Vector ARMA estimation: a reliable subspace approach

Mari, J.; Stoica, Petre; McKelvey, Tomas

doi:10.1109/78.847793

Cited by 55 publications

(77 citation statements)

References 37 publications

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“…Conservatism on the proposed stability constraint. With the additional ∞-norm constraint in the problem (13), we note that the minimized objective function will increase relatively to the objective of the unconstrained problem (4) or to the GC-constrained problem (8). In other words, to guarantee the stability and reveal a Granger causality, we trade off with the model accuracy.…”

Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

“…Neither the unconstrained LS estimation in (4) nor the GC-constrained LS estimation in (8) guarantees that the estimated model is stable. It was addressed in [8] that obtaining unstable estimated models may occur if some of the eigenvalues of the true model are too close to the unit circle.…”

Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

“…It was addressed in [8] that obtaining unstable estimated models may occur if some of the eigenvalues of the true model are too close to the unit circle. If the unstable estimated model is further used in time series prediction, spectrum analysis, or other purposes that require the stationarity of the AR model, this would lead to a meaningless interpretation.…”

Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

“…We refer to (8) as the GC-constrained LS formulation and it is regarded as a simple quadratic problem with linear constraints. Its closed-form solution can be efficiently computed and shown in [15].…”

Section: Wald Test For Granger Causalitymentioning

confidence: 99%

“…By estimating the system parameters with conditions from the Jury's array which formulated as bilinear terms in [6], the system is guaranteed to have a bounded input bounded output (BIBO) stability; however, this approach cannot be readily applied to (1) as it is a multi-input multi-output (MIMO) system. From [7,8], the Lyapunov's theory is applied to a vector autoregressive moving average (ARMA) model. The model parameters are estimated to be closest to the unconstrained estimate subject to the Lyapunov equation by using a change of variable and adjusting a weight matrix in the cost objective by P , the matrix variable in the Lyapunov equation.…”

Section: Introductionmentioning

confidence: 99%

See 4 more Smart Citations

Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests

Raksasri¹,

Songsiri²

2017

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Abstract. This paper aims to explain relationships between time series by using the Granger causality (GC) concept through autoregressive (AR) models and to assure the model stability. Examining such GC relationship is performed on the model parameters using the Wald test and the model stability is guaranteed by the infinity-norm constraint on the dynamic matrix of the AR process. The proposed formulation is a least-squares estimation with Granger causality and stability constraints which is a convex program with a quadratic objective subject to linear equality and inequality norm constraints. We show by simulations that various typical factors could lead to unstable estimated models when using an unconstrained method. Estimated models from our approach are guaranteed to be stable but the model fitting error could be conservatively increased due to the selected stability condition.

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Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

Section: Model Estimation With Stability Constraintsmentioning

confidence: 99%

Section: Wald Test For Granger Causalitymentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests

Raksasri¹,

Songsiri²

2017

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Trends in systems and signals

Katayama

McKelvey

Sano

et al. 2006

Annual Reviews in Control

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Disturbance-adaptive stochastic optimal control of energy harvesters, with application to ocean wave energy conversion

Scruggs¹,

Nie²

2015

Annual Reviews in Control

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This paper proposes a technique for optimizing the power generated from stationary stochastic vibratory disturbances, using a resonant energy harvester.Although the theory is general, the target application of the paper concerns ocean wave energy harvesting. The control technique involves the use of a causal discrete-time feedback algorithm to dynamically optimize the power extracted from the waves. The theory assumes that the input impedance of the converter is known precisely, but that a priori models are unavailable for the characterization of the stochastic behavior of the incident waves as well as the transfer functions characterizing their hydrodynamic excitation of the system.For these assumptions, we develop an adaptive control technique, which adapts the feedback law at each time step based on updated estimates for the stochastic disturbance model, obtained through a subspace-based system identification algorithm. The technique is demonstrated on a simulation example pertaining to a cylindrical surface-floating wave energy converter in heave.

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Vector ARMA estimation: a reliable subspace approach

Cited by 55 publications

References 37 publications

Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests

Guaranteed Stability of Autoregressive Models with Granger Causality Learned from Wald Tests

Trends in systems and signals

Disturbance-adaptive stochastic optimal control of energy harvesters, with application to ocean wave energy conversion

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