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13
Estimation of Parameters and Eigenmodes of Multivariate Autoregressive Models
, 2001
"... Dynamical characteristics of a complex system can often be inferred from analyses of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregre ..."
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Cited by 71 (2 self)
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Dynamical characteristics of a complex system can often be inferred from analyses of a stochastic time series model fitted to observations of the system. Oscillations in geophysical systems, for example, are sometimes characterized by principal oscillation patterns, eigenmodes of estimated autoregressive (AR) models of first order. This paper describes the estimation of eigenmodes of AR models of arbitrary order. AR processes of any order can be decomposed into eigenmodes with characteristic oscillation periods, damping times, and excitations. Estimated eigenmodes and confidence intervals for the eigenmodes and their oscillation periods and damping times can be computed from estimated model parameters. As a computationally efficient method of estimating the parameters of AR models from highdimensional data, a stepwise least squares algorithm is proposed. This algorithm computes model coefficients and evaluates criteria for the selection of the model order stepwise for AR models of successively decreasing order. Numerical simulations indicate that, with the least squares algorithm, the AR model coefficients and the eigenmodes derived from the coefficients are estimated reliably and that the approximate 95% confidence intervals for the coefficients and eigenmodes are rough approximations of the confidence intervals inferred from the simulations.
Algorithm 808: ARfit  A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models
 ACM TOMS
, 2001
"... ARfit is a collection of Matlab modules for modeling and analyzing multivariate time series with autoregressive (AR) models. ARfit contains modules for fitting AR models to given time series data, for analyzing eigenmodes of a fitted model, and for simulating AR processes. ARfit estimates the parame ..."
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Cited by 31 (2 self)
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ARfit is a collection of Matlab modules for modeling and analyzing multivariate time series with autoregressive (AR) models. ARfit contains modules for fitting AR models to given time series data, for analyzing eigenmodes of a fitted model, and for simulating AR processes. ARfit estimates the parameters of AR models from given time series data with a stepwise least squares algorithm that is computationally efficient, in particular when the data are highdimensional. ARfit modules construct approximate confidence intervals for the estimated parameters and compute statistics with which the adequacy of a fitted model can be assessed. Dynamical characteristics of the modeled time series can be examined by means of a decomposition of a fitted AR model into eigenmodes and associated oscillation periods, damping times, and excitations. The ARfit module that performs the eigendecomposition of a fitted model also constructs approximate confidence intervals for the eigenmodes and their oscillation periods and damping times.
A conceptual framework for predictability studies
 J. Climate
, 1999
"... A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate tra ..."
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Cited by 12 (0 self)
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A conceptual framework is presented for a unified treatment of issues arising in a variety of predictability studies. The predictive power (PP), a predictability measure based on information–theoretical principles, lies at the center of this framework. The PP is invariant under linear coordinate transformations and applies to multivariate predictions irrespective of assumptions about the probability distribution of prediction errors. For univariate Gaussian predictions, the PP reduces to conventional predictability measures that are based upon the ratio of the rms error of a model prediction over the rms error of the climatological mean prediction. Since climatic variability on intraseasonal to interdecadal timescales follows an approximately Gaussian distribution, the emphasis of this paper is on multivariate Gaussian random variables. Predictable and unpredictable components of multivariate Gaussian systems can be distinguished by predictable component analysis, a procedure derived from discriminant analysis: seeking components with large PP leads to an eigenvalue problem, whose solution yields uncorrelated components that are ordered by PP from largest to smallest. In a discussion of the application of the PP and the predictable component analysis in different types of predictability studies, studies are considered that use either ensemble integrations of numerical models or autoregressive models fitted to observed or simulated data. An investigation of simulated multidecadal variability of the North Atlantic illustrates the proposed methodology. Reanalyzing an ensemble of integrations of the Geophysical Fluid Dynamics Laboratory coupled general circulation model confirms and refines earlier findings. With an autoregressive model fitted to a single integration of the same model, it is demonstrated that similar conclusions can be reached without resorting to computationally costly ensemble integrations. 1.
Generalizing The Derivation Of The Schwarz Information Criterion
, 1999
"... The Schwarz information criterion (SIC, BIC, SBC) is one of the most widely known and used tools in statistical model selection. The criterion was derived by Schwarz (1978) to serve as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. Althoug ..."
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Cited by 4 (1 self)
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The Schwarz information criterion (SIC, BIC, SBC) is one of the most widely known and used tools in statistical model selection. The criterion was derived by Schwarz (1978) to serve as an asymptotic approximation to a transformation of the Bayesian posterior probability of a candidate model. Although the original derivation assumes that the observed data is independent, identically distributed, and arising from a probability distribution in the regular exponential family, SIC has traditionally been used in a much larger scope of model selection problems. To better justify the widespread applicability of SIC, we derive the criterion in a very general framework: one which does not assume any specific form for the likelihood function, but only requires that it satisfies certain nonrestrictive regularity conditions.
Hidden Markov multivariate autoregressive (HMMmAR)modeling of dynamic muscle association patterns in reaching movements
 in Proc. 29th Can. Med. Biolog. Soc. Conf. (CMBES29
, 2006
"... Abstract—As the primary noninvasive means to assess muscle activation, the surface electromyogram (sEMG) is of central importance for the study of motor behavior in both clinical and biomedical applications. However, multivariate sEMG analysis is complicated by the fact that data recorded during dyn ..."
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Cited by 3 (2 self)
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Abstract—As the primary noninvasive means to assess muscle activation, the surface electromyogram (sEMG) is of central importance for the study of motor behavior in both clinical and biomedical applications. However, multivariate sEMG analysis is complicated by the fact that data recorded during dynamic contractions are inherently nonstationary. To model this nonstationarity and to determine the dynamic muscle activity patterns during reaching movements, we propose combining hidden Markov models (HMMs) and multivariate autoregressive (mAR) models into a joint HMMmAR framework. We further propose constructing muscle networks statistically by performing a second level, group analysis on the subjectspecific models. Network structural features are subsequently investigated as input features for the purpose of classification. The proposed approach was applied to real sEMG recordings collected from healthy and stroke subjects during reaching movements. When examining group muscle networks, we note that specific muscle connection patterns were selectively recruited during reaching movements and were differentially recruited after stroke compared to healthy subjects. As the analysis was performed on the raw data, the amplitude and the underlying “carrier data ” of sEMG signals, we notice that the HMMmAR model fits the amplitude data well, but not the raw or carrier data. The proposed sEMG analysis framework represents a fundamental departure from existing methods where only the amplitude is typically analyzed or the mAR coefficients are directly used for classification. As the method may provide additional insights into motor control, it appears a promising approach warranting further study. Index Terms—Classification tree, expectation maximization (EM) algorithm, hidden Markov model (HMM), multivariate autoregressive (mAR) model, stroke, surface electromyography (sEMG).
Model selection, estimation and forecasting in VAR models with shortrun and longrun restrictions
 Journal of Econometrics
"... We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of shortrun parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have datadependent penalties for a lack o ..."
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Cited by 3 (2 self)
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We study the joint determination of the lag length, the dimension of the cointegrating space and the rank of the matrix of shortrun parameters of a vector autoregressive (VAR) model using model selection criteria. We consider model selection criteria which have datadependent penalties for a lack of parsimony, as well as the traditional ones. We suggest a new procedure which is a hybrid of traditional criteria and criteria with datadependant penalties. In order to compute the fit of each model, we propose an iterative procedure to compute the maximum likelihood estimates of parameters of a VAR model with shortrun and longrun restrictions. Our Monte Carlo simulations measure the improvements in forecasting accuracy that can arise from the joint determination of laglength and rank, relative to the commonly used procedure of selecting the laglength only and then testing for cointegration.
Some Pretesting Issues on . . .
, 1999
"... We compare testing strategies for Granger noncausality in vector autoregressions (VARs) that may or may not have unit roots and cointegration. Sequential testing methods are examined; these test for cointegration and use either a differenced VAR or a vector error correction model (VECM), in which to ..."
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We compare testing strategies for Granger noncausality in vector autoregressions (VARs) that may or may not have unit roots and cointegration. Sequential testing methods are examined; these test for cointegration and use either a differenced VAR or a vector error correction model (VECM), in which to undertake the main noncausality test. Basically, the pretesting strategies attempt to verify the validity of appropriate standard limit theory. These methods are contrasted with an augmented lag approach that ensures the limiting P 2 null distribution irrespective of the data’s nonstationarity characteristics. Our simulations involve bivariate and trivariate VARs in which we allow for the lag order to be selected by general to specific testing as well as by model selection criteria. We find that the current practice of pretesting for cointegration can result in severe overrejections of the noncausal null while overfitting suffers less size distortion with often little loss in power.
HORIZON MATTERS Author Contact:
, 2005
"... The extensive body of research that examines for (Granger, 1969) causality from exports to output for developing countries, including Bangladesh and Sri Lanka, using vector autoregressions and/or vector error correction models, is limited in only examining for oneperiod ahead or direct causality; t ..."
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The extensive body of research that examines for (Granger, 1969) causality from exports to output for developing countries, including Bangladesh and Sri Lanka, using vector autoregressions and/or vector error correction models, is limited in only examining for oneperiod ahead or direct causality; the exception is in bivariate systems. This (usually unrecognized) focus on oneperiod causality in multivariate systems has often led to conclusions that exports do not Grangercause economic output. We show that moving to Grangercausality at longer horizons, in a commonly used multivariate system, leads to bidirectional causality between exports and output, even when there is not oneperiod causality; the longer horizon causality arises indirectly through one or more of the auxiliary variables.
Working Paper 15/05Forecasting Accuracy and Estimation Uncertainty using VAR Models with Short and LongTerm Economic Restrictions: A MonteCarlo Study
, 2005
"... Using vector autoregressive (VAR) models and MonteCarlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The …rst reduces parameter space by imposing longterm restriction ..."
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Using vector autoregressive (VAR) models and MonteCarlo simulation methods we investigate the potential gains for forecasting accuracy and estimation uncertainty of two commonly used restrictions arising from economic relationships. The …rst reduces parameter space by imposing longterm restrictions on the behavior of economic variables as discussed by the literature on cointegration, and the second reduces parameter space by imposing shortterm restrictions as discussed by the literature on Acknowledgments: Parts os this paper were writen while Osmani T. Guillén and João Victor Issler were visiting Monash University, which hospitality is gratefully acknowledged. João Victor Issler and George Athanasopulos also acknowledge the hospitality of the Australian National University, where parts of this paper were writen. We gratefully acknowledge comments and suggestions given by Alain Hecq, Luiz Renato Lima, and of the participants of the conferences Common Features in London and Encontro Brasileiro de Econometria. Special thanks are due to Farshid Vahid for some of the ideas in this paper and his encouragement and support to Osmani T. Guillén during his visit to Monash University and to George Athanasopoulos. The usual disclaimers apply. João Victor Issler and Osmani T. Guillén acknowledge, respectively, the support of CNPqBrazil, PRONEX, and CAPES fellowship BEX0934/020.