Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes

Huitong Qiu, Sheng Xu, Fang Han, Han Liu, Brian Caffo
Proceedings of the 32nd International Conference on Machine Learning, PMLR 37:1843-1851, 2015.

Abstract

Gaussian vector autoregressive (VAR) processes have been extensively studied in the literature. However, Gaussian assumptions are stringent for heavy-tailed time series that frequently arises in finance and economics. In this paper, we develop a unified framework for modeling and estimating heavy-tailed VAR processes. In particular, we generalize the Gaussian VAR model by an elliptical VAR model that naturally accommodates heavy-tailed time series. Under this model, we develop a quantile-based robust estimator for the transition matrix of the VAR process. We show that the proposed estimator achieves parametric rates of convergence in high dimensions. This is the first work in analyzing heavy-tailed high dimensional VAR processes. As an application of the proposed framework, we investigate Granger causality in the elliptical VAR process, and show that the robust transition matrix estimator induces sign-consistent estimators of Granger causality. The empirical performance of the proposed methodology is demonstrated by both synthetic and real data. We show that the proposed estimator is robust to heavy tails, and exhibit superior performance in stock price prediction.

Cite this Paper

BibTeX
@InProceedings{pmlr-v37-qiu15, title = {Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes}, author = {Qiu, Huitong and Xu, Sheng and Han, Fang and Liu, Han and Caffo, Brian}, booktitle = {Proceedings of the 32nd International Conference on Machine Learning}, pages = {1843--1851}, year = {2015}, editor = {Bach, Francis and Blei, David}, volume = {37}, series = {Proceedings of Machine Learning Research}, address = {Lille, France}, month = {07--09 Jul}, publisher = {PMLR}, pdf = {http://proceedings.mlr.press/v37/qiu15.pdf}, url = {https://proceedings.mlr.press/v37/qiu15.html}, abstract = {Gaussian vector autoregressive (VAR) processes have been extensively studied in the literature. However, Gaussian assumptions are stringent for heavy-tailed time series that frequently arises in finance and economics. In this paper, we develop a unified framework for modeling and estimating heavy-tailed VAR processes. In particular, we generalize the Gaussian VAR model by an elliptical VAR model that naturally accommodates heavy-tailed time series. Under this model, we develop a quantile-based robust estimator for the transition matrix of the VAR process. We show that the proposed estimator achieves parametric rates of convergence in high dimensions. This is the first work in analyzing heavy-tailed high dimensional VAR processes. As an application of the proposed framework, we investigate Granger causality in the elliptical VAR process, and show that the robust transition matrix estimator induces sign-consistent estimators of Granger causality. The empirical performance of the proposed methodology is demonstrated by both synthetic and real data. We show that the proposed estimator is robust to heavy tails, and exhibit superior performance in stock price prediction.} }
Endnote
%0 Conference Paper %T Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes %A Huitong Qiu %A Sheng Xu %A Fang Han %A Han Liu %A Brian Caffo %B Proceedings of the 32nd International Conference on Machine Learning %C Proceedings of Machine Learning Research %D 2015 %E Francis Bach %E David Blei %F pmlr-v37-qiu15 %I PMLR %P 1843--1851 %U https://proceedings.mlr.press/v37/qiu15.html %V 37 %X Gaussian vector autoregressive (VAR) processes have been extensively studied in the literature. However, Gaussian assumptions are stringent for heavy-tailed time series that frequently arises in finance and economics. In this paper, we develop a unified framework for modeling and estimating heavy-tailed VAR processes. In particular, we generalize the Gaussian VAR model by an elliptical VAR model that naturally accommodates heavy-tailed time series. Under this model, we develop a quantile-based robust estimator for the transition matrix of the VAR process. We show that the proposed estimator achieves parametric rates of convergence in high dimensions. This is the first work in analyzing heavy-tailed high dimensional VAR processes. As an application of the proposed framework, we investigate Granger causality in the elliptical VAR process, and show that the robust transition matrix estimator induces sign-consistent estimators of Granger causality. The empirical performance of the proposed methodology is demonstrated by both synthetic and real data. We show that the proposed estimator is robust to heavy tails, and exhibit superior performance in stock price prediction.
RIS
TY - CPAPER TI - Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes AU - Huitong Qiu AU - Sheng Xu AU - Fang Han AU - Han Liu AU - Brian Caffo BT - Proceedings of the 32nd International Conference on Machine Learning DA - 2015/06/01 ED - Francis Bach ED - David Blei ID - pmlr-v37-qiu15 PB - PMLR DP - Proceedings of Machine Learning Research VL - 37 SP - 1843 EP - 1851 L1 - http://proceedings.mlr.press/v37/qiu15.pdf UR - https://proceedings.mlr.press/v37/qiu15.html AB - Gaussian vector autoregressive (VAR) processes have been extensively studied in the literature. However, Gaussian assumptions are stringent for heavy-tailed time series that frequently arises in finance and economics. In this paper, we develop a unified framework for modeling and estimating heavy-tailed VAR processes. In particular, we generalize the Gaussian VAR model by an elliptical VAR model that naturally accommodates heavy-tailed time series. Under this model, we develop a quantile-based robust estimator for the transition matrix of the VAR process. We show that the proposed estimator achieves parametric rates of convergence in high dimensions. This is the first work in analyzing heavy-tailed high dimensional VAR processes. As an application of the proposed framework, we investigate Granger causality in the elliptical VAR process, and show that the robust transition matrix estimator induces sign-consistent estimators of Granger causality. The empirical performance of the proposed methodology is demonstrated by both synthetic and real data. We show that the proposed estimator is robust to heavy tails, and exhibit superior performance in stock price prediction. ER -
APA
Qiu, H., Xu, S., Han, F., Liu, H. & Caffo, B.. (2015). Robust Estimation of Transition Matrices in High Dimensional Heavy-tailed Vector Autoregressive Processes. Proceedings of the 32nd International Conference on Machine Learning, in Proceedings of Machine Learning Research 37:1843-1851 Available from https://proceedings.mlr.press/v37/qiu15.html.

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