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GAMMA AUTOREGRESSIVE HARMONIC MODEL (GARHM) FOR NON-GAUSSIAN TIME SERIES DATASETS
(OLABISI ONABANJO UNIVERSITY, 2026-09-28) AKANNI, OLUKUNMI OLATUNJI
Seasonality and non-Gaussian properties have been the major concern when analysing and forecasting time series datasets. This is due to the fact that non-Gaussian nature is associated with the excess skewness and seasonality as the conventional Autoregressive and Harmonic models fail to capture datasets with seasonality and non-Gaussian properties. Based on this complexity, a new robust and efficient model called the Gamma Autoregressive Harmonic Model (GARHM) for handling seasonality and non-Gaussian property of the time series datasets has been developed since the transformation changes the structure of the original series. Hence, this study focused on developing, estimating and testing the performance of the Gamma Autoregressive Harmonic Model (GARHM) on datasets from economics, finance and environmental sciences for higher prediction and forecasting.
Exploratory data analysis was performed on Nigeria's monthly exchange rate spanning from January 1996 to February 2025, sourced from an investing website; Nigeria's annual CO_2 emission data from 1990 to 2020, retrieved from Macrotrends website and Nigeria’s annual data obtained from the World Bank website on temperature from 1901 to 2023 and inflation from 1961 to 2023. The Gamma Autoregressive Harmonic Model (GARHM) was fitted to the time series datasets. The fitness performance was examined using Coefficient of Determination (R2), Akaike Information Criterion (AIC), and Bayesian Information Criterion (BIC), while the forecasting evaluation of the developed model was compared using Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), Mean Absolute Scaled Error (MASE), and Mean Absolute Percentage Error (MAPE).
The result showed that the Gamma Autoregressive Harmonic Model (GARHM) outperformed the Autoregressive and Harmonic models as demonstrated by the lowest value of RMSE, MAE, MASE, and MAPE. Empirical analysis of the efficiency of the developed model compared with the existing models was carried out using two sets of financial and environmental time series datasets. The developed GARHM outperformed Autoregressive and Harmonic models, signifying its supremacy. Therefore, the new GARHM recorded higher values of R2 (0.9813, 0.7256, 0.7985, 0.8992) compared to the autoregressive model (0.9610, 0.4775, 0.6794, 0.6291) and Harmonic model (0.0008671, 0.005610, 0.08315, 0.09075), indicating better performance. Also, the least value of AIC for GARHM (3585.9030, 604.9300, 21.2908, 630.9437) compared to the Autoregressive model (3586.6410, 606.7600, 27.00422, 650.4725) and Harmonic model (4970.9360, 609.4900, 108.3971, 682.9147) for the four datasets implies superiority. The forecasting performance of GARHM has the least RMSE value (39.7097, 14.5380, 0.2410, 3780.2600) compared to the Autoregressive model (39.9794, 27.6210, 0.2580, 7254.2330) and Harmonic model (290.3159, 28.0260, 0.3522, 11358.8330), signifying better predicting power and flexibility.
The developed model showed better fitness and forecasting accuracy compared to the Autoregressive and Harmonic models. This finding is very crucial and important for individuals, stakeholders, and the government for decision-making and policy implementation. Also, the developed model is suitable for datasets from diverse fields with different sample sizes.
Keywords: Gamma Autoregressive Harmonic Model (GARHM), Non-Gaussian, Harmonic Model, Autoregressive, Environmental Sciences
Word Count: 458
Assessment of Diagnostic Reference Levels and Radiation-induced Lifetime Cancer Risk from Computed Tomograhpy Examinations in Selected south-western Nigerian Teaching Hospitals
(2026-07-16) Olawuni Caroline Olayemi
The growing utilisation of computed tomography (CT) has prompted greater attention to exposure of radiation and its potential health risk coupled with the lack of nationally established diagnostic reference levels (DRLs) in Nigeria. This study was therefore aimed at assessing DRLs and estimating lifetime attributable cancer risks (LAR) among population involved in CT examinations at the participated teaching hospitals in South-western Nigeria.
A retrospective study was adopted using CT examination data obtained from two University teaching hospitals in South-western Nigeria; Babcock and Obafemi University Teaching Hospitals. CT records from 266 patients who underwent CT examinations were analyzed. CTDIvol and DLP were recorded directly from CT scanner and size-specific conversion factor published by Romanyukha et al. (2016) was used to estimate effective doses. 75th percentile value of CTDIvol and DLP was adopted as local Diagnostic Reference Levels (DRLs). LAR was estimated using online X-ray risk software. Data were analysed using IBM SPSS.
The results showed considerable variability across anatomical regions and examination protocols, indicating a wide spread of patient doses. In centre A, the mean CTDIvol for non-contrast head examinations was 49.7±19.4 mGy, while contrast-enhanced head examinations recorded 69.7 ±32.8 mGy. Similarly, abdominal examinations showed substantial variation, with CTDIvol and DLP values of 31.3 ± 23.8 mGy and 1304.0 ± 905.9 mGy.cm respectively. In centre B, head examinations exhibited CTDIvol values of 58.5 ±19.4 mGy and DLP values of 1219.6 ± 431.0 mGy.cm. The adult local DRLs estimated for head CT showed CTDIvol values ranged from 57.6 – 65.3 mGy, while DLP ranged from 1393.5 – 2050.1 mGy.cm. Chest CT recorded CTDIvol values between 6.9 and 15.4 mGy while DLP recorded 495.6 and 819.0 mGy.cm. Abdomem examinations showed CTDIvol values 8.6 – 42.0 mGy and DLP values of 1621.9 – 1730.2 mGy.cm. some of the values recorded were within the ICRP recommended limits while some were greater than the ICRP CTDIvol and DLP values which are 60 mGy, 1050 mGy.cm, 30 mGy, 650 mGy.cm, and 35 mGy, 780 mGy.cm for head, chest, and abdomen respectively.
Among pediatric patients, head CTDIvol (30.6 - 45.8) mGy were below the ICRP reference levels of 70 mGy. However, pediatric head DLP values reached 1515.4 mGy.cm in centre A and 872.9 mGy.cm in centre B, exceeding the recommended value of 750 mGy.cm. The lifetime cancer risk ranged from 10 to 275 cases per 100,000 population and the highest recorded in the study (275 cases per 100,000 population) was associated with contrast-enhanced CT examinations while the lowest LAR (10 cases per 100,000 population) was observed among patients > 60 years. The statistical test employed demonstrated significant differences in LAR across gender, age groups, region, and contrast status (P < 0 .001).
CT examinations contributed significantly to patient radiation exposure and potential cancer risk, particularly when the recommended DRLs were consistently exceeded. Young patients, females, and patients that underwent contrast CT examinations exhibited LAR. Consequent to the findings, the study recommends establishment of separate national DRLs for adults, pediatrics, and contrast-enhanced CT examinations in Nigeria.
Key Words: Cancer, Contrast-enhanced, Diagnostics, patient, pediatrics,
Word counts: 493
DEVELOPMENT OF SOME INFLUENTIAL MEASURES IN ONE PARAMETER NEW RIDGE-TYPE ESTIMATORS OF LINEAR REGRESSION MODELS
(OLABISI ONABANJO UNIVERSITY, 2026-09-29) OLUWAROHUNBI Grace Olufunke
In linear regression analysis, influential points are observations that exert disproportionate impact on regression models. If not properly identified and addressed, they can distort parameter estimates, fitted values, and statistical inferences. Although, Ordinary Least Squares (OLS) estimator is widely used for estimating parameter coefficients in regression analysis, it performs poorly when multicollinearity and outliers are present. Many existing biased estimators are developed to mitigate only multicollinearity, while robust regressions are used to reduce the effect of outliers on regression estimates. In practice, these two problems often occur together. Similarly, traditional influential diagnostic measures developed under the OLS framework, such as Cook’s Distance (CD) and Difference in Fits (DFFITS), may not perform well when multicollinearity and outliers exist simultaneously. Hence, this study developed influential diagnostic measures within One-parameter new ridge-type estimator’s framework, to improve detection of influential points when multicollinearity and outliers co-exist in a dataset.
The Kibria–Lukman (KL) estimator was combined with six robust regression techniques, namely: Modified Maximum Likelihood (MM), Least Absolute Deviation (LAD), Least Median of Squares (LMS), Least Quartile of Squares (LQS), Least Trimmed Squares (LTS), and S estimators to produce a class of Robust Kibria–Lukman (RKL) estimators. Based on these estimators, generalized forms of Cook’s Distance, DFFITS, Difference in Betas (DFBETAS), Covariance Ratio’s, Hadi’s, Pena’s, and Atkinson’s statistics were derived, along with their approximate case-deletion expressions for Cook’s Distance and DFFITS. Their performance were evaluated through a Monte Carlo simulation study, replicated 1,000 times, with sample sizes from 10 to 500, correlation levels from 0.80 to 0.99, outlier magnitudes from 0 to 10, and contamination rates of 10% and 20%.
The findings showed that the Covariance Ratio based on the Robust Kibria–Lukman_M estimator (CVR_KL_M) was the overall best-performing diagnostic measure, with the highest total frequency of 100% detection (2,622). It was followed by CVR_KL_LAD (2,603) and CVR_KL_MM (2,325). CVR_KL_M also showed stable performance across different sample sizes, with detection frequencies of 314 at n=10, 330 at n=20, 30, 50, 100 and 250 and 329 at n=40 and 500. In real life data applications, the proposed measures identified observations 2, 16, 1, 12, and 9 as influential in the economic dataset, while several existing methods failed to detect observations 2, 12, and 9. In the Hussein dataset, the proposed methods consistently identified observations 15, 20, 16, 12, and 4 as influential.
The study concluded that the proposed Robust Kibria–Lukman influential measures were more effective, stable, and reliable than the existing diagnostic measures for detecting influential points in a dataset affected by both multicollinearity and outliers. Particularly, CVR_KL_M emerged as the most efficient diagnostic measure. The study therefore provides a statistically sound and practically useful approach for identifying influential points in linear regression models under these combined conditions. It is therefore recommended that applied researchers and data analysts should use the proposed Robust Kibria–Lukman-based diagnostic measures, especially CVR_KL_M, when analysing regression data affected by both multicollinearity and outliers.
A Trigonometric Fractional Polynomial Autoregressive Time Series Model for Complex Structure Datasets
(OLABISI ONABANJO UNIVERSITY, 2026-09-30) Jubril Oluwatoyin FANTOLA
Time series data exhibiting complex structures such as persistence, nonlinear trends, seasonal, cyclical and irregular variations are observed across many fields. Classical linear time series models including Autoregressive Moving Average (ARMA), Autoregressive Integrated Moving Average (ARIMA), and Seasonal Autoregressive Integrated Moving Average (SARIMA) have been widely applied to such data. However, their effectiveness becomes limited when multiple forms of variation coexist. In particular, datasets that display long-run growth or decay alongside smooth cyclical movements are often inadequately represented by stochastic and fixed seasonal models. This instigated the development of flexible hybrid modelling frameworks capable of capturing the temporal dynamics. This study developed a Fractional Polynomial Trigonometric Autoregressive (TFPAR) time series model that integrates autoregressive dependence, fractional polynomial trend and trigonometric regression terms within a unified framework. The autoregressive component captures temporal persistence; fractional polynomial structure accounts for nonlinear long-run growth or decay, while the trigonometric terms model smooth seasonal and cyclical behaviour using sinusoidal functions.
The development of the model was done based on the Box–Jenkins methodology comprising identification, estimation, diagnostic checking, validation and forecasting. Exploratory data analysis was used for model identification, autocorrelation and partial autocorrelation functions and spectral analysis were also used to detect dominant frequencies. Parameter estimation was carried out using Ordinary Least Squares (OLS) and Maximum Likelihood Estimation (MLE) techniques. Adequacy and performance of the model were evaluated using residual diagnostics, coefficients of determination (R² and adjusted R²), information criteria (AIC and BIC), and forecast accuracy measures (Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE)).
The exploratory analysis of Nigerian monthly temperature and carbon (IV) oxide (CO₂) emission series from the result revealed strong persistence, evident nonlinear trends and pronounced low-frequency cyclical behaviour. Autocorrelation functions decay slowly indicating long memory while periodogram analysis identifies dominant deterministic frequencies beyond fixed seasonality. Estimation results confirm the statistical significance of the autoregressive, fractional polynomial and trigonometric components. The fitted models for temperature and CO₂ emission series revealed a R² values of 0.94 and 0.96, with corresponding adjusted R² values of 0.93 and 0.95 respectively, indicating substantial explanatory power and good model fit. Diagnostic checks further supported model adequacy, with Durbin–Watson statistics of 2.01 for temperature and 1.98 for CO₂ emissions, suggesting no residual serial correlation. Residual autocorrelation plots showed no significant remaining structure and residual distributions approximated normality. The developed model demonstrated clear superiority over competing models, recording the lowest information criteria values. For temperature, AIC = −412.6 and BIC = −389.4, while for CO₂ emissions, AIC = −438.1 and BIC = −415.9, compared with higher values under other specifications. Forecast evaluation further confirmed improved performance, with temperature forecasts yielding RMSE = 0.42, MAE = 0.31, and MAPE = 2.9%, and CO₂ emission forecasts producing RMSE = 1.87, MAE = 1.42, and MAPE = 3.4%.
The study concluded that integrating fractional polynomial trends and trigonometric cycles within an autoregressive framework provides a reliable and effective alternative for modelling and forecasting time series data characterised by persistence, nonlinear evolution and smooth cyclical behaviour due to its superior explanatory and predictive performance, and therefore recommends the adoption of the TFPAR model for analysing and forecasting such complex time series.
SEMANTICS AND COMMUNICATION FUNCTIONS OF SELECTED SLANG EXPRESSIONS ON BIG BROTHER NAIJA
(OLABISI ONABANJO UNIVERSITY, 2026-07-30) KOLADE CECILIA DAMILOLA
Keywords: Slang, BBN, Meaning, Young Communication, Communication Strategies and Pragmatics