Time-Series Forecasting
Forecasting Highly Volatile Time Series: An Approach Based on Encoder-Only Transformers
This analysis provides a deep dive into advanced AI methodologies for predicting highly volatile time series, focusing on energy consumption and trading data. Discover how an Encoder-only Transformer architecture, coupled with systematic noise analysis, achieves superior precision in real-world applications.
Executive Impact
This paper introduces an Encoder-only Transformer architecture for day-ahead forecasting of power demand from highly volatile time series, common in energy trading. It addresses challenges like noise variability and its attenuation, and evaluates performance using the theoretical ceiling of the Pearson Correlation Coefficient. The proposed method achieves an impressive approximate prediction error of 11.63%, significantly outperforming classical statistical methods and other AI models, which typically yield errors around 30%. This framework enables reliable predictions even with significant data fluctuations.
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Total Accuracy (MAPE)
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Pearson Correlation
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Operational Efficiency Gained
Deep Analysis & Enterprise Applications
Select a topic to dive deeper, then explore the specific findings from the research, rebuilt as interactive, enterprise-focused modules.
Advanced Forecasting Models
This research explores the application of Encoder-only Transformer architectures for highly volatile time series. Unlike traditional models, this approach proves exceptionally resilient to noise, a critical factor in energy trading. It focuses on day-ahead predictions, demonstrating how a specialized Transformer can provide high-precision forecasts where others fall short, especially when optimized with brute-force methods.
Systematic Noise Analysis & Attenuation
A key novelty is the systematic analysis of noise, its variability, and effective attenuation techniques. By using Singular Spectrum Analysis (SSA), the signal is decomposed into long-term trend, seasonal components, and residual noise. Statistical tests like Kolmogorov-Smirnov (KS) and Jarque–Bera (JB) confirm non-normal distribution, leading to the application of a Moving Average to reduce noise, thereby optimizing the data for Transformer training.
Robust Performance Evaluation
The methodology introduces a novel approach to evaluating model performance by computing the theoretical ceiling of the Pearson Correlation Coefficient. This provides a robust benchmark, especially crucial for highly volatile series where conventional metrics may be unreliable. The model's practical Pearson Correlation of 0.53, achieving 78.78% of the theoretical limit, alongside a Mean Absolute Percentage Error (MAPE) of 11.63%, underscores its superior predictive power.
Key Performance Indicator
11.63% Approximate Prediction Error (MAPE)The Encoder-only Transformer achieved an approximate prediction error of 11.63%, significantly lower than typical errors of 30% or more with classical statistical methods. This highlights its resilience in handling volatile time series data.
Enterprise Process Flow
Input & Analyze Time Series Data
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Assess Normality & Noise Characteristics
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Apply Noise Attenuation (Moving Average)
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Estimate Pearson Correlation Ceiling
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Train Encoder-only Transformer Model
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Generate & Display Forecast Results
| Model | Key Innovation | Application Domain | Datasets | Noise Handling | Reported Performance (MAPE/MAE/MSE Trends) |
|---|---|---|---|---|---|
| LogSparse Transformer [4] | Sparse attention for long dependencies | Electricity consumption, solar energy production, and traffic | Real-world and synthetic | Moderate | 10-20% lower error across standard benchmarks with respect to ARIMA, ETS, TRMF, DeepAR, and DeepState |
| Temporal Fusion Transformer (TFT) [5] | Combines LSTM Encoder-Decoder with multi-head attention and gating mechanisms for interpretable multi-horizon forecasting | Energy demand, traffic, retail sales, and financial data | Real-world time series relating to electricity, traffic, volatility, retail | Moderate: robust to moderate noise due to gating, variable selection, and static covariate encoders | Outperformed ARIMA, ETS, TRMF, DeepAR, DSSM, etc. (MAE is typically 3-26% lower across the datasets) |
| Reformer [7] | Introduces LSH (Locality-Sensitive Hashing) attention and reversible layers to reduce memory and computation from O(L²) to O(L log L) | Energy demand, traffic, retail sales, and financial data | Character-level language modeling, image generation, and long-range associations between integers | Moderate: sparse attention reduces overfitting to noise by focusing on top-K relevant tokens | Demonstrated similar or slightly worse forecasting accuracy than Vanilla Transformer with much lower memory footprint; exact error metrics depend on dataset and fine-tuning. |
| Informer [9] | Introduces ProbSparse attention to reduce attention computation to O(L log L) and self-attention distillation for long-sequence forecasting | Energy, traffic, weather, and finance | ETTh1, ETTh2, ETTm1, weather, electricity consumption | High forecasting errors due to volatile component filtering | Outperformed LogTrans, Reformer, LSTM, DeepAr, ARIMA, and Prophet baselines; typically improved MSE/MAE by 10-25%, depending on the dataset |
| Autoformer [10] | Introduces series decomposition into trend and seasonal components and auto-correlation-based attention for long-term forecasting | Energy, traffic, weather, finance, medical sector | ETT, electricity, exchange, traffic, weather, ILI | High forecasting errors due to volatile component filtering | Outperformed LogTrans, LSTM, Informer, LSTNet, Reformer, and TCN in MSE/MAE by 15-30%, depending on the dataset and horizon |
| FEDformer [11] | Combines series decomposition with frequency-domain attention to capture both trend and periodic components for long-term forecasting | Energy, traffic, weather, climate, finance | ETTm2, exchange, traffic weather, ILI | High forecasting errors due to volatile component filtering | Outperformed Autoformer, Informer, LogTrans, and Reformer; typically improved MSE/MAE by 20-35%, depending on the dataset and forecasting horizon |
| PatchTST [12] | Partitions the time series into local temporal windows for attention (inspired by Vision Transformers); uses channel-independent attention for multivariate forecasting | Energy, traffic, weather, finance, and industrial | Traffic, electricity, ETTm1, ETTm2, ETTh1, ETTh2, weather, ILI | High forecasting errors due to further reduction in the magnitude of the micro-variations | Achieved state-of-the-art performance with a MAPE of approx. 10-15% on standard benchmarks, outperforming Autoformer, FEDformer, Informer, D-Linear, Pyraformer, and LogTrans |
| Hybrid Transformer-CNN [13] | Combines Transformer self-attention with CNN-based local feature extraction to capture both global dependencies and local patterns | Especially financial markets | Multivariate, containing 1 or 5 features | Good since it reduces the short-term impact of the noise, but the model is sometimes prone to noise saturation, given the architecture complexity | Outperforms the Transformer, 1D-CNN, LSTM, CNN-LSTM, and ARIMA by about 15% in MSE |
| CNN-Transformer Hybrid [14] | Integrates CNN layers to capture short-term local dependencies with Transformer attention for long-term dependencies in financial time series | Financial markets, stock prices, and multivariate financial indicators | S&P stock market prices | Good: CNN layers smooth high-frequency noise, but the model is sometimes prone to noise saturation, given the architecture complexity | Outperforms ARIMA, EMA, and DeepAR by approx. 1-15% in MAPE |
| Proposed method | Attenuates the noise, trains the Encoder-only Transformer on the attenuated noise time series, and compares the forecast with the actual demand | Specially designed for trading energy generated by renewable sources, containing more than 50% noise | Custom, coming from a real energy provider | Excellent: the architecture is adapted to avoid noise saturation | Achieves 11.63% in MAPE, which is very low, since less than 50% of the signal can be used in forecasting |
Real-World Application: Energy Demand Forecasting
The study utilized data from a Romanian energy producer owning various PV plants. The challenge involved forecasting highly volatile energy demand, comprising both direct consumption by clients and energy traded through OPCOM, where 100% of generated electrical energy is sold. The proposed Encoder-only Transformer architecture, combined with systematic noise analysis and attenuation using Moving Average, successfully achieved an 11.63% MAPE and a 78.78% Pearson Correlation Coefficient against the theoretical limit for the non-averaged signal. This demonstrates the framework's effectiveness in maximizing operational efficiency and resource allocation in highly volatile energy markets.
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Your AI Implementation Roadmap
A typical journey to integrate advanced AI forecasting within an enterprise. Each phase is tailored to ensure robust, scalable, and impactful deployment.
Phase 1: Data Acquisition & Preprocessing
Gather raw electricity consumption and trading data (15-min intervals, 1 year). Perform Singular Spectrum Analysis (SSA) for trend decomposition and noise estimation (54.75% noise contribution). Apply Kolmogorov-Smirnov (KS) and Jarque–Bera (JB) tests to assess normality and apply Moving Average for noise attenuation, reducing noise contribution to 45.79%.
Phase 2: Model Selection & Hyperparameter Optimization
Implement various forecasting models including ARIMA, Prophet, LSTM, CNN, GRU, SVR, Random Forest, XGBoost, DeepAR, N-BEATS, and Transformer variants. Optimize hyperparameters for Encoder-only Transformer using Brute Force, given the high data volatility, focusing on context length (192 steps) and prediction length (96 steps).
Phase 3: Performance Evaluation & Validation
Calculate key metrics: MAPE (11.63%), MAE, MSE, RMSE, R², Pearson Correlation Coefficient (0.53), and Directional Accuracy (77.89%). Implement Breusch-Pagan F (BP–F) test to confirm heteroscedastic noise. Estimate theoretical Pearson Correlation Coefficient ceiling (67.27%) to provide a robust benchmark against actual performance.
Phase 4: Deployment & Continuous Improvement
Integrate the Encoder-only Transformer model into an operational system for day-ahead electricity demand forecasting. Establish daily training routines to maintain forecast accuracy. Monitor model performance continuously and explore adaptive noise reduction techniques and integration into larger foundation models/LLMs for real-time decision support.
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