A novel structural AR modeling approach for a continuous time linear Markov system

Marina Demeshko, Takashi Washio, Yoshinobu Kawahara

Research output: Contribution to conferencePaper

2 Citations (Scopus)

Abstract

We often use a discrete time vector autoregressive (DVAR) model to analyse continuous time, multivariate, linear Markov systems through their time series data sampled at discrete time steps. However, the DVAR model has been considered not to be structural representation and hence not to have bijective correspondence with system dynamics in general. In this paper, we characterize the relationships of the DVAR model with its corresponding structural vector AR (SVAR) and continuous time vector AR (CVAR) models through finite difference approximation of time differentials. Our analysis shows that the DVAR model of a continuous time, multivariate, linear Markov system bijectively corresponds to the system dynamics. Further we clarify that the SVAR and the CVAR models are uniquely reproduced from their DVAR model under a highly generic condition. Based on these results, we propose a novel Continuous time and Structural Vector AutoRegressive (CSVAR) modeling approach for continuous time, linear Markov systems to derive the SVAR and the CVAR models from their DVAR model empirically derived from the observed time series. We demonstrate its superior performance through some numerical experiments on both artificial and real world data.

Original languageEnglish
Pages104-113
Number of pages10
DOIs
Publication statusPublished - Jan 1 2013
Event2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013 - Dallas, TX, United States
Duration: Dec 7 2013Dec 10 2013

Conference

Conference2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013
CountryUnited States
CityDallas, TX
Period12/7/1312/10/13

Fingerprint

Time series
Dynamical systems
Experiments

All Science Journal Classification (ASJC) codes

  • Software

Cite this

Demeshko, M., Washio, T., & Kawahara, Y. (2013). A novel structural AR modeling approach for a continuous time linear Markov system. 104-113. Paper presented at 2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013, Dallas, TX, United States. https://doi.org/10.1109/ICDMW.2013.17

A novel structural AR modeling approach for a continuous time linear Markov system. / Demeshko, Marina; Washio, Takashi; Kawahara, Yoshinobu.

2013. 104-113 Paper presented at 2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013, Dallas, TX, United States.

Research output: Contribution to conferencePaper

Demeshko, M, Washio, T & Kawahara, Y 2013, 'A novel structural AR modeling approach for a continuous time linear Markov system' Paper presented at 2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013, Dallas, TX, United States, 12/7/13 - 12/10/13, pp. 104-113. https://doi.org/10.1109/ICDMW.2013.17
Demeshko M, Washio T, Kawahara Y. A novel structural AR modeling approach for a continuous time linear Markov system. 2013. Paper presented at 2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013, Dallas, TX, United States. https://doi.org/10.1109/ICDMW.2013.17
Demeshko, Marina ; Washio, Takashi ; Kawahara, Yoshinobu. / A novel structural AR modeling approach for a continuous time linear Markov system. Paper presented at 2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013, Dallas, TX, United States.10 p.
@conference{50941c9d2cf0470ca708ecd5698152f3,
title = "A novel structural AR modeling approach for a continuous time linear Markov system",
abstract = "We often use a discrete time vector autoregressive (DVAR) model to analyse continuous time, multivariate, linear Markov systems through their time series data sampled at discrete time steps. However, the DVAR model has been considered not to be structural representation and hence not to have bijective correspondence with system dynamics in general. In this paper, we characterize the relationships of the DVAR model with its corresponding structural vector AR (SVAR) and continuous time vector AR (CVAR) models through finite difference approximation of time differentials. Our analysis shows that the DVAR model of a continuous time, multivariate, linear Markov system bijectively corresponds to the system dynamics. Further we clarify that the SVAR and the CVAR models are uniquely reproduced from their DVAR model under a highly generic condition. Based on these results, we propose a novel Continuous time and Structural Vector AutoRegressive (CSVAR) modeling approach for continuous time, linear Markov systems to derive the SVAR and the CVAR models from their DVAR model empirically derived from the observed time series. We demonstrate its superior performance through some numerical experiments on both artificial and real world data.",
author = "Marina Demeshko and Takashi Washio and Yoshinobu Kawahara",
year = "2013",
month = "1",
day = "1",
doi = "10.1109/ICDMW.2013.17",
language = "English",
pages = "104--113",
note = "2013 13th IEEE International Conference on Data Mining Workshops, ICDMW 2013 ; Conference date: 07-12-2013 Through 10-12-2013",

}

TY - CONF

T1 - A novel structural AR modeling approach for a continuous time linear Markov system

AU - Demeshko, Marina

AU - Washio, Takashi

AU - Kawahara, Yoshinobu

PY - 2013/1/1

Y1 - 2013/1/1

N2 - We often use a discrete time vector autoregressive (DVAR) model to analyse continuous time, multivariate, linear Markov systems through their time series data sampled at discrete time steps. However, the DVAR model has been considered not to be structural representation and hence not to have bijective correspondence with system dynamics in general. In this paper, we characterize the relationships of the DVAR model with its corresponding structural vector AR (SVAR) and continuous time vector AR (CVAR) models through finite difference approximation of time differentials. Our analysis shows that the DVAR model of a continuous time, multivariate, linear Markov system bijectively corresponds to the system dynamics. Further we clarify that the SVAR and the CVAR models are uniquely reproduced from their DVAR model under a highly generic condition. Based on these results, we propose a novel Continuous time and Structural Vector AutoRegressive (CSVAR) modeling approach for continuous time, linear Markov systems to derive the SVAR and the CVAR models from their DVAR model empirically derived from the observed time series. We demonstrate its superior performance through some numerical experiments on both artificial and real world data.

AB - We often use a discrete time vector autoregressive (DVAR) model to analyse continuous time, multivariate, linear Markov systems through their time series data sampled at discrete time steps. However, the DVAR model has been considered not to be structural representation and hence not to have bijective correspondence with system dynamics in general. In this paper, we characterize the relationships of the DVAR model with its corresponding structural vector AR (SVAR) and continuous time vector AR (CVAR) models through finite difference approximation of time differentials. Our analysis shows that the DVAR model of a continuous time, multivariate, linear Markov system bijectively corresponds to the system dynamics. Further we clarify that the SVAR and the CVAR models are uniquely reproduced from their DVAR model under a highly generic condition. Based on these results, we propose a novel Continuous time and Structural Vector AutoRegressive (CSVAR) modeling approach for continuous time, linear Markov systems to derive the SVAR and the CVAR models from their DVAR model empirically derived from the observed time series. We demonstrate its superior performance through some numerical experiments on both artificial and real world data.

UR - http://www.scopus.com/inward/record.url?scp=84898046818&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84898046818&partnerID=8YFLogxK

U2 - 10.1109/ICDMW.2013.17

DO - 10.1109/ICDMW.2013.17

M3 - Paper

AN - SCOPUS:84898046818

SP - 104

EP - 113

ER -