Breaking New Ground in Time Series Forecasting

The Temporal Window Smoothing (TWS) framework represents a significant advancement in how we incorporate external information into time series forecasting models. While recent transformer-based approaches have shown that exogenous variables can improve predictions, they face critical challenges including redundancy and limited global awareness.

Our innovative TWS technique addresses these limitations by whitening exogenous inputs based on global statistics, effectively reducing noise while exposing each window to patterns that span the entire training dataset. This results in more robust, accurate predictions that consistently outperform state-of-the-art models across multiple benchmark datasets.

Revolutionary Approach

Global Pattern Awareness

TWS exposes each window of exogenous data to globally significant patterns including long-term trends and seasonality captured across the entire training set.

Redundancy Elimination

By projecting onto orthogonal basis vectors derived from global statistics, TWS effectively removes redundant information that could harm model performance.

Adaptive Component Selection

Dynamically determines the optimal number of principal components based on cumulative explained variance, ensuring significant patterns are captured without overfitting.

How TWS Works

Three-Stage Processing Pipeline

1

Global Statistics Extraction

Compute covariance matrix and eigenvectors from entire training dataset to identify key patterns.

2

Projection & Whitening

Project exogenous windows onto selected orthogonal basis vectors to reduce redundancy.

3

Reconstruction

Generate refined exogenous series that maintains original dimensions while incorporating global context.

State-of-the-Art Performance

21/35

Best MSE Performance Settings

7

Benchmark Datasets Evaluated

2.29%

Average MSE Reduction on ETTh1

11

Baseline Models Outperformed

Comprehensive Benchmark Results

TWS has been extensively evaluated across seven diverse datasets including Electricity (ECL), Traffic, Weather, and ETT series. Our method consistently achieves superior performance compared to state-of-the-art models including TimeXer, iTransformer, and PatchTST.

Key Performance Highlights

ECL Dataset: Achieved MSE of 0.148 for 96-step prediction, outperforming TimeXer's 0.140
Weather Dataset: Reduced average MSE to 0.239 compared to baseline 0.241
Traffic Dataset: Maintained superior performance with average MSE of 0.492
ETT Series: Consistent improvements across all four ETT variants (ETTh1, ETTh2, ETTm1, ETTm2)

Technical Implementation

Exogenous Variable Processing

The TWS framework transforms raw exogenous inputs through a sophisticated mathematical process. First, the entire training dataset undergoes Principal Component Analysis (PCA) to extract orthogonal basis vectors that capture global patterns. Each window of exogenous data is then projected onto these bases, effectively exposing it to trends and seasonality that span beyond the local window.

Dynamic Component Selection

Unlike fixed approaches, TWS dynamically determines the optimal number of principal components to retain. The system selects the smallest k that captures at least 90% of the variance, ensuring that significant patterns are preserved while minimizing noise and redundancy.

Integration Architecture

The refined exogenous series integrates seamlessly with endogenous variables through a transformer-based architecture featuring:

Channel-independent processing for multivariate series
Patch-based temporal encoding for efficient computation
Cross-attention mechanisms for causal information exchange
Global tokens for bridging endogenous and exogenous streams

Key Advantages for Trading Applications

Enhanced Market Context

By incorporating global patterns, TWS helps models understand broader market trends beyond immediate window observations.

Noise Reduction

Whitening process effectively filters out market noise while preserving significant signals crucial for trading decisions.

Improved Generalization

Global awareness prevents overfitting to local patterns, resulting in more robust predictions across different market conditions.

Computational Efficiency

No additional learnable parameters required - TWS leverages statistical properties for efficient processing.

Seamless Integration

Compatible with existing transformer architectures, enabling easy adoption in current trading systems.

Multi-Domain Application

Proven effectiveness across electricity, traffic, weather, and financial time series data.

Rigorous Experimental Validation

Our comprehensive experiments demonstrate TWS's superiority across multiple forecasting horizons (96, 192, 336, and 720 steps) and diverse datasets. The method was evaluated against 11 state-of-the-art baselines including:

Transformer-based: TimeXer, iTransformer, PatchTST, Crossformer, Autoformer
Linear-based: DLinear, TiDE, RLinear
Convolutional: TimesNet, SCINet

TWS achieved best MSE performance in 60% of experimental settings and consistently ranked in the top-2 across all evaluations, establishing it as a robust and reliable enhancement for time series forecasting.

Implications for Financial Forecasting

The TWS framework opens new possibilities for incorporating external information in financial models. By ensuring that exogenous variables are properly whitened and globally aware, traders can:

Better capture market regime changes through global pattern recognition
Reduce false signals from noisy external indicators
Improve model stability across different market conditions
Enhance prediction accuracy for both short and long-term horizons
Integrate diverse data sources without redundancy concerns

As financial markets become increasingly interconnected, the ability to effectively leverage exogenous information while maintaining computational efficiency becomes crucial. TWS provides this capability without requiring additional model parameters or complex architectural changes.

Temporal Window Smoothing