Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics

Jie Ding; Mohammad Noshad; Vahid Tarokh

doi:10.1109/ICDMW.2015.209

Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics

Jie Ding
, Mohammad Noshad
, Vahid Tarokh

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

4 Scopus citations

Abstract

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

Original language	English (US)
Title of host publication	Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015
Editors	Xindong Wu, Alexander Tuzhilin, Hui Xiong, Jennifer G. Dy, Charu Aggarwal, Zhi-Hua Zhou, Peng Cui
Publisher	Institute of Electrical and Electronics Engineers Inc.
Pages	1441-1446
Number of pages	6
ISBN (Electronic)	9781467384926
DOIs	https://doi.org/10.1109/ICDMW.2015.209
State	Published - Jan 29 2016
Externally published	Yes
Event	15th IEEE International Conference on Data Mining Workshop, ICDMW 2015 - Atlantic City, United States Duration: Nov 14 2015 → Nov 17 2015

Publication series

Name	Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015

Other

Other	15th IEEE International Conference on Data Mining Workshop, ICDMW 2015
Country/Territory	United States
City	Atlantic City
Period	11/14/15 → 11/17/15

Bibliographical note

Publisher Copyright:
© 2015 IEEE.

Keywords

Gap statistics
Uniform distribution
stable autoregressive filters
time-varying autoregressive process

Publisher link

10.1109/ICDMW.2015.209

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Ding, J., Noshad, M., & Tarokh, V. (2016). Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics. In X. Wu, A. Tuzhilin, H. Xiong, J. G. Dy, C. Aggarwal, Z.-H. Zhou, & P. Cui (Eds.), Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015 (pp. 1441-1446). Article 7395839 (Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015). Institute of Electrical and Electronics Engineers Inc.. https://doi.org/10.1109/ICDMW.2015.209

Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics. / Ding, Jie; Noshad, Mohammad; Tarokh, Vahid.
Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015. ed. / Xindong Wu; Alexander Tuzhilin; Hui Xiong; Jennifer G. Dy; Charu Aggarwal; Zhi-Hua Zhou; Peng Cui. Institute of Electrical and Electronics Engineers Inc., 2016. p. 1441-1446 7395839 (Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015).

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

Ding, J, Noshad, M & Tarokh, V 2016, Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics. in X Wu, A Tuzhilin, H Xiong, JG Dy, C Aggarwal, Z-H Zhou & P Cui (eds), Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015., 7395839, Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015, Institute of Electrical and Electronics Engineers Inc., pp. 1441-1446, 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015, Atlantic City, United States, 11/14/15. https://doi.org/10.1109/ICDMW.2015.209

Ding J, Noshad M, Tarokh V. Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics. In Wu X, Tuzhilin A, Xiong H, Dy JG, Aggarwal C, Zhou ZH, Cui P, editors, Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015. Institute of Electrical and Electronics Engineers Inc. 2016. p. 1441-1446. 7395839. (Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015). doi: 10.1109/ICDMW.2015.209

Ding, Jie ; Noshad, Mohammad ; Tarokh, Vahid. / Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics. Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015. editor / Xindong Wu ; Alexander Tuzhilin ; Hui Xiong ; Jennifer G. Dy ; Charu Aggarwal ; Zhi-Hua Zhou ; Peng Cui. Institute of Electrical and Electronics Engineers Inc., 2016. pp. 1441-1446 (Proceedings - 15th IEEE International Conference on Data Mining Workshop, ICDMW 2015).

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abstract = "Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.",

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AB - Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable autoregressive (AR) processes. We introduce a new model selection technique based on Gap statistics to learn the appropriate number of AR filters needed to model a time series. We define a new distance measure between stable AR filters and draw a reference curve that is used to measure how much adding a new AR filter improves the performance of the model, and then choose the number of AR filters that has the maximum gap with the reference curve. To that end, we propose a new method in order to generate uniform random stable AR filters in root domain. Numerical results are provided demonstrating the performance of the proposed approach.

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Learning the Number of Autoregressive Mixtures in Time Series Using the Gap Statistics

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