<![CDATA[This study compares the performance of various GARCH models GARCH(1,1), GARCH(1,2), and GARCH(2,1) with different error innovations, focusing on the use of Student’s t-distributions, including sine-modulated, to model financial volatility dynamics. This study offers a novel approach to modeling volatility in financial time series data using GARCH models with sine Student's t error innovation. The analysis uses both simulated data and real-life data from the Nigerian Stock Exchange (NSE). The results reveal that the GARCH(1,1) model with sine-modulated Student’s t error innovation outperforms other models, showing superior model fit (lowest AIC and BIC) and forecasting accuracy (lowest MAE, MSE, and RMSE) in the simulation results. Additionally, GARCH(1,2) with sine-exponentiated Student’s t innovations is found to be the most effective for real-life data, capturing volatility clustering and extreme tail events. The study concludes that advanced error innovations, particularly sine-modulated Student’s t distributions, improve model accuracy by addressing the heavy tails, volatility clustering, and asymmetry typical of financial markets. The study findings also suggest that incorporating the Sine Student's t distribution in GARCH models can provide a more nuanced understanding of financial market dynamics.]]>
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