Scaling Law for Time Series Forecasting

Jingzhe Shi, Qinwei Ma, Huan Ma, Lei Li·May 24, 2024

Summary

The paper investigates the scaling laws for time series forecasting, challenging previous assumptions by focusing on the look-back horizon, an aspect previously overlooked. It proposes a theory that considers dataset size, model complexity, and data granularity, proposing that the optimal horizon depends on training data and may increase with more data. The study empirically evaluates various models on diverse datasets, confirming the influence of dataset size, model complexity, and the importance of the look-back horizon. The findings suggest that for small datasets, the optimal horizon remains stable, while for larger datasets, it increases, and the total loss is a combination of Bayesian and approximation components. The work contributes a new theoretical framework, highlights the need to consider horizon in model design, and suggests future research directions for time series analysis, particularly in limited-size datasets and large-scale forecasting.

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the influence of the horizon on scaling behaviors and the performance of time series forecasting models, considering factors such as dataset size, model complexity, and the impact of the horizon on overall performance . This paper delves into the optimal horizon for forecasting tasks and how it interacts with dataset size and model complexity, shedding light on the scaling behaviors in relation to these factors . While the specific focus on the impact of the horizon in time series forecasting is not entirely new, the detailed exploration of how dataset size, model complexity, and the horizon interact to affect forecasting performance contributes novel insights to the field .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate a scientific hypothesis related to the scaling law for time series forecasting. The hypothesis focuses on the impact of dataset size, model complexity, and the look-back horizon on the performance of time series forecasting models. It explores how more training data can improve performance, the behavior of more capable models compared to less capable ones, and how longer input horizons may affect model performance . The study delves into the influence of these factors on the scaling behaviors observed in time series forecasting, aiming to explain the complexities and interactions between dataset size, model complexity, and the look-back horizon in the context of time series forecasting .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper "Scaling Law for Time Series Forecasting" introduces several novel ideas, methods, and models in the field of time series analysis and forecasting :

  1. ModernTCN: The paper presents ModernTCN, a modern pure convolution structure designed for general time series analysis. This architecture enables a wide Effective Receptive Field, enhancing its ability to capture temporal dependencies in time series data .

  2. iTransformer: iTransformer proposes the use of attention mechanisms to capture relationships between different variables in time series data, offering a new approach to modeling temporal dependencies .

  3. Large Foundational Datasets and Models: The paper discusses the importance of foundational datasets and models for time series analysis. Some works propose foundational models capable of zero-shot forecasting, while others focus on open-source foundational datasets for transfer learning and model training .

  4. Scaling Laws and Theory: Extensive research has been conducted to investigate scaling laws in deep learning across various domains, including Natural Language Processing, Computer Vision, and Graph-based Neural Networks. The paper not only observes the existence of scaling laws but also proposes theories to explain them, providing insights into the underlying mechanisms .

  5. Optimal Horizon and Dataset Size: The study explores the concept of an optimal horizon in time series forecasting, influenced by the size of the dataset. It is noted that the dataset size impacts the optimal horizon, while the model size has a less significant effect. The paper discusses how an expanded horizon can lead to reduced Bayesian Error but may pose challenges for limited datasets and smaller models to effectively learn the data space .

  6. Downsampling for Performance Improvement: The paper suggests that downsampling, along with techniques like patches and low-pass filters, can enhance performance in time series prediction tasks. By filtering out high-frequency features that may be noise-dominated, downsampling can help the model focus on the most important dimensions of the intrinsic space, potentially improving forecasting accuracy .

These novel ideas, methods, and models proposed in the paper contribute to advancing the field of time series forecasting by introducing innovative approaches to modeling temporal dependencies, exploring scaling laws, and optimizing forecasting performance based on dataset characteristics and model design. The paper "Scaling Law for Time Series Forecasting" introduces several novel characteristics and advantages compared to previous methods in the field of time series forecasting:

  1. ModernTCN Architecture: The paper proposes the ModernTCN architecture, a modern pure convolution structure designed for general time series analysis. This architecture offers a wide Effective Receptive Field, enhancing its ability to capture temporal dependencies in time series data .

  2. iTransformer with Attention Mechanisms: iTransformer introduces the use of attention mechanisms to capture relationships between different variables in time series data, providing a new approach to modeling temporal dependencies .

  3. Large Foundational Datasets and Models: The paper discusses the significance of large foundational datasets and models for time series analysis. Some works propose foundational models capable of zero-shot forecasting, while others focus on open-source foundational datasets for transfer learning and model training .

  4. Exploration of Scaling Laws: Extensive research has been conducted to investigate scaling laws in deep learning across various domains. The paper not only observes the existence of scaling laws but also proposes theories to explain them, providing insights into the underlying mechanisms .

  5. Optimal Horizon Consideration: The study explores the concept of an optimal horizon in time series forecasting, influenced by the size of the dataset. It is noted that the dataset size impacts the optimal horizon, while the model size has a less significant effect. The paper discusses how an expanded horizon can lead to reduced Bayesian Error but may pose challenges for limited datasets and smaller models to effectively learn the data space .

  6. Performance Improvement through Downsampling: The paper suggests that downsampling, along with techniques like patches and low-pass filters, can enhance performance in time series prediction tasks. By filtering out high-frequency features that may be noise-dominated, downsampling can help the model focus on the most important dimensions of the intrinsic space, potentially improving forecasting accuracy .

These characteristics and advantages highlight the innovative approaches proposed in the paper, contributing to advancements in time series forecasting by addressing key challenges and introducing novel methodologies for improved forecasting accuracy and efficiency.


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research works exist in the field of time series forecasting. Noteworthy researchers in this field include:

  • A. Zeng, M. Chen, L. Zhang, and Q. Xu
  • S.-A. Chen, C.-L. Li, N. Yoder, S. O. Arik, and T. Pfister
  • Z. Xu, A. Zeng, and Q. Xu
  • H. Zhou, S. Zhang, J. Peng, S. Zhang, J. Li, H. Xiong, and W. Zhang
  • H. Wu, J. Xu, J. Wang, and M. Long
  • L. donghao and wang xue
  • H. Wang, J. Peng, F. Huang, J. Wang, J. Chen, and Y. Xiao
  • J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Radford, J. Wu, and D. Amodei

The key to the solution mentioned in the paper "Scaling Law for Time Series Forecasting" involves designing models and hyperparameters according to the dataset size and feature degradation property of the specific dataset. Additionally, conducting further experiments on larger foundational time series datasets to explore the optimal horizon concerning pretraining loss and the loss for transferring to specific datasets can provide valuable insights for future works on time series forecasting. The paper emphasizes the importance of the horizon and its potential impact on scaling behaviors in time series forecasting tasks .


How were the experiments in the paper designed?

The experiments in the paper were designed with specific considerations and settings:

  • The experiments were conducted on 8 datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Weather, ECL, and Traffic .
  • Different hyperparameters were adjusted for Dataset Size Scaling, Model Size Scaling, and Width Scaling experiments, such as modifying the look back horizon, channel dimension, depth-wise dimensions, learning rate, weight decay, and batch size .
  • Instance normalization was utilized for all models, and deep learning networks were implemented in PyTorch on GPUs like NVIDIA RTX 3080, RTX 3090, RTX 4090D, and A100 40GB .
  • Linear models and MLPs were used for the experiments, with variations in batch size, learning rate, weight decay, and training epochs based on the dataset size and type .
  • The experiments involved conducting multiple iterations for some datasets and drawing graphs with error bars to represent the standard error of these iterations .
  • The experiments aimed to validate theories related to the impact of the horizon on scaling behaviors and the performance of time series forecasting models, considering dataset size, model complexity, and the horizon's influence on performance .

What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study includes various datasets such as ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Weather, ECL, and Traffic . These datasets cover a range of domains including electricity consumption, exchange rates, weather factors, and transportation-related data . Regarding the availability of the code, the study does not explicitly mention whether the code used for the experiments is open source or publicly available. It focuses on detailing the experimental settings, models, and results obtained from the datasets .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide substantial support for the scientific hypotheses that needed verification. The study focuses on scaling laws for time series forecasting, considering factors like dataset size, model complexity, and the impact of the look-back horizon . The experiments conducted on various datasets of different sizes, ranging from 4 * 10^4 samples to 10^7 samples, validate the scaling law on dataset size and model complexity within the realm of time series forecasting . The empirical evaluations of different models using diverse time series forecasting datasets confirm the validity of the scaling law and the proposed theoretical framework, particularly regarding the influence of the look-back horizon .

Moreover, the study explores the impact of the horizon as an adjustable hyper-parameter for forecasting tasks, emphasizing its significance in improving performance with more historical information utilization . The findings reveal that while more training data enhances performance, more capable models do not always outperform less capable ones, and longer input horizons may not always benefit performance, highlighting the complexity of these relationships in practical datasets . The experiments conducted in the paper shed light on these seemingly abnormal behaviors and provide insights into the optimal horizon and its relationship with available training data .

Overall, the experiments and results in the paper offer valuable empirical evidence that supports the proposed theoretical framework and hypotheses related to scaling laws in time series forecasting. The study's comprehensive analysis of various models, datasets, and factors such as dataset size, model complexity, and look-back horizon contributes to a deeper understanding of the dynamics involved in time series forecasting tasks .


What are the contributions of this paper?

The paper makes several contributions in the field of time series forecasting:

  • Proposing new convolutional architectures like ModernTCN for general time series analysis .
  • Introducing foundational datasets and models for time series forecasting, including zero-shot forecasting models and transfer learning capabilities .
  • Investigating scaling laws in deep learning domains such as Natural Language Processing, Computer Vision, and Graph-based Neural Networks, providing insights into the underlying mechanisms and theories .
  • Establishing bounds for the quantization error of time series, contributing to the knowledge base on time series analysis .
  • Corroborating scaling behaviors related to data scaling and model-size scaling across various datasets and models, validating the proposed theoretical framework in time series forecasting .

What work can be continued in depth?

Further research in the field of time series forecasting can be expanded in several areas based on the existing works:

  • Investigating the impact of dataset size and model complexity: Future studies can delve deeper into how dataset size and model complexity influence time series forecasting performance, particularly focusing on the look-back horizon, which has been highlighted as a crucial aspect that warrants further exploration .
  • Exploring the scaling behaviors in time series forecasting: There is a need to continue exploring the scaling laws in time series forecasting, considering that while more training data tends to enhance performance, more capable models do not always outperform less capable ones, and longer input horizons may not always improve performance for certain models .
  • Validation of theoretical frameworks: It is essential to validate and refine theoretical frameworks proposed for time series forecasting, especially those that consider the influence of the horizon on scaling behaviors and model performance .
  • Empirical evaluation of various models: Conducting empirical evaluations of different time series forecasting models using diverse datasets can help verify the validity of scaling laws concerning dataset size and model complexity, as well as validate proposed theoretical frameworks .
  • Investigating the impact of horizon on model performance: Further studies can focus on understanding how the horizon parameter impacts the performance of time series forecasting models, especially in relation to dataset size and feature degradation properties .

By addressing these areas, researchers can contribute to a deeper understanding of time series forecasting, enhance model performance, and potentially uncover new insights that can improve forecasting accuracy and efficiency.


Introduction
Background
Previous research gaps in time series forecasting
Overlooked importance of look-back horizon
Objective
To propose a theory on optimal look-back horizon
Evaluate the impact of dataset size, model complexity, and data granularity
Method
Data Collection
Selection of diverse datasets for empirical analysis
Inclusion of varying dataset sizes
Data Preprocessing
Techniques used for cleaning and preparing time series data
Handling of different data granularities
Theoretical Framework
Optimal Look-Back Horizon
Relationship with training data size
Increase in optimal horizon with larger datasets
Bayesian and approximation loss components
Scaling Laws
Formulation of scaling laws for forecasting performance
Dependency on dataset characteristics
Empirical Evaluation
Model Selection
Overview of tested models (e.g., ARIMA, LSTM, Transformer)
Evaluation metrics (e.g., MAE, RMSE)
Results and Analysis
Impact of dataset size on forecasting accuracy
Influence of model complexity on horizon choice
Validation of the proposed theory
Contributions
Novel theoretical insights for time series forecasting
Highlighting the need to consider look-back horizon in model design
Importance for small and large-scale datasets
Future Research Directions
Limitations and extensions of the study
Applications in limited-size datasets
Challenges and opportunities in large-scale forecasting
Conclusion
Summary of key findings
Implications for the time series analysis community
Call to action for further research in the field
Basic info
papers
machine learning
artificial intelligence
Advanced features
Insights
According to the theory proposed, what factors does the optimal look-back horizon depend on?
What aspect of time series forecasting does the paper focus on that was previously overlooked?
What are the key contributions of the paper to the field of time series analysis?
How does the study's empirical evaluation support the theory regarding the influence of dataset size and model complexity?

Scaling Law for Time Series Forecasting

Jingzhe Shi, Qinwei Ma, Huan Ma, Lei Li·May 24, 2024

Summary

The paper investigates the scaling laws for time series forecasting, challenging previous assumptions by focusing on the look-back horizon, an aspect previously overlooked. It proposes a theory that considers dataset size, model complexity, and data granularity, proposing that the optimal horizon depends on training data and may increase with more data. The study empirically evaluates various models on diverse datasets, confirming the influence of dataset size, model complexity, and the importance of the look-back horizon. The findings suggest that for small datasets, the optimal horizon remains stable, while for larger datasets, it increases, and the total loss is a combination of Bayesian and approximation components. The work contributes a new theoretical framework, highlights the need to consider horizon in model design, and suggests future research directions for time series analysis, particularly in limited-size datasets and large-scale forecasting.
Mind map
Validation of the proposed theory
Influence of model complexity on horizon choice
Impact of dataset size on forecasting accuracy
Evaluation metrics (e.g., MAE, RMSE)
Overview of tested models (e.g., ARIMA, LSTM, Transformer)
Dependency on dataset characteristics
Formulation of scaling laws for forecasting performance
Bayesian and approximation loss components
Increase in optimal horizon with larger datasets
Relationship with training data size
Handling of different data granularities
Techniques used for cleaning and preparing time series data
Inclusion of varying dataset sizes
Selection of diverse datasets for empirical analysis
Evaluate the impact of dataset size, model complexity, and data granularity
To propose a theory on optimal look-back horizon
Overlooked importance of look-back horizon
Previous research gaps in time series forecasting
Call to action for further research in the field
Implications for the time series analysis community
Summary of key findings
Challenges and opportunities in large-scale forecasting
Applications in limited-size datasets
Limitations and extensions of the study
Importance for small and large-scale datasets
Highlighting the need to consider look-back horizon in model design
Novel theoretical insights for time series forecasting
Results and Analysis
Model Selection
Scaling Laws
Optimal Look-Back Horizon
Data Preprocessing
Data Collection
Objective
Background
Conclusion
Future Research Directions
Contributions
Empirical Evaluation
Theoretical Framework
Method
Introduction
Outline
Introduction
Background
Previous research gaps in time series forecasting
Overlooked importance of look-back horizon
Objective
To propose a theory on optimal look-back horizon
Evaluate the impact of dataset size, model complexity, and data granularity
Method
Data Collection
Selection of diverse datasets for empirical analysis
Inclusion of varying dataset sizes
Data Preprocessing
Techniques used for cleaning and preparing time series data
Handling of different data granularities
Theoretical Framework
Optimal Look-Back Horizon
Relationship with training data size
Increase in optimal horizon with larger datasets
Bayesian and approximation loss components
Scaling Laws
Formulation of scaling laws for forecasting performance
Dependency on dataset characteristics
Empirical Evaluation
Model Selection
Overview of tested models (e.g., ARIMA, LSTM, Transformer)
Evaluation metrics (e.g., MAE, RMSE)
Results and Analysis
Impact of dataset size on forecasting accuracy
Influence of model complexity on horizon choice
Validation of the proposed theory
Contributions
Novel theoretical insights for time series forecasting
Highlighting the need to consider look-back horizon in model design
Importance for small and large-scale datasets
Future Research Directions
Limitations and extensions of the study
Applications in limited-size datasets
Challenges and opportunities in large-scale forecasting
Conclusion
Summary of key findings
Implications for the time series analysis community
Call to action for further research in the field

Paper digest

What problem does the paper attempt to solve? Is this a new problem?

The paper aims to address the influence of the horizon on scaling behaviors and the performance of time series forecasting models, considering factors such as dataset size, model complexity, and the impact of the horizon on overall performance . This paper delves into the optimal horizon for forecasting tasks and how it interacts with dataset size and model complexity, shedding light on the scaling behaviors in relation to these factors . While the specific focus on the impact of the horizon in time series forecasting is not entirely new, the detailed exploration of how dataset size, model complexity, and the horizon interact to affect forecasting performance contributes novel insights to the field .


What scientific hypothesis does this paper seek to validate?

This paper aims to validate a scientific hypothesis related to the scaling law for time series forecasting. The hypothesis focuses on the impact of dataset size, model complexity, and the look-back horizon on the performance of time series forecasting models. It explores how more training data can improve performance, the behavior of more capable models compared to less capable ones, and how longer input horizons may affect model performance . The study delves into the influence of these factors on the scaling behaviors observed in time series forecasting, aiming to explain the complexities and interactions between dataset size, model complexity, and the look-back horizon in the context of time series forecasting .


What new ideas, methods, or models does the paper propose? What are the characteristics and advantages compared to previous methods?

The paper "Scaling Law for Time Series Forecasting" introduces several novel ideas, methods, and models in the field of time series analysis and forecasting :

  1. ModernTCN: The paper presents ModernTCN, a modern pure convolution structure designed for general time series analysis. This architecture enables a wide Effective Receptive Field, enhancing its ability to capture temporal dependencies in time series data .

  2. iTransformer: iTransformer proposes the use of attention mechanisms to capture relationships between different variables in time series data, offering a new approach to modeling temporal dependencies .

  3. Large Foundational Datasets and Models: The paper discusses the importance of foundational datasets and models for time series analysis. Some works propose foundational models capable of zero-shot forecasting, while others focus on open-source foundational datasets for transfer learning and model training .

  4. Scaling Laws and Theory: Extensive research has been conducted to investigate scaling laws in deep learning across various domains, including Natural Language Processing, Computer Vision, and Graph-based Neural Networks. The paper not only observes the existence of scaling laws but also proposes theories to explain them, providing insights into the underlying mechanisms .

  5. Optimal Horizon and Dataset Size: The study explores the concept of an optimal horizon in time series forecasting, influenced by the size of the dataset. It is noted that the dataset size impacts the optimal horizon, while the model size has a less significant effect. The paper discusses how an expanded horizon can lead to reduced Bayesian Error but may pose challenges for limited datasets and smaller models to effectively learn the data space .

  6. Downsampling for Performance Improvement: The paper suggests that downsampling, along with techniques like patches and low-pass filters, can enhance performance in time series prediction tasks. By filtering out high-frequency features that may be noise-dominated, downsampling can help the model focus on the most important dimensions of the intrinsic space, potentially improving forecasting accuracy .

These novel ideas, methods, and models proposed in the paper contribute to advancing the field of time series forecasting by introducing innovative approaches to modeling temporal dependencies, exploring scaling laws, and optimizing forecasting performance based on dataset characteristics and model design. The paper "Scaling Law for Time Series Forecasting" introduces several novel characteristics and advantages compared to previous methods in the field of time series forecasting:

  1. ModernTCN Architecture: The paper proposes the ModernTCN architecture, a modern pure convolution structure designed for general time series analysis. This architecture offers a wide Effective Receptive Field, enhancing its ability to capture temporal dependencies in time series data .

  2. iTransformer with Attention Mechanisms: iTransformer introduces the use of attention mechanisms to capture relationships between different variables in time series data, providing a new approach to modeling temporal dependencies .

  3. Large Foundational Datasets and Models: The paper discusses the significance of large foundational datasets and models for time series analysis. Some works propose foundational models capable of zero-shot forecasting, while others focus on open-source foundational datasets for transfer learning and model training .

  4. Exploration of Scaling Laws: Extensive research has been conducted to investigate scaling laws in deep learning across various domains. The paper not only observes the existence of scaling laws but also proposes theories to explain them, providing insights into the underlying mechanisms .

  5. Optimal Horizon Consideration: The study explores the concept of an optimal horizon in time series forecasting, influenced by the size of the dataset. It is noted that the dataset size impacts the optimal horizon, while the model size has a less significant effect. The paper discusses how an expanded horizon can lead to reduced Bayesian Error but may pose challenges for limited datasets and smaller models to effectively learn the data space .

  6. Performance Improvement through Downsampling: The paper suggests that downsampling, along with techniques like patches and low-pass filters, can enhance performance in time series prediction tasks. By filtering out high-frequency features that may be noise-dominated, downsampling can help the model focus on the most important dimensions of the intrinsic space, potentially improving forecasting accuracy .

These characteristics and advantages highlight the innovative approaches proposed in the paper, contributing to advancements in time series forecasting by addressing key challenges and introducing novel methodologies for improved forecasting accuracy and efficiency.


Do any related researches exist? Who are the noteworthy researchers on this topic in this field?What is the key to the solution mentioned in the paper?

Several related research works exist in the field of time series forecasting. Noteworthy researchers in this field include:

  • A. Zeng, M. Chen, L. Zhang, and Q. Xu
  • S.-A. Chen, C.-L. Li, N. Yoder, S. O. Arik, and T. Pfister
  • Z. Xu, A. Zeng, and Q. Xu
  • H. Zhou, S. Zhang, J. Peng, S. Zhang, J. Li, H. Xiong, and W. Zhang
  • H. Wu, J. Xu, J. Wang, and M. Long
  • L. donghao and wang xue
  • H. Wang, J. Peng, F. Huang, J. Wang, J. Chen, and Y. Xiao
  • J. Kaplan, S. McCandlish, T. Henighan, T. B. Brown, B. Chess, R. Child, S. Gray, A. Radford, J. Wu, and D. Amodei

The key to the solution mentioned in the paper "Scaling Law for Time Series Forecasting" involves designing models and hyperparameters according to the dataset size and feature degradation property of the specific dataset. Additionally, conducting further experiments on larger foundational time series datasets to explore the optimal horizon concerning pretraining loss and the loss for transferring to specific datasets can provide valuable insights for future works on time series forecasting. The paper emphasizes the importance of the horizon and its potential impact on scaling behaviors in time series forecasting tasks .


How were the experiments in the paper designed?

The experiments in the paper were designed with specific considerations and settings:

  • The experiments were conducted on 8 datasets, including ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Weather, ECL, and Traffic .
  • Different hyperparameters were adjusted for Dataset Size Scaling, Model Size Scaling, and Width Scaling experiments, such as modifying the look back horizon, channel dimension, depth-wise dimensions, learning rate, weight decay, and batch size .
  • Instance normalization was utilized for all models, and deep learning networks were implemented in PyTorch on GPUs like NVIDIA RTX 3080, RTX 3090, RTX 4090D, and A100 40GB .
  • Linear models and MLPs were used for the experiments, with variations in batch size, learning rate, weight decay, and training epochs based on the dataset size and type .
  • The experiments involved conducting multiple iterations for some datasets and drawing graphs with error bars to represent the standard error of these iterations .
  • The experiments aimed to validate theories related to the impact of the horizon on scaling behaviors and the performance of time series forecasting models, considering dataset size, model complexity, and the horizon's influence on performance .

What is the dataset used for quantitative evaluation? Is the code open source?

The dataset used for quantitative evaluation in the study includes various datasets such as ETTh1, ETTh2, ETTm1, ETTm2, Exchange, Weather, ECL, and Traffic . These datasets cover a range of domains including electricity consumption, exchange rates, weather factors, and transportation-related data . Regarding the availability of the code, the study does not explicitly mention whether the code used for the experiments is open source or publicly available. It focuses on detailing the experimental settings, models, and results obtained from the datasets .


Do the experiments and results in the paper provide good support for the scientific hypotheses that need to be verified? Please analyze.

The experiments and results presented in the paper provide substantial support for the scientific hypotheses that needed verification. The study focuses on scaling laws for time series forecasting, considering factors like dataset size, model complexity, and the impact of the look-back horizon . The experiments conducted on various datasets of different sizes, ranging from 4 * 10^4 samples to 10^7 samples, validate the scaling law on dataset size and model complexity within the realm of time series forecasting . The empirical evaluations of different models using diverse time series forecasting datasets confirm the validity of the scaling law and the proposed theoretical framework, particularly regarding the influence of the look-back horizon .

Moreover, the study explores the impact of the horizon as an adjustable hyper-parameter for forecasting tasks, emphasizing its significance in improving performance with more historical information utilization . The findings reveal that while more training data enhances performance, more capable models do not always outperform less capable ones, and longer input horizons may not always benefit performance, highlighting the complexity of these relationships in practical datasets . The experiments conducted in the paper shed light on these seemingly abnormal behaviors and provide insights into the optimal horizon and its relationship with available training data .

Overall, the experiments and results in the paper offer valuable empirical evidence that supports the proposed theoretical framework and hypotheses related to scaling laws in time series forecasting. The study's comprehensive analysis of various models, datasets, and factors such as dataset size, model complexity, and look-back horizon contributes to a deeper understanding of the dynamics involved in time series forecasting tasks .


What are the contributions of this paper?

The paper makes several contributions in the field of time series forecasting:

  • Proposing new convolutional architectures like ModernTCN for general time series analysis .
  • Introducing foundational datasets and models for time series forecasting, including zero-shot forecasting models and transfer learning capabilities .
  • Investigating scaling laws in deep learning domains such as Natural Language Processing, Computer Vision, and Graph-based Neural Networks, providing insights into the underlying mechanisms and theories .
  • Establishing bounds for the quantization error of time series, contributing to the knowledge base on time series analysis .
  • Corroborating scaling behaviors related to data scaling and model-size scaling across various datasets and models, validating the proposed theoretical framework in time series forecasting .

What work can be continued in depth?

Further research in the field of time series forecasting can be expanded in several areas based on the existing works:

  • Investigating the impact of dataset size and model complexity: Future studies can delve deeper into how dataset size and model complexity influence time series forecasting performance, particularly focusing on the look-back horizon, which has been highlighted as a crucial aspect that warrants further exploration .
  • Exploring the scaling behaviors in time series forecasting: There is a need to continue exploring the scaling laws in time series forecasting, considering that while more training data tends to enhance performance, more capable models do not always outperform less capable ones, and longer input horizons may not always improve performance for certain models .
  • Validation of theoretical frameworks: It is essential to validate and refine theoretical frameworks proposed for time series forecasting, especially those that consider the influence of the horizon on scaling behaviors and model performance .
  • Empirical evaluation of various models: Conducting empirical evaluations of different time series forecasting models using diverse datasets can help verify the validity of scaling laws concerning dataset size and model complexity, as well as validate proposed theoretical frameworks .
  • Investigating the impact of horizon on model performance: Further studies can focus on understanding how the horizon parameter impacts the performance of time series forecasting models, especially in relation to dataset size and feature degradation properties .

By addressing these areas, researchers can contribute to a deeper understanding of time series forecasting, enhance model performance, and potentially uncover new insights that can improve forecasting accuracy and efficiency.

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