A weierstrass-based fractal feature framework with monte carlo parameter optimization for financial time-series forecasting
Stock-market forecasting is challenging because financial time series exhibit nonlinearity, volatility clustering, scale-dependent fluctuations, and irregular self-similar behavior. The goal of this research is to create a hybrid forecasting framework for improved stock-price prediction by combining fractal feature extraction, Monte Carlo parameter optimization, and Long Short-Term Memory (LSTM) neural networks. A Weierstrass-based fractal representation is used to describe multiscale oscillatory behavior in financial returns. Several fractal descriptors, including Weierstrass oscillatory features, generalized fractalintegral features, local roughness, volatility scaling, Hurst-exponent features, and fractal-dimension features, are extracted from moving windows of historical stock returns. These features are then incorporated as auxiliary input channels into an LSTM forecasting architecture. The fractal-parameter vector that minimizes validation-set forecasting loss is selected via Monte Carlo optimization. Using actual stock market data, the proposed Monte Carlo fractal-LSTM model is evaluated and compared with benchmark models such as naïve persistence, moving-average forecasting, classical LSTM, and non-optimized fractal- LSTM models. RMSE, MAE, MAPE, and directional accuracy are used to measure forecasting performance. The empirical findings show that the LSTM model’s capacity to represent nonlinear, memory-dependent, and multiscale market dynamics is enhanced by the addition of fractal features. The Monte Carlo fractal–LSTM model achieves lower forecasting errors and higher directional accuracy than the benchmark models in the out-of-sample validation experiment. These results imply that, in addition to raw return sequences, optimized fractal descriptors offer valuable additional information. The present investigation is unique in that it combines LSTM-based time-series forecasting and Monte Carlo parameter selection with Weierstrass-based fractal features. The proposed methodology offers an interpretable approach for incorporating roughness, self-similarity, volatility scaling, and memory effects into financial forecasting by connecting a mathematical fractal model with data-driven deep learning.
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