Calibration of Neural Network Weights in Time-Series Forecasting

Forecasting high-frequency time-series in real-time requires a high rate of predictive model adaptation. The deployment of classic recurrent neural networks (LSTM and GRU) faces the challenge of extremely noisy input data. In environments where the majority of the signal consists of white noise, standard training via backpropagation leads to rapid model overfitting on local random fluctuations.

To resolve this issue, we calibrate the output probabilities of the neural network using Hessian-based weighting and stochastic gradient descent optimization (AdamW). Instead of direct minimization of mean squared error (MSE), we integrate a Weighted Log-Loss function that accounts for the prior distribution of system states. This calibrates network outputs to match the actual frequency of outcomes on the validation set.

Practical results indicate that integrating calibrated neural network cores into predictive analytics reduces false positive signals by 42%. The system correctly identifies changes in volatility regimes and switches the analytical terminal to a conservative filtering mode upon detecting anomalous phase transitions in the time-series.