Abstract
In this paper, we propose a new method in estimating transition matrices of high dimensional vector autoregressive (VAR) models. Here the data are assumed to come from a stationary Gaussian VAR time series. By formulating the problem as a linear program, we provide a new approach to conduct inference on such models. In theory, under a doubly asymptotic framework in which both the sample size T and dimensionality d of the time series can increase (with possibly d ≫ T), we provide explicit rates of convergence between the estimator and the population transition matrix under different matrix norms. Our results show that the spectral norm of the transition matrix plays a pivotal role in determining the final rates of convergence. This is the first work analyzing the estimation of transition matrices under a high dimensional doubly asymptotic framework. Experiments are conducted on both synthetic and real-world stock data to demonstrate the effectiveness of the proposed method compared with the existing methods. The results of this paper have broad impact on different applications, including finance, genomics, and brain imaging.
| Original language | English (US) |
|---|---|
| Title of host publication | 30th International Conference on Machine Learning, ICML 2013 |
| Publisher | International Machine Learning Society (IMLS) |
| Pages | 831-839 |
| Number of pages | 9 |
| Edition | PART 1 |
| State | Published - 2013 |
| Externally published | Yes |
| Event | 30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA, United States Duration: Jun 16 2013 → Jun 21 2013 |
Other
| Other | 30th International Conference on Machine Learning, ICML 2013 |
|---|---|
| Country | United States |
| City | Atlanta, GA |
| Period | 6/16/13 → 6/21/13 |
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ASJC Scopus subject areas
- Human-Computer Interaction
- Sociology and Political Science
Cite this
Transition Matrix Estimation in High Dimensional Time Series. / Han, Fang; Liu, Han.
30th International Conference on Machine Learning, ICML 2013. PART 1. ed. International Machine Learning Society (IMLS), 2013. p. 831-839.Research output: Chapter in Book/Report/Conference proceeding › Conference contribution
}
TY - GEN
T1 - Transition Matrix Estimation in High Dimensional Time Series
AU - Han, Fang
AU - Liu, Han
PY - 2013
Y1 - 2013
N2 - In this paper, we propose a new method in estimating transition matrices of high dimensional vector autoregressive (VAR) models. Here the data are assumed to come from a stationary Gaussian VAR time series. By formulating the problem as a linear program, we provide a new approach to conduct inference on such models. In theory, under a doubly asymptotic framework in which both the sample size T and dimensionality d of the time series can increase (with possibly d ≫ T), we provide explicit rates of convergence between the estimator and the population transition matrix under different matrix norms. Our results show that the spectral norm of the transition matrix plays a pivotal role in determining the final rates of convergence. This is the first work analyzing the estimation of transition matrices under a high dimensional doubly asymptotic framework. Experiments are conducted on both synthetic and real-world stock data to demonstrate the effectiveness of the proposed method compared with the existing methods. The results of this paper have broad impact on different applications, including finance, genomics, and brain imaging.
AB - In this paper, we propose a new method in estimating transition matrices of high dimensional vector autoregressive (VAR) models. Here the data are assumed to come from a stationary Gaussian VAR time series. By formulating the problem as a linear program, we provide a new approach to conduct inference on such models. In theory, under a doubly asymptotic framework in which both the sample size T and dimensionality d of the time series can increase (with possibly d ≫ T), we provide explicit rates of convergence between the estimator and the population transition matrix under different matrix norms. Our results show that the spectral norm of the transition matrix plays a pivotal role in determining the final rates of convergence. This is the first work analyzing the estimation of transition matrices under a high dimensional doubly asymptotic framework. Experiments are conducted on both synthetic and real-world stock data to demonstrate the effectiveness of the proposed method compared with the existing methods. The results of this paper have broad impact on different applications, including finance, genomics, and brain imaging.
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M3 - Conference contribution
AN - SCOPUS:84897500521
SP - 831
EP - 839
BT - 30th International Conference on Machine Learning, ICML 2013
PB - International Machine Learning Society (IMLS)
ER -