DeepVARwT: deep learning for a VAR model with trend

Area of Science:

• Statistics
• Machine Learning
• Econometrics

Background:

• Vector Autoregressive (VAR) models are standard for analyzing multiple time series dependencies.
• Existing VAR models often require separate trend estimation, limiting their efficiency.
• Time series analysis is crucial in economics, finance, and engineering.

Purpose of the Study:

• To develop a deep learning method for simultaneous estimation of trend and dependence structure in time series.
• To apply Long Short-Term Memory (LSTM) networks for enhanced time series modeling.
• To evaluate the proposed model's performance against established methods.

Main Methods:

• Utilizing a Long Short-Term Memory (LSTM) network for maximum likelihood estimation.
• Implementing a deep learning methodology for integrated trend and dependence structure estimation.
• Conducting simulation studies with realistic trend functions and real-world data applications.

Main Results:

• The proposed LSTM-based model demonstrates effective simultaneous estimation of trend and dependence.
• Simulation results show accurate estimation of trend functions and parameter values.
• Real-data applications indicate superior prediction performance compared to state-of-the-art models.

Conclusions:

• Deep learning, specifically LSTM networks, offers a powerful approach for advanced time series modeling.
• The novel method provides a unified framework for estimating both trend and dependence structures.
• This approach enhances prediction accuracy in complex time series analysis.