Showing papers on "STAR model published in 2012"
TL;DR: In this article, the authors introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series, which can be applied to time series with non-linear dependences.
Abstract: We introduce graphical time series models for the analysis of dynamic relationships among variables in multivariate time series. The modelling approach is based on the notion of strong Granger causality and can be applied to time series with non-linear dependences. The models are derived from ordinary time series models by imposing constraints that are encoded by mixed graphs. In these graphs each component series is represented by a single vertex and directed edges indicate possible Granger-causal relationships between variables while undirected edges are used to map the contemporaneous dependence structure. We introduce various notions of Granger-causal Markov properties and discuss the relationships among them and to other Markov properties that can be applied in this context. Examples for graphical time series models include nonlinear autoregressive models and multivariate ARCH models.
154 citations
TL;DR: It is shown that the fitted MS-AR models are interpretable and provide a good description of important properties of the data such as the marginal distributions, the second-order structure or the length of the stormy and calm periods.
Abstract: In this paper, non-homogeneous Markov-Switching Autoregressive (MS-AR) models are proposed to describe wind time series. In these models, several autoregressive models are used to describe the time evolution of the wind speed and the switching between these different models is controlled by a hidden Markov chain which represents the weather types. We first block the data by month in order to remove seasonal components and propose a MS-AR model with non-homogeneous autoregressive models to describe daily components. Then we discuss extensions where the hidden Markov chain is also non-stationary to handle seasonal and interannual fluctuations. The different models are fitted using the EM algorithm to a long time series of wind speed measurement on the Island of Ouessant (France). It is shown that the fitted models are interpretable and provide a good description of important properties of the data such as the marginal distributions, the second-order structure or the length of the stormy and calm periods.
135 citations
TL;DR: It is shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill, compared against persistence and autoregressive models.
Abstract: Wind power production data at temporal resolutions of a few minutes exhibit successive periods with fluctuations of various dynamic nature and magnitude, which cannot be explained (so far) by the evolution of some explanatory variable. Our proposal is to capture this regime-switching behaviour with an approach relying on Markov-switching autoregressive (MSAR) models. An appropriate parameterization of the model coefficients is introduced, along with an adaptive estimation method allowing accommodation of long-term variations in the process characteristics. The objective criterion to be recursively optimized is based on penalized maximum likelihood, with exponential forgetting of past observations. MSAR models are then employed for one-step-ahead point forecasting of 10 min resolution time series of wind power at two large offshore wind farms. They are favourably compared against persistence and autoregressive models. It is finally shown that the main interest of MSAR models lies in their ability to generate interval/density forecasts of significantly higher skill. Copyright © 2010 John Wiley & Sons, Ltd.
135 citations
TL;DR: In this article, a Bayesian graphical VAR (BGVAR) model is proposed to identify the causal structures of the structural VAR model, which is shown to be quite effective in dealing with model identification and selection in multivariate time series of moderate dimension.
Abstract: This paper proposes a Bayesian, graph-based approach to identification in vector autoregressive (VAR) models. In our Bayesian graphical VAR (BGVAR) model, the contemporaneous and temporal causal structures of the structural VAR model are represented by two different graphs. We also provide an efficient Markov chain Monte Carlo algorithm to estimate jointly the two causal structures and the parameters of the reduced-form VAR model. The BGVAR approach is shown to be quite effective in dealing with model identification and selection in multivariate time series of moderate dimension, as those considered in the economic literature. In the macroeconomic application the BGVAR identifies the relevant structural relationships among 20 US economic variables, thus providing a useful tool for policy analysis. The financial application contributes to the recent econometric literature on financial interconnectedness. The BGVAR approach provides evidence of a strong unidirectional linkage from financial to non-financial super-sectors during the 2007-2009 financial crisis and a strong bidirectional linkage between the two sectors during the 2010-2013 European sovereign debt crisis.
129 citations
TL;DR: The generalized linear models' framework provides convenient tools for implementing model fitting and prediction using standard software and provides a natural extension to the traditional ARMA methodology.
Abstract: We review regression models for count time series. We discuss the approach that is based on generalized linear models and the class of integer autoregressive processes. The generalized linear models' framework provides convenient tools for implementing model fitting and prediction using standard software. Furthermore, this approach provides a natural extension to the traditional ARMA methodology. Several models have been developed along these lines, but conditions for stationarity and valid asymptotic inference were given in the literature only recently. We review several of these facts. In addition, we consider integer autoregressive models for count time series and discuss estimation and possible extensions based on real data applications.
93 citations
TL;DR: Empirical results with three well-known real data sets indicate that the proposed model can be an effective way in order to construct a more accurate hybrid model than ARIMA model, and can be used as an appropriate alternative model for forecasting tasks, especially when higher forecasting accuracy is needed.
82 citations
TL;DR: In this article, the authors apply a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure.
Abstract: SUMMARY
This paper applies a general trans-dimensional Bayesian inference methodology and hierarchical autoregressive data-error models to the inversion of microtremor array dispersion data for shear wave velocity (vs) structure. This approach accounts for the limited knowledge of the optimal earth model parametrization (e.g. the number of layers in the vs profile) and of the data-error statistics in the resulting vs parameter uncertainty estimates. The assumed earth model parametrization influences estimates of parameter values and uncertainties due to different parametrizations leading to different ranges of data predictions. The support of the data for a particular model is often non-unique and several parametrizations may be supported. A trans-dimensional formulation accounts for this non-uniqueness by including a model-indexing parameter as an unknown so that groups of models (identified by the indexing parameter) are considered in the results. The earth model is parametrized in terms of a partition model with interfaces given over a depth-range of interest. In this work, the number of interfaces (layers) in the partition model represents the trans-dimensional model indexing.
In addition, serial data-error correlations are addressed by augmenting the geophysical forward model with a hierarchical autoregressive error model that can account for a wide range of error processes with a small number of parameters. Hence, the limited knowledge about the true statistical distribution of data errors is also accounted for in the earth model parameter estimates, resulting in more realistic uncertainties and parameter values. Hierarchical autoregressive error models do not rely on point estimates of the model vector to estimate data-error statistics, and have no requirement for computing the inverse or determinant of a data-error covariance matrix. This approach is particularly useful for trans-dimensional inverse problems, as point estimates may not be representative of the state space that spans multiple subspaces of different dimensionalities. The order of the autoregressive process required to fit the data is determined here by posterior residual-sample examination and statistical tests.
Inference for earth model parameters is carried out on the trans-dimensional posterior probability distribution by considering ensembles of parameter vectors. In particular, vs uncertainty estimates are obtained by marginalizing the trans-dimensional posterior distribution in terms of vs-profile marginal distributions. The methodology is applied to microtremor array dispersion data collected at two sites with significantly different geology in British Columbia, Canada. At both sites, results show excellent agreement with estimates from invasive measurements.
81 citations
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TL;DR: In particular, the tests developed by Phillips and Perron as discussed by the authors seem more sensitive to model misspecification that the high-order autoregressive approximation suggested by Said and Dickey (1984, 1985, and 1986).
Abstract: Recent work by Said and Dickey (1984, 1985), Phillips (1987), and Phillips and Perron (1988) examines tests for unit roots in the autoregressive part of mixed autoregressive integrated moving average models (tests for stationarity). Monte Carlo experiments show that these unit-root tests have different finite-sample distributions from the unit-root tests developed by Fuller (1976) and Dickey and Fuller (1979, 1981) for autoregressive processes. In particular, the tests developed by Phillips (1987) and Phillips and Perron (in press) seem more sensitive to model misspecification that the high-order autoregressive approximation suggested by Said and Dickey (1984).
75 citations
TL;DR: A model-based approach for forecasting regime shifts and identifying alternative stable states overcomes limitations of other common metric-based approaches and is a useful addition to the toolbox of methods for analyzing nonlinear time series.
Abstract: Interest is growing in methods for predicting and detecting regime shifts—changes in the structure of dynamical processes that cause shifts among alternative stable states. Here, we use locally linear, autoregressive state-space models to statistically identify nonlinear processes that govern the dynamics of time series. We develop both time-varying and threshold models. In time-varying autoregressive models with p time lags, AR(p), and vector autoregressive models for n-dimensional systems of order p = 1, VAR(1), we assume that coefficients vary with time. We can infer an approaching regime shift if the coefficients indicate critical slowing down of the local dynamics of the system. In self-excited threshold models, we assume that the time series is governed by two autoregressive processes; the state variable switches between them when the time series crosses a threshold value. We use the existence of a statistically significant threshold as an indicator of alternative stable states. All models are fit to data using a state-space form that incorporates measurement error, and maximum likelihood estimation allows for statistically testing alternative hypotheses about the processes governing dynamics. Our model-based approach for forecasting regime shifts and identifying alternative stable states overcomes limitations of other common metric-based approaches and is a useful addition to the toolbox of methods for analyzing nonlinear time series.
63 citations
TL;DR: It is argued that the developed theory forms a necessary basis for modelling and application of these count time series and is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models.
Abstract: In this paper an overview is given over recent theoretical developments in autoregressive count time series. The focus is on generalized autoregressive models where the autoregressive structure is incorporated via a link function. Starting from an ordinary autoregressive model the difficulties in extending standard theory of statistical inference to count time series are highlighted. Special attention is given to the issues of ergodicity and asymptotic theory of estimation. Two main approaches are mentioned, a perturbation approach and the use of a weak dependence concept. The main emphasis is on the former. Linear as well as log-linear and nonlinear models are treated. It is argued that the developed theory forms a necessary basis for modelling and application of these count time series. The setting of the paper is one of simple models and conditional distributions of Poisson type. But it is claimed that the framework is general enough to handle many extensions with an accompanying flexibility in applications of these models.
47 citations
TL;DR: In this paper, a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables is introduced and parameter estimation is also addressed.
Abstract: In this article, we introduce a class of self-exciting threshold integer-valued autoregressive models driven by independent Poisson-distributed random variables. Basic probabilistic and statistical properties of this class of models are discussed. Moreover, parameter estimation is also addressed. Specifically, the methods of estimation under analysis are the least squares-type and likelihood-based ones. Their performance is compared through a simulation study.
TL;DR: In this article, several simple estimation methods for vector autoregressive moving-average models are compared among each other and with pure vector auto-regressive modeling using ordinary least squares by means of a Monte Carlo study.
Abstract: Recently, there has been a renewed interest in modeling economic time series by vector autoregressive moving-average models. However, this class of models has been unpopular in practice because of estimation problems and the complexity of the identification stage. These disadvantages could have led to the dominant use of vector autoregressive models in macroeconomic research. In this article, several simple estimation methods for vector autoregressive moving-average models are compared among each other and with pure vector autoregressive modeling using ordinary least squares by means of a Monte Carlo study. Different evaluation criteria are used to judge the relative performances of the algorithms.
01 Jan 2012
TL;DR: The forecasting capability of the RBF-AR model is compared to those of other competing time series models, which shows that the RBFs model is as good as or better than other models for the postsample forecasts.
Abstract: Varying-coefficient models have attracted great attention in nonlinear time series analysis recently. In this paper, we consider a semi-parametric functional-coefficient autoregressive model, called the radial basis function network-based state-dependent autoregressive (RBF-AR) model. The stability conditions and existing conditions of limit cycle of the RBF-AR model are discussed. An efficient structured parameter estimation method and the modified multi-fold cross-validation criterion are applied to identify the RBF-AR model. Application of the RBF-AR model to the famous Canadian lynx data is presented. The forecasting capability of the RBF-AR model is compared to those of other competing time series models, which shows that the RBF-AR model is as good as or better than other models for the postsample forecasts.
TL;DR: In this paper, a stationary integer-valued autoregressive process with negative binomial marginals is considered and a set of estimators are considered and their asymptotic distributions are derived.
Abstract: The authors consider a stationary integer-valued autoregressive process of the first order with negative binomial marginals (NBINAR(1)). A set of estimators are considered and their asymptotic distributions are derived. Some numerical results of the estimates are presented. Also, the authors discuss a possible application of the process.
TL;DR: The empirical log-likelihood ratio statistics are proposed and the nonparametric versions of the Wilk’s theorem are obtained and derive a test statistic to test the stationary–ergodicity based on the conditional least-squares method.
TL;DR: It is shown theoretically that the dependence structure for the spillovers and disturbances can differ and that estimates from a simple separable model show little bias in all the scenarios.
Abstract: The single spatial parameter in the spatial autoregressive model affects both the estimation of spillovers and the estimation of spatial disturbances. Consequently, the spatial autoregressive model has the undesirable property that if the degree of spatial dependence in the disturbances differs from that in the spillovers, neither may be estimated correctly. We show theoretically that the dependence structure for the spillovers and disturbances can differ and conduct a Monte Carlo experiment that verifies these findings. In contrast, estimates from a simple separable model show little bias in all the scenarios. We also show differences between the spatial autoregressive model and the separable model on five empirical examples.
TL;DR: New practical criteria to assess the predictability of regimes and the predictive skill of such coarse-grained approximations through empirical information theory in stationary and periodically-forced environments are tested.
TL;DR: A new automatic procedure to the model selection problem by using the genetic algorithm, where the Bayesian information criterion is used as a tool to identify the order of the PAR model.
Abstract: Periodic autoregressive (PAR) models extend the classical autoregressive models by allowing the parameters tovary with seasons. Selecting PAR time-series models can be computationally expensive, and the results are notalways satisfactory. In this article, we propose a new automatic procedure to the model selection problem by usingthe genetic algorithm. The Bayesian information criterion is used as a tool to identify the order of the PAR model.The success of the proposed procedure is illustrated in a small simulation study, and an application with monthlydata is presented.Keywords: Periodic time series; identification; genetic algorithms; parameter constraints; BIC.
TL;DR: In this article, a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias was compared.
Abstract: The aim of this study was to compare the small sample (N = 1, 3, 5, 10, 15) performance of a Bayesian multivariate vector autoregressive (BVAR-SEM) time series model relative to frequentist power and parameter estimation bias. A multivariate autoregressive model was developed based on correlated autoregressive time series vectors of varying lengths (T = 25, 50, 75, 100, 125) using Statistical Analysis System (SAS) version 9.2. Autoregressive components for the 5 series vectors included coefficients of .80, .70, .65, .50 and .40. Error variance components included values of .20, .20, .10, .15, and .15, with cross-lagged coefficients of .10, .10, .15, .10, and .10. A Monte Carlo study revealed that in comparison to frequentist methods, the Bayesian approach provided increased sensitivity for hypothesis testing and detecting Type I error.
TL;DR: In the empirical study on the range data of an Australian stock market index, the CARGPR model outperforms the CARR model in both in-sample estimation and out-of-sample forecast.
TL;DR: It is shown that AIC and its variants are asymptotically efficient in integrated autoregressive processes of infinite order (AR(~).
TL;DR: It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition and the least-squares algorithm to estimate the unknown parameter vectors.
Abstract: This paper studies least-squares parameter estimation algorithms for input nonlinear systems, including the input nonlinear controlled autoregressive (IN-CAR) model and the input nonlinear controlled autoregressive autoregressive moving average (IN-CARARMA) model. The basic idea is to obtain linear-in-parameters models by overparameterizing such nonlinear systems and to use the least-squares algorithm to estimate the unknown parameter vectors. It is proved that the parameter estimates consistently converge to their true values under the persistent excitation condition. A simulation example is provided.
01 Jan 2012
TL;DR: In this article, a further development of Creal, Koopman, and Lucas (2012) which is based on the score function of the predictive model density at time t is discussed.
Abstract: To capture the dynamic behavior of univariate and multivariate time series processes, we can allow parameters to be time-varying by having them as functions of lagged dependent variables as well as exogenous variables. Although other approaches of introducing time dependence exists, the GAS models, Generalized Autoregressive Score, particular approach have become popular in applied statistics and econometrics. Here we discuss a further development of Creal, Koopman, and Lucas (2012) which is based on the score function of the predictive model density at time t.
TL;DR: This correspondence presents a new second-order statistical approach to blind identification of single-input multiple-output (SIMO) autoregressive and moving average (ARMA) system models that exploits the dynamical autore progressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block Toeplitz structure of the channel convolution matrix used by classical subspace methods.
Abstract: This correspondence presents a new second-order statistical approach to blind identification of single-input multiple-output (SIMO) autoregressive and moving average (ARMA) system models. The proposed approach exploits the dynamical autoregressive information of the model contained in the autocorrelation matrices of the system outputs but does not require the block Toeplitz structure of the channel convolution matrix used by classical subspace methods. For the multi-channel model with the same autoregressive (AR) polynomial, sufficient conditions and an efficient identification algorithm are given such that the multi-channel model can be uniquely identified up to a constant scaling factor. Furthermore, an extension of the result to blind identification of multi-channel models with different AR polynomials is presented. Simulation results are given to show the effectiveness of the proposed approach.
TL;DR: A genetic algorithm for identifying and estimating nonlinear nonstationary models for time series, where the series is generated from an autoregressive equation whose coefficients change both according to time and the delayed values of the series itself, switching between several regimes.
Abstract: Nonlinear nonstationary models for time series are considered, where the series is generated from an autoregressive equation whose coefficients change both according to time and the delayed values of the series itself, switching between several regimes. The transition from one regime to the next one may be discontinuous (self-exciting threshold model), smooth (smooth transition model) or continuous linear (piecewise linear threshold model). A genetic algorithm for identifying and estimating such models is proposed, and its behavior is evaluated through a simulation study and application to temperature data and a financial index.
TL;DR: In this paper, a hybrid model of autoregressive moving average (ARMA) and generalized ARIA (CARIA) is proposed to forecast wind speed, where the conditional variance of an observation depends linearly on the conditional variances of the previous observations and on the previous prediction errors.
Abstract: SUMMARY
In this paper, a hybrid model of autoregressive moving average and generalized autoregressive conditional heteroscedasticity is proposed to forecast wind speed. In this model, the conditional variance of an observation depends linearly on the conditional variance of the previous observations and on the previous prediction errors. This conditional variance can capture the feature that the predictability of meteorological variables is not constant but shows regular variations. The quasi-maximum likelihood estimator was used to estimate parameters of the proposed model. An improved particle swarm optimization was proposed to solve the solution of the autoregressive moving average/generalized autoregressive conditional heteroscedasticity model through the log-quasi-likelihood function. Four different indices are introduced to demonstrate the performance of the proposed model. Generated results of different season sample sets were compared with their corresponding values when using the autoregressive moving average model. The simulation results validate the effectiveness, accuracy, and superiority of the proposed model for wind speed prediction. Copyright © 2011 John Wiley & Sons, Ltd.
TL;DR: In this paper, the authors investigated the dynamics of credit default swap (CDS) spread by employing detrended cross-correlation analysis (DCCA) and employed smooth transition autoregressive (STAR) models to characterize the regime switching behavior of 28 US corporate CDS series.
Abstract: This paper investigates the dynamics of credit default swap (CDS) spread. We first find auto-correlations and cross-correlations of the CDS series and the CDS average by employing detrended cross-correlation analysis (DCCA). We then employ smooth transition autoregressive (STAR) models to characterize the regime switching behavior of 28 US corporate CDS series from January 2007 through October 2009. In each case, we find clear evidence for transitions between low-price and high-price regimes. The threshold estimations of the STAR model effectively differentiate the price regimes, where the first transition consistently coincides with the explosion of the crisis in late 2008.
01 Dec 2012
TL;DR: STAR specifications that parallel geostatistical model specifications commonly used to describe space–time variation are summarized, with the goal of establishing synergies between these two modeling approaches.
Abstract: Many geospatial science subdisciplines analyze variables that vary over both space and time. The space–time autoregressive (STAR) model is one specification formulated to describe such data. This paper summarizes STAR specifications that parallel geostatistical model specifications commonly used to describe space–time variation, with the goal of establishing synergies between these two modeling approaches. Resulting expressions for space–time correlograms derived from 1st-order STAR models are solved numerically, and then linked to appropriate space–time semivariogram models.
TL;DR: This study reports a statistical analysis of monthly sunspot number time series and observes nonhomogeneity and asymmetry within it, using the Mann-Kendall test a linear trend is revealed.
Abstract: This study reports a statistical analysis of monthly sunspot number time series and observes nonhomogeneity and asymmetry within it. Using the Mann-Kendall test a linear trend is revealed. After identifying stationarity within the time series we generate autoregressive AR(p) and autoregressive moving average (ARMA(p, q) . Based on the minimization of AIC we find 3 and 1 as the best values for p and q , respectively. In the next phase, autoregressive neural network (AR-NN(3)) is generated by training a generalized feedforward neural network (GFNN). Assessing the model performances by means of Willmott’s index of second order and the coefficient of determination, the performance of AR-NN(3) is identified to be better than AR(3) and ARMA(3,1).
TL;DR: A state space form of the autoregressive linear mixed effects model is proposed to calculate the marginal likelihood without using large matrices so that the regression coefficients of the fixed effects can be concentrated out of the likelihood in this model.
Abstract: The assessment of the dose-response relationship is important but not straightforward when the therapeutic agent is administered repeatedly with dose-modification in each patient and a continuous response is measured repeatedly. We recently proposed an autoregressive linear mixed effects model for such data in which the current response is regressed on the previous response, fixed effects, and random effects. The model represents profiles approaching each patient's asymptote, takes into account the past dose history, and provides a dose-response relationship of the asymptote as a summary measure. In an autoregressive model, intermittent missing data mean the missing values in previous responses as covariates. We previously provided the marginal (unconditional on the previous response) form of the proposed model to deal with intermittent missing data. Irregular timings of dose-modification or measurement can also be treated as equally spaced data with intermittent missing values by selecting an adequately small unit of time. The likelihood is, however, expressed by matrices whose sizes depend on the number of observations for a patient, and the computational burden is large. In this study, we propose a state space form of the autoregressive linear mixed effects model to calculate the marginal likelihood without using large matrices. The regression coefficients of the fixed effects can be concentrated out of the likelihood in this model by the same way of a linear mixed effects model. As an illustration of the approach, we analyzed immunologic data from a clinical trial for multiple sclerosis patients and estimated the dose-response curves for each patient and the population mean.