Time Series Transformer Architecture

• Time Series Transformer architecture is defined as an advanced encoder-decoder model tailored for continuous time-series forecasting through specialized attention masking and sinusoidal positional encoding.
• It improves traditional methods by replacing discrete embeddings with dense layers to effectively capture both long-term and short-term dependencies, enhancing forecast accuracy.
• The model’s effectiveness is demonstrated in tourism and other domains, achieving lower MAE, RMSE, and MAPE through rigorous evaluations and ablation studies.

The Time Series Transformer architecture is an extension of the transformative models originally developed for natural language processing (as introduced in "Tsformer: Time series Transformer for tourism demand forecasting" (Yi et al., 2021)). Specifically designed to address the complexities inherent in time-series data, the Time Series Transformer builds on traditional transformer architectures by incorporating novel features such as attention mechanisms, positional encodings, and adaptative structures to improve forecasting accuracy and interpretability across varying time horizons.

Architecture Design

The Time Series Transformer, particularly embodied in the "Tsformer" model (Yi et al., 2021), adopts a classic encoder-decoder Transformer architecture to model time-series data. This structure allows the model to efficiently process sequences with varying temporal dependencies. The encoder component specializes in capturing long-term dependencies across the input sequence, whereas the decoder addresses short-term dependencies and generates the output sequence.

A significant modification for time-series data, where variables are generally continuous rather than discrete tokens, is the replacement of the embedding layer of traditional Transformers with a fully connected layer. This allows the model to process continuous variables more naturally. A sinusoidal positional encoding is added to the input to encode the time-step information. This encoding uses fixed functions, typically defined for position $pos$ and dimension index $2i$ as:

$\text{PE(pos, 2i)} = \sin\!\left(\frac{\text{pos}}{10000^{\frac{2i}{d_{model}}}\right), \quad \text{PE}_{(pos, 2i+1)} = \cos\!\left(\frac{pos}{10000^{\frac{2i}{d_{model}\right)$

Innovations and Improvements

Attention Masking Mechanisms

Tsformer (Yi et al., 2021) employs advanced attention masking mechanisms to address the inherent sequential and directional nature of time-series data:

• Encoder Source Masking: Limits each time step in the encoder to attend only to its past states to avoid information leakage from the future.
• Decoder Target Masking: For multi-step forecasting, decoder tokens are prevented from attending to future tokens, ensuring the autoregressive generation process remains causally correct.
• Decoder Memory Masking: Ensures that the decoder uses only relevant historical data while attending to encoder outputs, excluding future time steps.

These targeted use of masks simplify attention interactions and highlight time-appropriate influences, improving both the model's performance and interpretability.

Performance and Evaluation

Results on Tourism Data

The Tsformer (Yi et al., 2021) was applied to tourism demand datasets from Jiuzhaigou Valley and Siguniang Mountain. It outperformed nine baseline models across both short-term (1-day ahead) and longer-term forecasts (7, 15, and 30-day horizons). Performance metrics, including Mean Absolute Error (MAE), Root Mean Squared Error (RMSE), and Mean Absolute Percentage Error (MAPE) consistently showed lower forecasting errors with the Tsformer architecture. This emphasizes the model's superior ability to extract long-term dependencies compared to existing state-of-the-art models.

Ablation Studies

To assess the contribution of specific model components, comprehensive ablation studies were conducted. These studies confirmed: - Calendar Integration: Incorporating the calendar of days to be forecasted, inclusive of known attributes like weekdays and months, enhances the model's predictive capacity for capturing seasonality and periodic behaviors. - Attention Weight Visualization: Visualization of attention weights elucidated that the Tsformer has substantial interpretability. By focusing attention weights according to seasonal and recent-time step information, it demonstrates how historical data impacts the forecasts.

Methodologies for Adaptations

The Tsformer framework has introduced several significant modifications to the classic Transformer architecture to better suit time series analysis:

1. Encoder-Decoder Framework:
   • Designed specifically to handle time dependencies uniquely, the architecture includes an encoder for long-term dependencies of input sequences and a decoder for capturing short-term dependencies, resulting in effective multi-step forecasts.
2. Input Representations: The model eschews the traditional embedding approach used in NLP Transformers in favor of a dense layer, facilitating continuous value input processing. Sinusoidal positional encodings are used for time-step encoding, with the form:

$$\text{PE}(\text{pos}, 2i) = \sin\left(\text{pos} / 10,000^{2i/d_{model}}\right), \text{PE}(\text{pos}, 2i+1) = \cos\left(\text{pos} / 10,000^{2i/d_{model}}\right)$$

1. Contributions to Time Series Forecasting and Interpretability

The Time Series Transformer architecture, as proposed in the Tsformer, brings focused innovations designed to enhance the model's capabilities specifically for forecasting applications:

• The encoder-decoder split allows concurrent modeling of long-term and short-term dependencies, an improvement over RNN-based models which may suffer from gradient vanishing problems.
• The attention mechanisms (multi-head) have been simplified by utilizing targeted attention masks that limit time steps to only attend to their immediate past. This ensures causal correctness and emphasizes dominant influences over the series.
• The inclusion of a “calendar of days to be forecasted” augments forecasting performance by allowing seasonal and periodic features to be integrated directly into the prediction process.
• Attention weight visualization from the decoder–encoder interactions highlights how the model prioritizes historical and seasonal features for interpretability.

Performance and Evaluation

The performance of Tsformer on tourism datasets (Jiuzhaigou Valley and Siguniang Mountain) demonstrates its superiority over conventional deep learning and statistical baselines. It consistently achieves lower errors in short-term (1-day ahead) as well as longer-term forecasts (7, 15, and 30-day horizons), using metrics like MAE, RMSE, and MAPE. Ablation studies further substantiate that incorporating calendar features significantly bolsters forecasting efficacy.

Broader Implications and Applications

While specifically designed for tourism demand forecasting, the architectural innovations within Tsformer have broader applicability across multiple domains requiring accurate time series analysis. Potential applications include financial market prediction (leveraging trends and calendar-based features), energy consumption forecasting (to account for seasonal cyclical patterns), traffic flow prediction, and weather forecasting.

The paper propels the broader field of time series Transformer architectures toward models that couple both short-term and long-term dependencies, highlighting improved accuracy, model robustness, and interpretability as key benefits. By enhancing input representation techniques and attitude transformers to the specificity of sequential, continuous time series, Tsformer paves the way for improved handling of complex data with valuable real-world applications.