Transition Matrix Estimation in High Dimensional Time Series

Fang Han, Han Liu

Research output: Chapter in Book/Report/Conference proceedingConference contribution

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 languageEnglish (US)
Title of host publication30th International Conference on Machine Learning, ICML 2013
PublisherInternational Machine Learning Society (IMLS)
Pages831-839
Number of pages9
EditionPART 1
StatePublished - 2013
Externally publishedYes
Event30th International Conference on Machine Learning, ICML 2013 - Atlanta, GA, United States
Duration: Jun 16 2013Jun 21 2013

Other

Other30th International Conference on Machine Learning, ICML 2013
CountryUnited States
CityAtlanta, GA
Period6/16/136/21/13

Fingerprint

time series
Time series
brain
finance
Finance
experiment
Brain
Imaging techniques
Experiments

ASJC Scopus subject areas

  • Human-Computer Interaction
  • Sociology and Political Science

Cite this

Han, F., & Liu, H. (2013). Transition Matrix Estimation in High Dimensional Time Series. In 30th International Conference on Machine Learning, ICML 2013 (PART 1 ed., pp. 831-839). International Machine Learning Society (IMLS).

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 proceedingConference contribution

Han, F & Liu, H 2013, Transition Matrix Estimation in High Dimensional Time Series. in 30th International Conference on Machine Learning, ICML 2013. PART 1 edn, International Machine Learning Society (IMLS), pp. 831-839, 30th International Conference on Machine Learning, ICML 2013, Atlanta, GA, United States, 6/16/13.
Han F, Liu H. Transition Matrix Estimation in High Dimensional Time Series. In 30th International Conference on Machine Learning, ICML 2013. PART 1 ed. International Machine Learning Society (IMLS). 2013. p. 831-839
Han, Fang ; Liu, Han. / Transition Matrix Estimation in High Dimensional Time Series. 30th International Conference on Machine Learning, ICML 2013. PART 1. ed. International Machine Learning Society (IMLS), 2013. pp. 831-839
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