Evaluation and Comparison of EEG Traces: Latent Structure in Nonstationary Time Series

West, Mike; Prado, Raquel; Krystal, Andrew D.

doi:10.1080/01621459.1999.10474128

Cited by 32 publications

(38 citation statements)

References 21 publications

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“…with p t ¼ an integer, gives rise to a host of time series models that subsumes many earlier models. For example, for p t Ñ Òºt ½ p» one obtains the ADº p» models; for p t p the class of time-varying parameter autoregressive (TVAR) models of Kitagawa & Gersch (1985) and West, Prado & Krystal (1999) are obtained. Finally, (11) for arbitrary p t reduces to the variable-order antedependence models (Macchiavelli & Arnold, 1994), and for p t p and t t j j it reduces to the standard ARº p» models.…”

Section: Antedependence and Time-varying Modelsmentioning

confidence: 99%

Graphical Diagnostics for Modeling Unstructured Covariance Matrices

Pourahmadi¹

2002

Int Statistical Rev

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Prudent statistical analysis of correlated data requires accounting for the correlation among the measurements. Specifying a form for the covariance matrix of the data could reduce the high number of parameters of the covariance and increase efficiency of the inferences about the regression parameters. Motivated by the success of ordinary, partial and inverse correlograms in identifying parsimonious models for stationary time series, we introduce generalizations of these plots for nonstationary data. Their roles in detecting heterogeneity and correlation of the data and identifying parsimonious models for the covariance matrix are illuminated using a longitudinal dataset. Decomposition of a covariance matrix into "variance" and "dependence" components provides the necessary ingredients for the proposed graphs. This amounts to replacing a 3-D correlation plot by a pair of 2-D plots, providing complementary information about dependence and heterogeneity. Models identified and fitted using the variance-correlation decomposition of a covariance matrix are not guaranteed to be positive definite, but those using the modified Cholesky decomposition are. Limitations of our graphical diagnostics for general multivariate data where the measurements are not (time-) ordered are discussed.

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Section: Antedependence and Time-varying Modelsmentioning

confidence: 99%

Graphical Diagnostics for Modeling Unstructured Covariance Matrices

Pourahmadi¹

2002

Int Statistical Rev

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“…The decompositions depend on factorizations of the characteristic polynomial of the state evolution matrix G into relatively prime factors. This generalizes the method of West (1997) which considers one decomposition in the particular case where G is diagonalizable. Conditions are derived for a decomposition to be independent.…”

mentioning

confidence: 93%

“…These results show that no autoregressive process of order d has an independent decomposition for any integer d. Two illustrations of this procedure are discussed in detail.where, for a suitable integer d, h t is a d Â 1 state vector, F is a d Â 1 vector of known terms and the d Â d state evolution matrix G is known; m t and the d Â 1 state evolution noise vector x t are assumed to be mutually independent and the evolution noise variance matrix E½x t x 0 t ¼ W . West and Harrison (1997) propose that the trend terms are included in the state vector h t so that the model (1.2) is essentially derived from (1.1). However, this proposal is indeterminate in the sense that several nontrivially different trend specifications can result in exactly the same model (1.2).…”

mentioning

confidence: 99%

“…Furthermore, Pierce (1979), Hillmer andTiao (1982) and Pole et al (1994, §3.6) focus attention on decompositions of time series whose component terms are mutually independent; however, it sometimes happens that the irreducible decomposition does not possess this property even though other independent decompositions exist.The purpose of this paper is to derive the admissible decompositions for a TSDLM, provided only that the model is observable, and to specify conditions for a decomposition to be independent. The approach is more general but formally simpler than that of West (1997). It is shown that not all eigenvalues of G need to be found and the use of time series models with complex-valued parameters is avoided.…”

mentioning

confidence: 99%

“…The purpose of this paper is to derive the admissible decompositions for a TSDLM, provided only that the model is observable, and to specify conditions for a decomposition to be independent. The approach is more general but formally simpler than that of West (1997). It is shown that not all eigenvalues of G need to be found and the use of time series models with complex-valued parameters is avoided.…”

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confidence: 99%

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Decomposition of Time Series Dynamic Linear Models

Odolphin

Johnson

2003

Journal Time Series Analysis

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This paper derives the admissible decompositions for a time series dynamic linear model, assuming only that the model is observable. The decompositions depend on factorizations of the characteristic polynomial of the state evolution matrix G into relatively prime factors. This generalizes the method of West (1997) which considers one decomposition in the particular case where G is diagonalizable. Conditions are derived for a decomposition to be independent. These results show that no autoregressive process of order d has an independent decomposition for any integer d. Two illustrations of this procedure are discussed in detail.where, for a suitable integer d, h t is a d Â 1 state vector, F is a d Â 1 vector of known terms and the d Â d state evolution matrix G is known; m t and the d Â 1 state evolution noise vector x t are assumed to be mutually independent and the evolution noise variance matrix E½x t x 0 t ¼ W . West and Harrison (1997) propose that the trend terms are included in the state vector h t so that the model (1.2) is essentially derived from (1.1). However, this proposal is indeterminate in the sense that several nontrivially different trend specifications can result in exactly the same model (1.2). This raises the questions of how many decompositions (1.1) are admissible for a given TSDLM with specified F and G and which of these decompositions can be regarded as useful and meaningful.West (1997) identifies a restricted class of TSDLMs in which each model is expressed as a linear combination of AR or ARMA models of a low order. Huerta andWest (1999a, 1999b) use this result in a Bayesian analysis of AR(d) models, where d is large, and West et al. (1999) describe an interesting application in the field of clinical neurophysiology. This approach realizes only the one decomposition (referred to here as the irreducible decomposition) and the argument depends on the existence of interim AR models which have complex-valued parameters. It is also required that the d eigenvalues of the state evolution matrix are distinct; however, there are economic and several other applications where G has at least one eigenvalue which is repeated several times. For example, if a TSDLM includes a polynomial trend then G has a repeated eigenvalue unity whose multiplicity is one more than the polynomial degree (Godolphin and Harrison, 1975). The TSDLM representations of the forward-shifted models of Box and Jenkins (1976, §5.3) require G to have repeated eigenvalue zero, as shown by Johnson (1999) who generalizes a result of Godolphin and Stone (1980). Models with polynomial trends or forward-shifted components or indeed any components resulting from a repeated eigenvalue structure are not decomposable by West's method. Furthermore, Pierce (1979), Hillmer andTiao (1982) and Pole et al. (1994, §3.6) focus attention on decompositions of time series whose component terms are mutually independent; however, it sometimes happens that the irreducible decomposition does not possess this property even though other independent deco...

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EEG effects of ECT: Implications for rTMS

et al. 2000

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Electroconvulsive therapy (ECT) involves the use of electrical stimulation to elicit a series of generalized tonic–clonic seizures for therapeutic purposes and is the most effective treatment known for major depression. These treatments have significant neurophysiologic effects, many of which are manifest in the electroencephalogram (EEG). The relationship between EEG data and the response to ECT has been studied since the 1940s, but for many years no consistent correlates were found. Recent studies indicate that a number of specific EEG features recorded during the induced seizures (ictal EEG) as well as before and after a course of treatment (interictal EEG) are related to both the therapeutic efficacy and cognitive side effects. Similar to ECT, repetitive transcranial magnetic stimulation (rTMS), which involves focal electromagnetic stimulation of cortical neurons, has also been studied as an antidepressant therapy and also appears to have neurophysiologic effects, although these have not been as fully investigated as is the case with ECT. Given the similarity of these treatments, it is natural to consider whether advances in understanding the electrophysiologic correlates of the ECT response might have implications for rTMS. The present article reviews the literature on the EEG effects of ECT and discusses the implications in terms of the likely efficacy and side effects associated with rTMS in specific anatomic locations, the potential for producing an antidepressant response with rTMS without eliciting seizure activity, eliciting focal seizures with rTMS, and the possibility of using rTMS to focally modulate seizure induction and spread with ECT to optimize treatment. Depression and Anxiety 12:157–165, 2000. © 2000 Wiley‐Liss, Inc.

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Evaluation and Comparison of EEG Traces: Latent Structure in Nonstationary Time Series

Cited by 32 publications

References 21 publications

Graphical Diagnostics for Modeling Unstructured Covariance Matrices

Graphical Diagnostics for Modeling Unstructured Covariance Matrices

Decomposition of Time Series Dynamic Linear Models

EEG effects of ECT: Implications for rTMS

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