Department of Statistics
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Item GAMMA AUTOREGRESSIVE HARMONIC MODEL (GARHM) FOR NON-GAUSSIAN TIME SERIES DATASETS(OLABISI ONABANJO UNIVERSITY, 2026-09-28) AKANNI, OLUKUNMI OLATUNJISeasonality 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