In addition, the results reveal that the BVAR4 model is a viable model for forecasting. Therefore, we recommend that the levels of collinearity and autocorrelation, and the time series length should be considered in using an appropriate model for forecasting.Item Open Access APPLICATION OF OKUN’S LAW ON NIGERIAN ECONOMY: EVIDENCE FROM SPATIAL ECONOMETRICS ANALYSIS(Department of Statistics, Nasarawa Sate University Keffi., 2021-03-06) Okoro-Ugochukwu, N.A.; Adenomon, Monday OsagieSpatial econometrics should be viewed in a wide sense involving developments of models and statistical tools for the analysis of externalities, spillovers, interactions etc., in various areas including economics, geography and regional science, etc. This study examined application of Okun’s law on the Nigerian Economy using 2018 cross-sectional data of Gross Domestic product (GDP) and unemployment rate data sourced from the National Bureau of Statistics (NBS), Nigeria and from an economics website. In economics, Okun’s law is an empirically observed relationship between unemployment rate and GDP of any country. Results from the Ordinary Least Squares (OLS) reveal that there is positive relationship between unemployment rate and GDP in Nigeria though not significant while autocorrelation is present in the estimated model at 5% level of significance. The Moran I statistic for spatial autocorrelation test is significant at 5% while the Monte- Carlo simulation of Moran I statistic at 10,000 simulations revealed the presence of spatial autocorrelation at 5% level of significant. The following spatial models namely: Spatial Lag Model (SLM), Spatial Error Model (SEM) and Spatial Autoregressive with autoregressive error structure (SARAR) were applied in this study. In addition, result from Spatial Lag Model shows a unit increase in GDP leads to an increase of 0.0497 with increase in Unemployment rate in Nigeria. In addition, a unit increase of GDP in one state of Nigeria produces a total impact of increment of 0.1306 in Unemployment rate. The findings contradict Okun’s Law but the relationship is not significant in the case of the Nigerian Economy.Item Open Access A Simulation Study on the Performances of Classical Var and Sims-Zha Bayesian Var Models in the Presence of Autocorrelated Errors(Department of Statistics, Nasarawa Sate University Keffi., 2015-04-04) Adenomon, Monday Osagie; Evans, Patience O.It is well known that a high degree of positive dependency among the errors generally leads to 1) se- rious underestimation of standard errors for regression coefficients; 2) prediction intervals that are excessively wide. This paper set out to study the performances of classical VAR and Sims-Zha Bayesian VAR models in the presence of autocorrelated errors. Autocorrelation levels of (−0.99, −0.95, −0.9, −0.85, −0.8, 0.8, 0.85, 0.9, 0.95, 0.99) were considered for short term (T = 8, 16); medium term (T = 32, 64) and long term (T = 128, 256). The results from 10,000 simulation revealed that BVAR model with loose prior is suitable for negative autocorrelations and BVAR model with tight prior is suitable for positive autocorrelations in the short term. While for medium term, the BVAR model with loose prior is suitable for the autocorrelation levels considered except in few cases. Lastly, for long term, the clas- sical VAR is suitable for all the autocorrelation levels considered except in some cases where the BVAR models are preferred. This work therefore concludes that the performance of the classical VAR and Sims-Zha Bayesian VAR varies in terms of the autocorrelation levels and the time series lengths.Item Open Access Short Term Forecasting Performances of Classical VAR and Sims-Zha Bayesian VAR Models for Time Series with Collinear Variables and Correlated Error Terms(Department of Statistics, Nasarawa Sate University Keffi., 2015-01-07) Adenomon, Monday Osagie; Evans, Patience O.Forecasts can either be short term, medium term or long term. In this work, we consider short term forecast because of the problem of limited data or time series data that often encounter in time series analysis. This simulation study considers the performances of the classical VAR and Sims-Zha Bayesian VAR for short term series at different levels of collinearity and correlated error terms. The results from 10,000 iteration reveal that the BVAR models are excellent for time series length of T = 8 for all levels of collinearity while the classical VAR is effective for time series length of T = 16 for all collinearity levels except when ρ = −0.9 and ρ = −0.95. Therefore, we recommend that for effective short term forecasting, the time series length, forecasting horizon and the colli- nearity level should be considered.Item Open Access Optimal Budget Allocation for University Research and Publication Agenda through Integer Programming(Department of Statistics, Nasarawa State University Keffi., 2017-09-20) Maijamaa, Bilkisu; Muhammad, Engku Nazri; Bakar, Abu EngkuFor the past few years, government-funded universities in Malaysia faced an uphill battle to strategize their management budget due to significant budget cut by the Malaysian Government. One portion of the budget will be spent towards achieving the key performance indicators (KPIs) set by the universities to achieve their annual targets. Unfortunately, some universities set up their specific strategies to achieve the KPIs without ample consideration to the limited available resources where less attention is channeled to the cost of achieving the KPIs. Setting priorities and making decisions on allocation and reallocation of resources based on the direction of the strategies must be executed with transparency and accountability and will be of great importance. In this paper we illustrate how integer programming was applied to allocate budget based on the KPIs set for one of the government-funded Malaysian universities’ (U-XYZ’s) research and publication agenda. Two models were developed and successfully solved. The first model was to determine the total budget needed if all the KPIs were to be achieved while the second model was to distribute the allocated budget set by U-XYZ, for all the activities planned for the agenda. The result showed that in order to achieve the target, U-XYZ has to increase its budget allocation by RM2.164 million. Otherwise, U-XYZ can only expect to obtain 1.578 out of 1.593 points that is required to be achieved.
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