Journal of the Royal Statistical Society Nigeria Group (JRSS-NIG Group) ISSN NUMBER: 1116-249X

AN EFFICIENT SHORT CUT METHOD FOR COMPUTING THE COEFFICIENTS OF THE BEST LINEAR UNBIASED ESTIMATOR OF POPULATION MEAN FOR CORRELATED RANDOM VARIABLES

E. Onyemachi — 2026-05-20

An efficient short cut method for computing the coefficients of the best linear unbiased
estimator (BLUE) of the population mean for correlated random variables with a defined
covariance structure has been proposed in the paper. For correlated random variables with a
moving average process of order one covariance structure, the existing method involves
minimizing the variance of BLUE subject to the linear constraint that arises from the
unbiasedness condition. To propose a new efficient short cut method, the symmetric pattern
of BLUE�s vector of coefficients or weights was generalized using mathematical induction.
The existing quadratic programming problem was further simplified to obtain an efficient
short cut computational method by adding the developed symmetric pattern of the vector of
coefficients, along with the unbiasedness condition, as constraints. Hence, it reduces the
computational time and complexity involved in evaluating the covariance and/or correlation
matrix of the correlated variables. The efficacy of the proposed efficient method was
demonstrated with ease through the applicability of the method to compute the algebraic
expressions of weights or coefficients of BLUE when the number of observations; kn2? and
12??kn at fixed 8,...,2,1?k . Then, the estimates of BLUE�s weights when the number of
observations; 2;12???kkn were computed as an illustrative example. Empirical example
on BLUE�s weights computation was demonstrated using four purposively selected real life
data sets (each with varying sample sizes) that admit moving average process of order one.
The results indicate that BLUE�s weights computed using the proposed method estimate
population mean with high precision than the arithmetic mean (AM) across the varying
sample sizes of the four purposively selected data sets.

DYNAMICS OF CRUDE OIL PRICE, PRODUCTION AND EXPORTATION IN NIGERIA (2006 � 2024): A TIME-SERIES ANALYSIS

G. C. Ibeh — 2026-05-20

This study examines the dynamic relationships between crude oil prices, domestic production,
and exportation in Nigeria from January 2006 to December 2024 using advanced time-series
methodologies. Monthly data sourced from the Central Bank of Nigeria was analyzed,
encompassing crude oil prices (USD/barrel), production, and export volumes (million
barrels/day). A missing data point for April 2023 was addressed using linear interpolation.
Seasonal-Trend Decomposition using Loess (STL) revealed underlying trend structures, though
statistical tests confirmed no significant seasonal effects across the variables. Stationarity was
established through differencing, and a Vector Autoregressive (VAR) model with Granger
causality testing found no significant lagged influence of price fluctuations on production.
Volatility analysis using a Dynamic Conditional Correlation GARCH (DCC-GARCH) model
identified strong persistence in crude oil price and production volatility but no short-term
volatility spillovers. Comparative analysis across pre- and post-2014 and COVID-19 periods
highlighted structural shifts in volatility patterns and a decline in output and export volumes. The
study concludes with policy recommendations aimed at improving resilience in Nigeria�s oil
sector amidst external market shocks.

ANALYZING THE DYNAMIC RELATIONSHIP BETWEEN MACROECONOMIC VARIABLES IN NIGERIA WITH VECTOR TIME SERIES MODELS.

Y. A. Ibrahim — 2026-05-20

This study examines the dynamic relationship among key macroeconomic variables in
Nigeria, namely Gross Domestic Product (GDP), Exchange Rate (EXCR), Inflation
Rate (INFLR), and Unemployment Rate (UNEMPR ), using annual data from 1993 to
2022 obtained from the National Bureau of Statistics (NBS). By applying Vector
Error Correction Model (VECM) and Vector Autoregression (VAR) frameworks, the
analysis explores long-term equilibrium relationships and short-term dynamics.
Cointegration tests confirm the existence of two long-run equilibria, justifying the use
of VECM. The findings reveal that exchange rate stability has a significant effect on
GDP growth (? = 2.70, p < 0.01), while inflation and unemployment exert substantial
long-term negative effects (? = -3.89 and ? = -46.72, p < 0.01). Short-term dynamics
highlight structural rigidities in labour markets (p = 0.335). Policy priorities include
exchange rate stabilization, inflation control through monetary tightening, and labour
market reforms. This study provides a roadmap for fostering sustainable economic
growth and macroeconomic resilience in Nigeria.

Spatial Patterns and Healthcare Access in Early-Onset Breast Cancer Diagnosis in Lagos, Nigeria: A Bayesian Multilevel Analysis

Paul Omoh Olopha — 2026-05-20

Early-onset breast cancer (diagnosis before age 40) is an emerging public health concern in Nigeria,
yet its spatial distribution and determinants remain poorly understood, particularly in urban settings
with unequal access to diagnostic services. This study analysed retrospective breast cancer registry
data from the Lagos University Teaching Hospital (LUTH), with early-onset diagnosis defined as a
binary outcome. A Bayesian structured additive logistic regression model was used to assess socio-
demographic, clinical, and spatial effects. Nonlinear effects of age and distance to LUTH were
modelled using smooth functions, while spatial heterogeneity across Local Government Areas
(LGAs) was captured using a Gaussian Markov Random Field. A three-level hierarchical structure
accounted for clustering, and estimation was performed using Integrated Nested Laplace
Approximation (INLA). The unadjusted model showed geographic variation, but this was
substantially attenuated after adjustment, with no strong evidence of elevated risk across LGAs.
Distance to LUTH showed a decreasing nonlinear relationship with early-onset diagnosis, indicating
higher probabilities among individuals living closer to the facility. Age also exhibited a declining
nonlinear association. Overall, spatial variation is modest after adjustment and largely reflects
diagnostic access rather than true geographic clustering.

THE IMPACT OF AIR POLLUTION ON MORTALITY RATES IN NIGERIA: A STATISTICAL PERSPECTIVE.

B. A. Ogunwole — 2026-05-20

This study examined the association between air pollution indicators and mortality rates in
Nigeria over the period 2000 - 2024, the data obtained were mainly secondary data sourced from
the World Health Organization�s Global Health Observatory and National Bureau of Statistics.
In this paper, the independent variables are: Particulate matter concentrations (PM 2.5 and PM 10 ),
Nitrogen dioxide (NO 2 ) concentrations, Sulfur dioxide (SO 2 ) concentrations and Ozone (O 3 )
concentrations where the response variable is Mortality rate. The study employed Multiple
regression and correlation to investigate the influence of five air pollutants (PM 2.5 , PM 10 , NO 2 ,
SO 2 , and O 3 ) on mortality rates. From the regression models formed through Multiple Regression
Analysis; Y = 16.109 - 0.050(PM2.5) + 0.028(PM10) - 0.083(NO 2 ) - 0.031(SO 2 ) + 0.028(O 3 ).
The negative coefficients observed for PM 2.5 , NO?, and SO? suggest that their annual mean
concentrations were inversely related to mortality rates, whereas PM 10 and O? exhibited positive
associations. The opposing signs for PM 2.5 and PM 10 , despite PM 2.5 being a component of PM 10 ,
further suggest model misspecification or omitted variable bias rather than divergent health
effects. Similarly, the positive association observed for O? may be attributable to seasonal
confounding with temperature or other unmeasured covariates. These results diverge from
established epidemiological evidence and are best interpreted as exploratory, hypothesis-
generating associations that likely reflect residual confounding and shared temporal patterns
rather than causal exposure effects. Furthermore, diagnostic tests for multicollinearity,
heteroskedasticity, and autocorrelation confirmed that the dataset was free from these statistical
issues.

A Panel Data Modeling of the Impacts of Demographic Indicators on Human Development in Nigeria

E. I. Aniah-Betiang — 2026-05-20

This study investigates the impact of demographic indicators on human development in
Nigeria using panel data modeling approach. The study employed annual panel data spanning
1994-2024 across the six geopolitical regions in Nigeria. The annual data was sourced from
National Bureau of Statistics (NBS), National Population Commission (NPC), Harmonized
Nigeria Living Standard Survey (HNLSS) and Nigerian Demographic and Health Survey
(NDHSS). The study employed descriptive statistics and normality measures, fixed effect
model, random effect model and diagnostic tests. The descriptive statistics showed that HDI
had the highest mean (347.01) and FLP had the lowest mean (98.60). The demographic
indicators are positively skewed and leptokurtic in nature. The demographic indicators are
not normal. The diagnostic tests revealed that random effect model is appropriate for
modeling the demographic indicators in Nigeria and the presence of autocorrelation must be
addressed to ensure valid inference. The study revealed that fertility rate (FR), urbanization
rate (UR) and dependency ratio (DR) had negative impact whereas life expectancy at birth
(LEB) and Female Labour participation (FLP) had positive impact on human development in
Nigeria. The fixed and random effect model showed that 97.14% and 85.43% respectively of
the variations in human development were explained by the demographic indicators
(explanatory variables). The study concludes that LEB and FLP are important drivers of
human development whereas FR, UR and DR hinders the growth of human development in
Nigeria within the studied period. Based on the findings, It was recommended that
government should prioritize healthcare financing, maternal and child health services, and
policies enabling women�s employment as life expectancy at birth and female labour force
participation had positive impact on HDI. The software for estimation is E-Views.

MODELLING THE NIGERIAN STOCK EXCHANGE SERIES USING EVENT- BASED ARIMAX MODEL

A. A. Akintunde — 2026-05-20

Current investigation looked into dynamics of the Nigerian Stock Exchange with the aid of time
series modeling techniques. The All-share index was adopted, with a specific focus on
incorporating major economic and political events through event-based ARIMAX models.
Weekly ASI data were collected and subjected to analysis and diagnostic checks. The series was
differenced to achieve stationarity, and ARIMAX models were fitted. Notably, exogenous
variables such as the COVID-19 pandemic, the 2023 general elections, and the removal of fuel
subsidy in 2023 were encoded as dummy variables and integrated into the ARIMAX model.
Multicollinearity diagnostics using the Variance Inflation Factor (VIF) indicated no serious
multicollinearity among the exogenous variables. Comparison was achieved using the Akaike
Information Criterion (AIC). The result revealed that the ARIMAX model with lagged event
dummies provided improved explanatory power over the standard ARIMA model. Residual
diagnostics including the Ljung-Box test confirmed the models� adequacy. Macroeconomic
shocks on market behavior and the usefulness of incorporating event-based structures in time
series forecasting can be seen to be of great significance from the obtained results.

POISSON BAGUI-LIU-ZHANG DISTRIBUTION: A FLEXIBLE MIXED-POISSON MODEL FOR HEAVY-TAILED COUNT DATA

S. N. Gideon — 2026-05-20

Some over-dispersed count poses varying characteristics such as uni-modal or multi-modal,
right or left skewed, platokurtic or leptokurtic and therefore requires more flexible discrete
distributions than the existing ones in order to minimize estimation error. A new discrete
distribution named Poisson Bagui-Liu-Zhang distribution for modelling over-dispersed count
data has been proposed and its properties such as - hazard function, probability generating
function, characteristic function, rth factorial moment, raw and central moments, the
dispersion index, the coefficient of variation, the coefficient of skewness and the coefficient
kurtosis - derived. Conventional estimation methods were used to obtain the estimators for
the parameter of the distribution and their performances compared using simulated data. The
results from the simulation study showed that the maximum likelihood estimator and the
method of proportion estimator of the distribution, have positive bias and showed consistency
property while the method of moment estimator and weighted least squares estimator were
not consistent and were negatively biased. Generally, the maximum likelihood estimator of
the new distribution performed better than the other estimators obtained. Again the new
distribution was fitted to two real life data sets and its performance compared to that of the
Poisson-Lindley distribution, the Poisson-Akash distribution, the Poisson-Bilal distribution,
the geometric distribution and the negative binomial distribution. The results from the data
sets, with features; dispersion indices (419.13, 3.527), positive skeweness (3.50, 3.44) and
leptokurtic (15.38, 15.69), showed that the new distribution, having produced the minimum
values of Akaike information criterion (565.6158, 401.7164), Bayesian information criterion
(567.4000,404.4259), negative loglikelihood (281.8079,199.8582) and the highest values
Klomogrov-Smirnov/p-value (0.1651/0.3200,0.0942/0.1351) respectively for the two data
sets, performed better than the other distributions.

A SINGLE ACCEPTANCE SAMPLING PLAN FOR THE TRUNCATED LIFE TESTS BASED ON THE PERCENTILES OF ZECH DISTRIBUTION AND APPLICATIONS

John Sunday Adeyeye — 2026-05-20

This study proposes a Single Acceptance Sampling Plan (SASP) for the truncated life test based
on the percentiles of Zech distribution. The methodology is designed to address quality
assessment in both industrial and biomedical contexts, thereby demonstrating the distribution�s
dual applicability across the two domains. The use of percentiles, over the conventional median,
provides a more flexible and informative approach in evaluating product reliability with the
lower and upper percentiles accounting for the early and late failures in improving decision-
making accuracy. This research constructs an efficient sampling scheme that minimizes the
required sample size while simultaneously satisfying consumer�s and producer�s risk. This is
achieved by formulating and solving constrained optimization problems tailored towards the
proposed plan. The performance of the SASP is examined through simulated datasets, arbitrarily
chosen parameter values, and real-life data. To validate its practical utility, the proposed plan is
benchmarked against SASPs derived from other lifetime distributions. Furthermore, the adoption
of multiple percentiles enhances the robustness of the plan, offering a significant improvement
over earlier models that focus solely on the median. Comparative study indicates that the
proposed SASP based on the Zech distribution consistently yields lower sample sizes and fewer
inspection cycles, thereby reducing both inspection time and cost.

MODELLING AND FORECASTING BOND RATE OF NIGERIA ECONOMY USING AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) TECHNIQUES

Abimbola Hamidu Bello — 2026-05-20

This study is on modelling and forecasting bond rate of Nigeria economy. The bond market in
Nigeria, especially for FGN bonds, facilitates government borrowing to meet monetary policy
goals, infrastructure development, and budget deficits. Autoregressive Integrated Moving
Average (ARIMA) modeling technique was used to analyze and forecast key indicators of the
Nigerian 10-year Federal Government Bond market, specifically focusing on Total Subscription,
Total Successful Bids, and Bond Rate from 2013 to 2023. Using time series analysis in R
software package, the data was tested for stationarity and ARIMA models were then fitted, with
ARIMA(0,1,2)(0,0,2)[12] selected for Total Subscription, ARIMA(0,1,1) for Total Successful
Bids, and ARIMA(1,1,0) for Bond Rate. Model diagnostics, including the Ljung-Box test,
confirmed the adequacy of the fitted models. The resulting forecasts indicated stable future bond
rates around 14.1%, while subscription and bid values showed fluctuations consistent with market
dynamics. The models captured trends, seasonality and short term dependencies effectively. The
study demonstrates that ARIMA modeling offers a robust framework for forecasting bond market
behavior in Nigeria, providing valuable insights for policymakers, investors, and financial
analysts in planning, risk management, and policy

ENHANCING VOLATILITY FORECASTING IN THE NIGERIAN STOCK MARKET USING GARCH MODELS WITH ADVANCED INNOVATION DENSITIES

Samuel Ohiorhenuan Oboh — 2026-05-20

This study investigates the role of advanced innovation densities in improving volatility
forecasting accuracy in the Nigerian stock market. Using daily All Share Index (ASI) data
spanning 2012 to 2023, the study applies GARCH-type models, including GARCH (1,1),
EGARCH (1,1), and APARCH (1,1), under multiple error distributions such as Normal,
Student-t, Generalized Error Distribution (GED), and their skewed variants. Preliminary
analyses confirm the presence of volatility clustering, non-normality, and ARCH effects in the
return series. Model parameters are estimated using Maximum Likelihood Estimation (MLE),
while forecasting performance was evaluated using Root Mean Square Error (RMSE).
Empirical findings reveal that models incorporating heavy-tailed and skewed innovation
densities significantly outperform the conventional normal distribution in forecasting
volatility. In particular, the APARCH (1,1) model with GED innovation density demonstrates
superior predictive performance, capturing extreme market fluctuations more effectively. This
results once again underscore the importance of selecting appropriate innovation densities in
volatility modelling, especially in emerging markets characterized by structural instability
and frequent shocks. The study provides valuable insights for investors, risk managers, and
policymakers seeking to improve forecasting accuracy and enhance financial decision
making.

ON COMPARATIVE STUDY OF NEURAL NETWORK AND MARKOV-SWITCHING MODELS FOR INFLATION FORECASTING

Mutairu Oyewale Akintunde — 2026-05-20

This study examines the effectiveness of forecasting inflation in Nigeria over the period 2000 to
2024 using Artificial Neural Networks (ANN) and Markov-Switching Models (MSM). It
assesses the ability of each model to capture nonlinear dynamics and structural shifts in inflation
behaviour during the study period. Monthly inflation data obtained from the National Bureau of
Statistics, the official data source, were analysed. Model performance was evaluated using
standard forecast accuracy measures, including the Mean Absolute Error (MAE), Root Mean
Square Error (RMSE), and Theil’s U-statistic. The results show that the ANN model delivers
higher forecasting accuracy by effectively capturing complex nonlinear relationships in the data.
In contrast, the MSM performs better in identifying transitions between low- and high-inflation
regimes, thereby providing useful insights into the structural behaviour of the economy. Overall,
the findings suggest that integrating machine learning techniques with regime-switching models
can enhance forecast accuracy and provide valuable support for monetary and fiscal policy
formulation in Nigeria.

COVARIANCE MONITORING OF HIGH DIMENSIONAL TIME SERIES HEALTH DATA UNDER VIOLATION OF SELECTED ASSUMPTIONS

M. O. Adenomon — 2026-05-20

Monitoring covariance structures in high-dimensional time series is crucial for understanding
evolving dependencies in complex systems such as healthcare, finance, and industrial processes.
Traditional covariance estimators often fail when the number of variables exceeds the sample
size or when data contain outliers, non-stationarity, and structural changes. This study examines
robust and sparse covariance estimation techniques for high-dimensional time series, with
application to healthcare data in Nigeria. A simulation study based on multivariate
autoregressive models was conducted under stationary and non-stationary conditions. Sample
sizes (n = 100, 300), dimensions (p = 10, 15, 150), contamination levels (0%, 5%, 10%), and
mean shifts were considered. Data were generated from normal and heavy-tailed distributions.
Performance was evaluated using Mean Squared Error, Frobenius Norm Error, Condition
Number, and change-detection metrics. Three estimators were compared: Minimum Covariance
Determinant (MCD), Ridge, and Graphical LASSO, with covariance changes detected using the
CUSUM procedure. Results show that MCD consistently provides superior robustness across
contamination levels and dimensions. Ridge and LASSO perform well under clean normal data
but deteriorate with outliers and structural shifts, especially in small samples. Robust covariance
estimation, particularly MCD, offers a reliable framework for monitoring high-dimensional
healthcare time series.

COMPARATIVE PERFORMANCE OF ESTAR AND AFRIMA MODELS IN FORECASTING THE NIGERIAN EXCHANGE RATE.

Mutairu Oyewale Akintunde — 2026-06-18

This study examines and compares the predictive performance of the Exponential Smooth
Transition Autoregressive (ESTAR) and Autoregressive Fractionally Integrated Moving Average
(ARFIMA) frameworks for modelling and forecasting Nigeria’s exchange rate dynamics. Using
monthly observations spanning January 2000 to December 2025, the study investigates whether
exchange rate behaviour is better captured by nonlinear adjustment mechanisms or long-memory
dependence structures. Preliminary time-series diagnostics indicate evidence of persistence,
gradual adjustment toward equilibrium, and nonlinear characteristics in the underlying data-
generating process, suggesting that exclusive reliance on conventional linear specifications may
be inadequate. The competing models were estimated and assessed using both in-sample
adequacy and out-of-sample forecasting criteria. Model selection and forecast evaluation
employed the Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC), Root
Mean Square Error (RMSE), and Mean Absolute Percentage Error (MAPE). The empirical
results indicate that the ESTAR specification achieves superior short-term forecasting
performance, reflecting its capacity to capture regime-dependent movements and nonlinear
correction dynamics in exchange rate fluctuations. Conversely, the ARFIMA model exhibits
greater forecast stability over longer horizons, consistent with its ability to accommodate
fractional persistence and long-range dependence. The findings underscore the importance of
incorporating nonlinear and long-memory econometric structures into exchange rate forecasting,
particularly in emerging market contexts characterised by structural adjustments and market
frictions. By combining nonlinear transition modelling with long-memory representation, the
study provides empirical evidence that may strengthen forecasting practice and inform
macroeconomic surveillance, monetary policy formulation, and exchange-rate risk assessment in
Nigeria.

HYBRID MODELING OF NIGERIAN CRUDE OIL PRICES UNDER STRUCTURAL BREAKS AND VOLATILITY

Joseph Elekhekhatse ALEMHO — 2026-06-18

Accurate forecasting of crude oil prices is vital for robust economic planning, risk management, and policy
formulation in Nigeria. This study introduces an innovative hybrid forecasting framework that integrates the
statistical strengths of FB Prophet, ARIMA, and SARIMA models with machine learning techniques. The proposed
framework is designed to capture the complex dynamics of Nigeria’s daily crude oil prices, including long-term
trends, seasonal patterns, non-linear behaviors, volatility clustering, and structural breaks. The analysis utilizes a
longitudinal dataset of daily prices spanning from January 1986 to December 2025. Empirical results reveal
significant non-linearity, heavy-tailed distributions, and multiple structural breaks triggered by global shocks, such
as the 2014–2016 price collapse and the COVID-19 pandemic. Stationarity tests indicate that while price levels are
non-stationary, the return series remain stationary, justifying the application of integrated econometric models. The
ARIMA and SARIMA components deliver superior short-term accuracy, whereas the FB Prophet model excels at
identifying medium- to long-term trajectories. By synthesizing these methodologies, the hybrid model maintains the
rigor of traditional statistical approaches while enhancing reliability amidst heightened volatility. The resulting
forecasts offer high statistical precision and practical utility for trend and risk analysis. These insights provide a
critical foundation for investors, policymakers, and stakeholders dedicated to bolstering Nigeria’s economic
resilience in the global market.