Transition Matrix Estimation in High Dimensional Time Series

Fang Han, Han Liu
Proceedings of the 30th International Conference on Machine Learning, PMLR 28(2):172-180, 2013.

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, 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.

Cite this Paper

BibTeX
@InProceedings{pmlr-v28-han13a, title = {Transition Matrix Estimation in High Dimensional Time Series}, author = {Han, Fang and Liu, Han}, booktitle = {Proceedings of the 30th International Conference on Machine Learning}, pages = {172--180}, year = {2013}, editor = {Dasgupta, Sanjoy and McAllester, David}, volume = {28}, number = {2}, series = {Proceedings of Machine Learning Research}, address = {Atlanta, Georgia, USA}, month = {17--19 Jun}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v28/han13a.pdf}, url = {https://proceedings.mlr.press/v28/han13a.html}, 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, 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.} }
Endnote
%0 Conference Paper %T Transition Matrix Estimation in High Dimensional Time Series %A Fang Han %A Han Liu %B Proceedings of the 30th International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2013 %E Sanjoy Dasgupta %E David McAllester %F pmlr-v28-han13a %I PMLR %P 172--180 %U https://proceedings.mlr.press/v28/han13a.html %V 28 %N 2 %X 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, 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.
RIS
TY - CPAPER TI - Transition Matrix Estimation in High Dimensional Time Series AU - Fang Han AU - Han Liu BT - Proceedings of the 30th International Conference on Machine Learning DA - 2013/05/13 ED - Sanjoy Dasgupta ED - David McAllester ID - pmlr-v28-han13a PB - PMLR DP - Proceedings of Machine Learning Research VL - 28 IS - 2 SP - 172 EP - 180 L1 - http://proceedings.mlr.press/v28/han13a.pdf UR - https://proceedings.mlr.press/v28/han13a.html 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, 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. ER -
APA
Han, F. & Liu, H.. (2013). Transition Matrix Estimation in High Dimensional Time Series. Proceedings of the 30th International Conference on Machine Learning, in Proceedings of Machine Learning Research 28(2):172-180 Available from https://proceedings.mlr.press/v28/han13a.html.

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