TimeCatcher: A Variational Framework for Volatility-Aware Forecasting of Non-Stationary Time Series

TL;DR

TimeCatcher addresses non-stationary time series forecasting by introducing a volatility-aware variational framework that adds a latent dynamic pathway to a lightweight MLP backbone. The model decomposes the forecast into deterministic trend $\hat{\mathbf{X}}^{(x)}$, latent $\hat{\mathbf{X}}^{(z)}$ from a variational encoder, and a volatility-emphasis term $\Delta_{emphasis}$, yielding $\hat{\mathbf{X}} = \hat{\mathbf{X}}^{(x)} + \hat{\mathbf{X}}^{(z)} + \Delta_{emphasis}$. The latent pathway leverages a VAE with ELBO optimization $\mathcal{L}_{ELBO} = \mathbb{E}_{q_{\phi}(\mathbf{z}|\mathbf{X})}[\log p_{\theta}(\mathbf{X}|\mathbf{z})] - \mathrm{KL}(q_{\phi}(\mathbf{z}|\mathbf{X}) || p(\mathbf{z}))$, and the volatility module uses a dynamic mask and learnable weighting to amplify significant changes. Empirical results across nine real-world datasets show TimeCatcher delivers state-of-the-art long-horizon forecasting, particularly in high-volatility domains, while maintaining efficiency suitable for resource-constrained deployment.

Abstract

Recent lightweight MLP-based models have achieved strong performance in time series forecasting by capturing stable trends and seasonal patterns. However, their effectiveness hinges on an implicit assumption of local stationarity assumption, making them prone to errors in long-term forecasting of highly non-stationary series, especially when abrupt fluctuations occur, a common challenge in domains like web traffic monitoring. To overcome this limitation, we propose TimeCatcher, a novel Volatility-Aware Variational Forecasting framework. TimeCatcher extends linear architectures with a variational encoder to capture latent dynamic patterns hidden in historical data and a volatility-aware enhancement mechanism to detect and amplify significant local variations. Experiments on nine real-world datasets from traffic, financial, energy, and weather domains show that TimeCatcher consistently outperforms state-of-the-art baselines, with particularly large improvements in long-term forecasting scenarios characterized by high volatility and sudden fluctuations. Our code is available at https://github.com/ColaPrinceCHEN/TimeCatcher.

Figures (8)

• Figure 1: Visualize the performance of predicting non-stationary sequences, where $X_t$ and $Y_t$ are input sequences and $\hat{X}_t$ and $\hat{Y}_t$ are predicted sequences. By capturing latent and Volatility information, TimeCatcher can significantly improve forecasting performance.
• Figure 2: The TimeCatcher framework. The input time series is processed through three additive residual pathways: (1) Part 1: Trend Modeling processes the raw input to preserve global patterns; (2) Part 2: Latent Dynamic Encoding uses a VAE-based encoder to capture underlying temporal structures in a compact latent space; (3) Part 3: Volatility Enhancement adaptively amplifies local fluctuations via a lightweight module with learnable weights. The final prediction is formed by summing the outputs of all three pathways. This decomposition enables TimeCatcher to simultaneously achieve high efficiency, inherit historical dynamics, and respond sensitively to abrupt changes in non-stationary series.
• Figure 3: Prediction visualization on the Electricity dataset (lookback=96, forecast horizon=96). We compare TimeCatcher with TimeMixer (state-of-the-art) and TimeBase (latest lightweight model). TimeCatcher more accurately captures abrupt load changes and sustained volatility patterns in the long-term horizon, demonstrating superior temporal fidelity under non-stationarity.
• Figure 4: Ablation experiments show the predicted MSE and MAE values for different cases on the Solar Energy, Electricity, and Exchange Rate datasets. The MSE and MAE values for each case are the averages of the MSE and MAE values for four prediction lengths: $\{96, 192, 336, 720\}$.
• Figure 5: T-SNE visualizations of latent representations in TimeCatcher on ETTm1 (left), Exchange Rate (center), and Weather (right). Red: original sequences; Blue: synthetic sequences from the variational encoder. The strong overlap and compact clustering indicate that TimeCatcher’s latent space preserves the underlying data distribution and captures structured temporal patterns. Additional visualizations are provided in Appendix B.