Estimation of Dynamic Networks for High-Dimensional Nonstationary Time Series.
Mengyu Xu1, Xiaohui Chen2, Wei Biao Wu3
1Department of Statistics and Data Science, University of Central Florida, 4000 Central Florida Blvd, Orlando, FL 32816, USA.
Entropy (Basel, Switzerland)
|December 8, 2020
Summary
This study introduces a novel two-step method to estimate time-varying networks in high-dimensional data, effectively identifying both abrupt structural breaks and smooth changes for improved network analysis.
Area of Science:
- Statistics
- Time Series Analysis
- Network Science
Background:
- High-dimensional nonstationary time series exhibit complex dynamic behaviors, including structural breaks and smooth changes.
- Accurate estimation of time-varying networks is crucial for understanding evolving systems.
Purpose of the Study:
- To develop a robust method for estimating time-varying networks in high-dimensional nonstationary time series.
- To simultaneously address abrupt structural breaks and gradual smooth changes in network structures.
Main Methods:
- A two-step approach is proposed: change point detection using localized averages of sample covariance matrices, followed by graph support recovery using kernelized time-varying constrained L1-minimization for inverse matrix estimation (CLIME) on segmented data.
- Theoretical analysis provides convergence rates for change point and precision matrix estimation under mild conditions.
Main Results:
- The proposed method consistently estimates change points and piecewise smooth precision matrix functions under high-dimensional scaling limits.
- Demonstrated effectiveness in analyzing the evolving network structure of the S&P 500 index from 2003 to 2008.
Conclusions:
- The developed two-step methodology offers a consistent and effective approach for modeling dynamic network structures in nonstationary financial data.
- This method advances the field of time-varying network estimation, particularly for high-dimensional financial time series.
Related Concept Videos
01:24One-Compartment Open Model: Wagner-Nelson and Loo Riegelman Method for ka Estimation
935
This lesson introduces two critical methods in pharmacokinetics, the Wagner-Nelson and Loo-Riegelman methods, used for estimating the absorption rate constant (ka) for drugs administered via non-intravenous routes. The Wagner-Nelson method relates ka to the plasma concentration derived from the slope of a semilog percent unabsorbed time plot. However, it is limited to drugs with one-compartment kinetics and can be impacted by factors like gastrointestinal motility or enzymatic degradation.
On...
On...
935
01:21Linear Approximation in Time Domain
212
Nonlinear systems often require sophisticated approaches for accurate modeling and analysis, with state-space representation being particularly effective. This method is especially useful for systems where variables and parameters vary with time or operating conditions, such as in a simple pendulum or a translational mechanical system with nonlinear springs.
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
For a simple pendulum with a mass evenly distributed along its length and the center of mass located at half the pendulum's length,...
212
01:06Model Approaches for Pharmacokinetic Data: Distributed Parameter Models
174
Pharmacokinetic models are mathematical constructs that represent and predict the time course of drug concentrations in the body, providing meaningful pharmacokinetic parameters. These models are categorized into compartment, physiological, and distributed parameter models.
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
The distributed parameter models are specifically designed to account for variations and differences in some drug classes. This model is particularly useful for assessing regional concentrations of anticancer or...
174
00:56Noncompartmental Analysis: Statistical Moment Theory
277
Noncompartmental analyses leverage statistical moment theory to examine time-related changes in macroscopic events, encapsulating the collective outcomes stemming from the constituent elements in play. Statistical moment theory is a mathematical approach used to describe the time course of drug concentration in the body without assuming a specific compartmental model. SMT provides insights into drug absorption, distribution, metabolism, and elimination by treating drug concentration versus time...
277
01:05Estimation of the Physical Quantities
6.9K
On many occasions, physicists, other scientists, and engineers need to make estimates of a particular quantity. These are sometimes referred to as guesstimates, order-of-magnitude approximations, back-of-the-envelope calculations, or Fermi calculations. The physicist Enrico Fermi was famous for his ability to estimate various kinds of data with surprising precision. Estimating does not mean guessing a number or a formula at random. Instead, estimation means using prior experience and sound...
6.9K
01:26Distributions to Estimate Population Parameter
4.8K
The accurate values of population parameters such as population proportion, population mean, and population standard deviation (or variance) are usually unknown. These are fixed values that can only be estimated from the data collected from the samples. The estimates of each of these parameters are sample proportion, the sample mean, and sample standard deviation (or variance). To obtain the values of these sample statistics, data are required that have particular distribution and central...
4.8K