Variants of GRNN for time-series predictions: dilated variant and hybrid model with CNN

General Regression Neural Networks (GRNN) are simple yet powerful nonparametric models for regression tasks. In this work, we investigate how GRNN can be adapted for time series forecasting by incorporating temporal decay into the similarity easure, as well as how its performance can be enhanced by combining it with convolutional encoders. We first introduce two novel time–decay GRNN variants that penalize distant observations either by modifying the distance or directly scaling the kernel. Second, we propose a new CNN$\to$GRNN hybrid architecture that embeds lagged inputs through one-dimensional convolutional layers with pooling, bottleneck, and unit-norm normalization, followed by a GRNN operating in the learned embedding space. This architecture supports dilated convolutions, median–based initialization of the GRNN bandwidth, and efficient training with anchor subsampling and leave-one-out masking. We compare both proposed methods against baseline GRNN, linear regression, and shallow neural networks on both public market data (equity and crypto) and proprietary energy consumption and generation series. Across equities and commodity proxies, GRNN variants-especially the time-decay GRNN-achieved the lowest MSEs on most series, consistently outperforming linear and shallow neural baselines. On proprietary energy data, a compact ANN performed best, while the proposed CNN-GRNN hybrid still surpassed classical baselines and added predictive value even with short training windows.