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Smooth online parameter estimation for time varying VAR models with application to rat local field potential activity
Anass El Yaagoubi Bourakna1, Marco Pinto2, Norbert Fortin3
1King Abdullah University of Science and Technology.
Statistics and Its Interface
|April 24, 2025
Summary
This study introduces a new online method for estimating time-varying spectral properties in non-stationary multivariate time series data. The smooth online parameter estimation (SOPE) approach provides real-time, computationally efficient brain connectivity estimates, outperforming traditional methods for high-dimensional data.
Area of Science:
- Statistics
- Neuroscience
- Signal Processing
Background:
- Multivariate time series often exhibit non-stationary processes with evolving covariance or spectral matrices.
- Current methods for estimating time-varying spectral properties are typically retrospective, limiting real-time adaptive control applications.
- Real-time estimation of spectral brain connectivity is crucial for understanding dynamic brain function.
Purpose of the Study:
- To develop an online estimation procedure for real-time updates of time-varying parameters in multivariate time series.
- To address the computational challenges of online estimation for high-dimensional time-varying vector autoregressive (tv-VAR) models.
- To propose a robust method for estimating spectral brain connectivity in real-time.
Main Methods:
- Developed a smooth online parameter estimation (SOPE) approach for real-time parameter updates.
- SOPE controls the smoothness of estimates with reasonable computational complexity, enabling real-time fitting for high-dimensional time series.
- Compared SOPE with the Kalman filter in terms of mean-squared error and computational cost.
Main Results:
- SOPE demonstrates comparable mean-squared error to the Kalman filter for small dimensions.
- SOPE offers lower computational cost than the Kalman filter, making it scalable for higher dimensions.
- The SOPE method successfully captured dynamic connectivity changes in rat hippocampal local field potential data during an odor memory task.
Conclusions:
- The proposed SOPE method provides an efficient and scalable solution for real-time estimation of time-varying spectral properties in high-dimensional non-stationary time series.
- SOPE is particularly valuable for applications requiring real-time analysis, such as adaptive control and neuroscience research.
- SOPE effectively tracks dynamic brain connectivity, offering insights into neural processes during cognitive tasks.
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