Modelling of high-dimension chaotic, noisy, and non-stationary time series of complex fractal dynamics is a big challenge. In this research work, a novel approach of Leverage Convolution LC ARFIMA– GARCH model is presented for sequential learning of irregular, fractal dynamic patterns of stochastic time series dynamics. Different classical methods including the auto-regressive approach indecently are unable to capture fragile patterns and consequently convert some weak signals into random errors by creating white noise patterns. The Convolution Leverage provides an additional degree of freedom for critical noisy points and asymmetrical distribution dynamics to regulate the frequency of imbalance and skewed observation. The designed transformation in the ARFIMA model preserves the loss of information by shifting the skewed data distribution toward a normal pattern. The pattern of population parameters in the proposed leverage paradigm provides out of box approach to track and extract additional information on population variance patterns in the form of an additional degree of freedom to stabilize imbalance signals. The model can provide reliable performance for long-range dependence, particularly for mean reversion chaotic phase variation at critical non-differentiable points. The performance of the dynamic model is verified on chaotic real data of the Ireland Stock Market (ISEQ). The result statistics confirmed the optimized outcome with the addition of the GARCH heteroscedastic multimodal and radial basis neural network. The novel technique can help to address inherited challenges in the imbalance learning and extreme events of the time series modeling by monitoring the chaotic trajectory of fractal physical phenomena, particularly in, finance healthcare, climate, and intelligent sustainability.