Randomized deep Hopfield network with multiple output layers for volatility time series forecasting.

Volatility forecasting plays a critical role in risk management and financial decision-making by facilitating the prediction of market fluctuations. However, the inherent complexity and irregular variations in volatility time series data present significant challenges for accurate modeling. This study proposes a novel ensemble deep randomized Hopfield network (edRHN) for volatility forecasting. The proposed network incorporates multiple stacked hidden layers with randomly generated parameters within a predefined range, which remains fixed while the output weights are determined using a closed-form solution. Each hidden layer representation contributes to training an output layer, and the aggregation of these output layers forms the final output. Technical indicators are used to identify market trends to allow more informed decision-making. The neuron pruning strategy and feature analysis are further used to eliminate noisy information and less relevant features from randomly generated features, optimizing network efficiency and performance. A comprehensive comparative study was conducted against various state-of-the-art models across ten diverse volatility time-series datasets. The experimental results highlight the superior predictive performance of the proposed model, as demonstrated by three error metrics and statistical tests.