Estimation of the Exponential Autoregressive Time Series Model by Using the Genetic Algorithm

Shi, Zhen; Aoyama, Hisayuki

doi:10.1006/jsvi.1997.1048

Cited by 15 publications

(13 citation statements)

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“…Haggan and Ozaki7 developed some conditions to check that the ExpAr model exhibits a limit cycle behavior or that a fixed point, if it exists, is stable. Haggan and Ozaki7, Shi and Aoyama8 and Baragona9 proposed estimation procedures to obtain the maximum likelihood estimates of the parameters of the ExpAr time series models. These procedures, however, involve computational difficulties and are not suitable for use in (real‐time) manufacturing systems, where CPU‐time and memory are important.…”

Section: Process Modelsmentioning

confidence: 99%

Control charts based on models derived from differential equations

Weihs

Messaoud

Raabe

2010

Quality & Reliability Eng

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The development of technical processes over time can often be adequately modelled by means of differential equations. In order to monitor such processes, control charts may be derived from stochastic models based on such differential equations. In this work, this is demonstrated for a deep-hole drilling process used for producing holes with a high length-to-diameter ratio, good surface finish and straightness. The process is subject to dynamic disturbances classified as either chatter vibration or spiraling. For chatter, a differential equation for the drilling torque and a model known to well approximate processes with similar characteristics are used to set up monitoring procedures. For spiraling a control chart can be based on a statistical model for the spectrum of the structure-born vibrations derived from a differential equation for the deflection of the boring bar.

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Section: Process Modelsmentioning

confidence: 99%

Control charts based on models derived from differential equations

Weihs

Messaoud

Raabe

2010

Quality & Reliability Eng

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“…The EAR model was originally defined by a second order autoregressive form by making coefficients amplitude dependent [3,4,7]: …”

Section: Exponential Autoregressive Modelmentioning

confidence: 99%

“…, which makes the series globally non-linear [7]. If non-linear parameter γ is set to zero, the equation will become an ordinary linear AR model with coefficients a p = φ p + π p such that…”

Section: Exponential Autoregressive Modelmentioning

confidence: 99%

“…In order to achieve this task, BGA hybridised with RLS algorithm is used following a previous study [7]. The nonlinear coefficient, γ, is determined with BGA, and once this coefficient is obtained the model becomes a linear regression problem in which the linear coefficients {φ i , π i | i=1,2,…,p} are determined by RLS algorithm.…”

Section: Exponential Autoregressive Modelmentioning

confidence: 99%

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EEG time series analysis with exponential autoregressive modelling

Balli

Palaniappan

2008

2008 Canadian Conference on Electrical and Computer Engineering

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This paper proposes the use of exponential autoregressive (EAR) model for modelling of time series that are known to exhibit non-linear dynamics such as random fluctuations of amplitude and frequency. Biological signal (bio-signal) such as electroencephalogram (EEG) is known to exhibit nonlinear dynamics. Such signals cannot be modelled with traditional linear modelling techniques like autoregressive (AR) models as these models are known to provide only an approximation to the underlying properties of the non-linear signals. In this study, the suitability of EAR models as compared to AR models is shown using EEG signals in addition to several non-linear benchmark time series data where improved signal to noise ratio (SNR) values are indicated by the EAR models. Overall, the results indicate that use of EAR modelling which has yet to be exploited for bio-signal time series analysis has the huge potential in the characterisation and classification of EEG signals.

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“…A class of nonparametric tests on the Pareto tail index of the innovation distribution in the linear autoregressive model is proposed [2]. A study of the autoregressive models with exponential white noise can be found in the literature [3]- [8]. A form of time series models where marginal distributions are in fact exponential distributions is presented in [3].…”

Section: Introductionmentioning

confidence: 99%

A New Estimation Procedure Using a Reversible Jump McMc Algorithm for Ar Models of Exponential White Noise

Suparman¹

2018

GEOMATE

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ABSTRACT:The autoregressive model generally has a Gaussian error. If an autoregressive model that has a Gaussian error is used to model data, the assumption of normality is often not obeyed by the data. In addition, the parameters of the autoregressive model are generally unknown. The parameters of the autoregressive model include order model, model coefficient, error mean and error variance. This paper aims to determine the parameter estimation procedure of an autoregressive model that has an exponential error. In this paper, the autoregressive model parameter estimation is worked out in a hierarchical Bayesian framework. Since the autoregressive order is also part of the model parameter, the Bayes estimator has a complex form so that the Bayes estimator cannot be explicitly calculated. To solve the problem, the reversible jump MCMC is implemented. The results show that model order, model coefficient, error mean and error variance can be calculated simultaneously. In addition, the resulting autoregressive model is always a stationary autoregressive model.

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Estimation of the Exponential Autoregressive Time Series Model by Using the Genetic Algorithm

Cited by 15 publications

References 0 publications

Control charts based on models derived from differential equations

Control charts based on models derived from differential equations

EEG time series analysis with exponential autoregressive modelling

A New Estimation Procedure Using a Reversible Jump McMc Algorithm for Ar Models of Exponential White Noise

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