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35
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 100 (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 43 (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 28 (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.
Some Observations On Turkish Inflation: A “Random Walk” Down the Past Decade
 Unpublished; Istanbul: Bogazici University) Atiyas, Izak, and Hasan Ersel (1994), “The Impact of Financial Reform: the Turkish Experience”, in Financial Reform: Theory and Experience, edited by
, 1998
"... Reducing inflation has become a key polic issue in Turkey. We study shortterm dynamics of Turkish inflation to contribute to a better understanding of this important problem. We provide a broadbrushed review of issues related to high and chronic inflation, offer some observations on the Turkish in ..."
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Cited by 20 (0 self)
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Reducing inflation has become a key polic issue in Turkey. We study shortterm dynamics of Turkish inflation to contribute to a better understanding of this important problem. We provide a broadbrushed review of issues related to high and chronic inflation, offer some observations on the Turkish inflation, and discuss the implications of all these on disinflation. It is hard to contest that inflation is a fiscal problem in Turkey. Nevertheless, there are some additional issues that are worth thinking about, namely that, inflation seems largely inertial, has some characteristics typical of high and chronic inflation processes elsewhere, and there are reasons to believe that the economy might have been stuck in a high inflation equilibrium largely resulting from a host of coordination problems rather than economic fundamentals, per se. One implication of all these for a disinflation program is that overall costs of disinflation might be less severe than one might think.
Lag length estimation in large dimensional systems. Universidad Carlos III de
, 1996
"... We study the impact of the system dimension on commonly used model selection criteria (AIC,BIC, HQ) and LR based general to specic testing strategies for lag length estimation in VAR's. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away f ..."
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Cited by 11 (1 self)
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We study the impact of the system dimension on commonly used model selection criteria (AIC,BIC, HQ) and LR based general to specic testing strategies for lag length estimation in VAR's. We show that AIC's well known overparameterization feature becomes quickly irrelevant as we move away from univariate models, with the criterion leading to consistent estimates under suÆciently large system dimensions. Unless the sample size is unrealistically small, all model selection criteria will tend to point towards low orders as the system dimension increases, with the AIC remaining by far the best performing criterion. This latter point is also illustrated via the use of an analytical power function for model selection criteria. The comparison between the model selection and general to specic testing strategy is discussed within the context of a new penalty term leading to the same choice of lag length under both approaches.
A new method for analyzing sequential processes: Dynamic multilevel analysis
 Small Group Research
, 2005
"... The online version of this article can be found at: ..."
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Cited by 10 (2 self)
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The online version of this article can be found at:
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 7 (2 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.
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 5 (3 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.
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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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).