From general state-space to VARMAX models

Casals, José Francisco Forniés; García‐Hiernaux, Alfredo; Jerez, Miguel

doi:10.1016/j.matcom.2012.01.001

Cited by 13 publications

(8 citation statements)

References 13 publications

(14 reference statements)

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“…State-space equations and VARMA models can be interchangeably transformed [CGHJ12], so we can refer to the generated model as state-space or VARMA model with sparse GC pattern.…”

Section: Generating Eeg Datamentioning

confidence: 99%

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Manomaisaowapak

Nartkulpat

Songsiri

2022

IEEE Trans. Neural Netw. Learning Syst.

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This paper considers a problem of estimating brain effective connectivity from EEG signals using a Granger causality (GC) concept characterized on state-space models. We propose a state-space model for explaining coupled dynamics of the source and EEG signals where EEG is a linear combination of sources according to the characteristics of volume conduction. Our formulation has a sparsity prior on the source output matrix that can further classify active and inactive sources. The scheme is comprised of two main steps: model estimation and model inference to estimate brain connectivity. The model estimation consists of performing a subspace identification and the active source selection based on a group-norm regularized least-squares. The model inference relies on the concept of state-space GC that requires solving a discrete-time Riccati equation for the covariance of estimation error. We verify the performance on simulated data sets that represent realistic human brain activities under several conditions including percentages of active sources, a number of EEG electrodes and the location of active sources. The performance of estimating brain networks is compared with a two-stage approach using source reconstruction algorithms and VAR-based Granger analysis. Our method achieved better performances than the two-stage approach under the assumptions that the true source dynamics are sparse and generated from state-space models. The method is applied to a real EEG SSVEP data set and we found that the temporal lobe played a role of a mediator of connections between temporal and occipital areas, which agreed with findings in previous studies.

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“…State-space equations and VARMA models can be interchangeably transformed [CGHJ12], so we can refer to the generated model as state-space or VARMA model with sparse GC pattern.…”

Section: Generating Eeg Datamentioning

confidence: 99%

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Manomaisaowapak

Nartkulpat

Songsiri

2022

IEEE Trans. Neural Netw. Learning Syst.

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“…We use standard form of the Kalman filter here, instead of (8) which has a single noise term , as these representations are generally equivalent (see Casals et al (1999Casals et al ( , 2012).…”

Section: State Space Model For Kf1 Kf1 * and Kf4mentioning

confidence: 99%

“…Remark. In Casals et al (2012), it was shown that it can be possible to find a matrix T (see the referenced paper for the corresponding algorithm) for the conversion between two state space forms ( 9) and (8), i.e. : Ã = T −1 AT , B = T −1 B.…”

Section: State Space Model For Kf1 Kf1 * and Kf4mentioning

confidence: 99%

Data-driven modeling of beam loss in the LHC

Krymova¹,

Obozinski²,

Coyle³

et al. 2022

Preprint

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In the Large Hadron Collider, the beam losses are continuously measured for machine protection. By design, most of the particle losses occur in the collimation system, where the particles with high oscillation amplitudes or large momentum error are scraped from the beams. The level of particle losses typically is optimized manually by changing multiple control parameters, among which are, for example, currents in the focusing and defocusing magnets along the collider. It is generally challenging to model and predict losses based on the control parameters due to various (non-linear) effects in the system, such as electron clouds, resonance effects, etc, and multiple sources of uncertainty. At the same time understanding the influence of control parameters on the losses is extremely important in order to improve the operation and performance, and future design of accelerators. Existing results showed that it is hard to generalize the models Coyle (2018), which assume the regression model of losses depending on control parameters, from fills carried out throughout one year to the data of another year. To circumvent this, we propose to use an autoregressive modeling approach, where we take into account not only the observed control parameters but also previous loss values. We use an equivalent Kalman Filter (KF) formulation in order to efficiently estimate models with different lags. The results on the data from 2017 show that the proposed modeling significantly improves the prediction quality for the year 2018 and successfully identifies both local and global trends in the losses.

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“…The state space model in (2) and (3) can be written as an observationally equivalent vector ARMA model, see, e.g., Shumway and Stoffer (1982) and Casals et al (2012). For the present case, define first the characteristic polynomial to (1),…”

Section: Equivalent Arma Parametrizationmentioning

confidence: 99%

“…The additional MA parameters (B 1 , , B k , ) are found from ( , , 1 , , k−1 , H * , G) by matching the variance structure of (7) and (8), see Casals et al (2012) for an explicit algorithm. For a model with k = 1, i.e., A(z) = I p − A 1 z with A 1 = ( + I p ), this amounts to solving…”

Section: Equivalent Arma Parametrizationmentioning

confidence: 99%

The Co-Integrated Vector Autoregression with Errors–in–Variables

Nielsen

2014

Econometric Reviews

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The co-integrated vector autoregression is extended to allow variables to be observed with classical measurement errors (ME). For estimation, the model is parametrized as a time invariant state-space form, and an accelerated expectation-maximization algorithm is derived. A simulation study shows that (i) the finite-sample properties of the maximum likelihood (ML) estimates and reduced rank test statistics are excellent (ii) neglected measurement errors will generally distort unit root inference due to a moving average component in the residuals, and (iii) the moving average component may-in principlebe approximated by a long autoregression, but a pure autoregression cannot identify the autoregressive structure of the latent process, and the adjustment coefficients are estimated with a substantial asymptotic bias. An application to the zero-coupon yield-curve is given.

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From general state-space to VARMAX models

Cited by 13 publications

References 13 publications

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Granger Causality Inference in EEG Source Connectivity Analysis: A State-Space Approach

Data-driven modeling of beam loss in the LHC

The Co-Integrated Vector Autoregression with Errors–in–Variables

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