Showing papers on "STAR model published in 2008"
TL;DR: In this article, the authors introduce the class of integer-valued autoregressive (INAR) Poisson models for the time series analysis of traffic accidents in Great Britain and show that the performance of these two classes of models is quite similar in terms of coefficient estimates and goodness of fit for the case of aggregated time series traffic accident data.
207 citations
TL;DR: The statistical properties of the autoregressive distance between ARIMA processes are investigated and the asymptotic distribution of the squared AR distance and an approximation which is computationally efficient are derived.
203 citations
TL;DR: In this paper, a multiple regime smooth transition extension of the Heterogeneous Autoregressive (HAR) model is proposed to model the behavior of the volatility inherent in financial time series.
147 citations
TL;DR: The results demonstrate that the approaches are useful in forecasting alternatives for interval-valued time series and indicate that the hybrid model is an effective way to improve the forecasting accuracy achieved by any one of the models separately.
130 citations
TL;DR: In this article, change in any of these over time is a sign of disturbance that is important to detect and can be used to test for a temporary change, and the test statistics are based on the efficient score vector.
99 citations
TL;DR: The generalized autoregressive score model (GAS) as discussed by the authors is a new class of observation driven time series models, which allows for a wide range of new observation driven models such as multivariate point process models with time-varying parameters.
Abstract: We propose a new class of observation driven time series models that we refer to as generalized autoregressive score models. The driving mechanism of the model is the scaled score of the likelihood function. This approach provides a unified, consistent framework for the introduction of time-varying parameters in a wide class of non-linear models. The autoregressive score model class encompasses well-known models such as the generalized autoregressive conditional heteroskedasticity, the autoregressive conditional duration and the time-varying Poisson count models. In addition, it allows for a wide range of new observation driven models. Notable and new examples include multivariate point process models with time-varying parameters and pooling restrictions, models for time-varying copula functions and observation driven mixture models. We develop the dynamic model specifications in detail and provide several illustrations of their application.
87 citations
05 Jul 2008
TL;DR: This approach points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients, and proposes an estimation method shown to be consistent.
Abstract: Causal analysis of continuous-valued variables typically uses either autoregressive models or linear Gaussian Bayesian networks with instantaneous effects. Estimation of Gaussian Bayesian networks poses serious identifiability problems, which is why it was recently proposed to use non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. We show that such a non-Gaussian model is identifiable without prior knowledge of network structure, and we propose an estimation method shown to be consistent. This approach also points out how neglecting instantaneous effects can lead to completely wrong estimates of the autoregressive coefficients.
81 citations
TL;DR: In this paper, a logistic smooth transition and Markov switching autoregressive model of the monthly US unemployment rate are estimated by Markov chain Monte Carlo methods. But both models provide very similar descriptions, Bayes factors and predictive efficiency tests (both Bayesian and classical) favor the smooth transition model.
Abstract: Logistic smooth transition and Markov switching autoregressive models of a logistic transform of the monthly US unemployment rate are estimated by Markov chain Monte Carlo methods. The Markov switching model is identified by constraining the first autoregression coefficient to differ across regimes. The transition variable in the LSTAR model is the lagged seasonal difference of the unemployment rate. Out-of-sample forecasts are obtained from Bayesian predictive densities. Although both models provide very similar descriptions, Bayes factors and predictive efficiency tests (both Bayesian and classical) favor the smooth transition model. Copyright © 2008 John Wiley & Sons, Ltd.
76 citations
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TL;DR: In this paper, a generalized two-stages least squares estimator for the regression parameters of the model was proposed, and the moment conditions and the optimal weighting matrix for a generalized moments (GM) estimation procedure of the spatial regressive parameters were derived.
Abstract: This paper generalizes the approach to estimating a first-order spatial autoregressive model with spatial autoregressive disturbances (SARAR(1,1)) in a cross-section with heteroskedastic innovations by Kelejian and Prucha (2008) to the case of spatial autoregressive models with spatial autoregressive disturbances of arbitrary (finite) order (SARAR(R,S)). We derive the moment conditions and the optimal weighting matrix for a generalized moments (GM) estimation procedure of the spatial regressive parameters of the disturbance process and define a generalized two-stages least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their (joint) asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.
75 citations
01 Jul 2008
TL;DR: In this paper, a new process called integer-valued autoregressive process of order p with signed binomial thinning (INARS(p)) is introduced to handle a non-stationary integervalued time series with a large dispersion.
Abstract: It is frequent to encounter a time series of counts which are small in value and show a trend having relatively large fluctuation. To handle such a non-stationary integer-valued time series with a large dispersion, we introduce a new process called integer-valued autoregressive process of order p with signed binomial thinning (INARS(p)). This INARS(p) uniquely exists and is stationary under the same stationary condition as in the AR(p) process. We provide the properties of the INARS(p) as well as the asymptotic normality of the estimates of the model parameters. This new process includes previous integer-valued autoregressive processes as special cases. To preserve integer-valued nature of the INARS(p) and to avoid difficulty in deriving the distributional properties of the forecasts, we propose a bootstrap approach for deriving forecasts and confidence intervals. We apply the INARS(p) to the frequency of new patients diagnosed with acquired immunodeficiency syndrome (AIDS) in Baltimore, Maryland, U.S. during the period of 108 months from January 1993 to December 2001.
74 citations
TL;DR: In this article, the authors study an autoregressive time series model with a possible change in the regression parameters and obtain approximate estimates to the critical values for change-point tests through various bootstrapping methods.
TL;DR: In this paper, the authors give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes.
Abstract: We analyze vector autoregressive processes using the matrix valued characteristic polynomial. The purpose of this article is to give a survey of the mathematical results on inversion of a matrix polynomial in case there are unstable roots, to study integrated and cointegrated processes. The new results are in the I(2) representation, which contains explicit formulas for the first two terms and a useful property of the third. We define a new error correction model for fractional processes and derive a representation of the solution.
TL;DR: In this article, the authors compared the short-term load performance of several forecasting models, including a new class of nonlinear models known as smooth transition periodic autoregressive (STPAR) models.
TL;DR: In this article, the authors established strong consistency and asymptotic normality of the least squares estimator in generalized space-time autoregressive (STAR) models under minimal conditions on the sequence of innovations.
Abstract: Space-time autoregressive (STAR) models, introduced by Cliff and Ord [Spatial autocorrelation (1973) Pioneer, London] are successfully applied in many areas of science, particularly when there is prior information about spatial dependence. These models have significantly fewer parameters than vector autoregressive models, where all information about spatial and time dependence is deduced from the data. A more flexible class of models, generalized STAR models, has been introduced in Borovkovaet al. [Proc. 17th Int. Workshop Stat. Model. (2002), Chania, Greece] where the model parameters are allowed to vary per location. This paper establishes strong consistency and asymptotic normality of the least squares estimator in generalized STAR models. These results are obtained under minimal conditions on the sequence of innovations, which are assumed to form a martingale difference array. We investigate the quality of the normal approximation for finite samples by means of a numerical simulation study, and apply a generalized STAR model to a multivariate time series of monthly tea production in west Java, Indonesia. © 2008 VVS.
15 Sep 2008
TL;DR: In this article, it was discovered that the average size of volatility is not constant but changes with time and is predictable, which is a key parameter used in many financial applications, from derivatives valuation to asset management and risk management Volatility measures the size of the errors made in modeling returns and other financial variables.
Abstract: Volatility is a key parameter used in many financial applications, from derivatives valuation to asset management and risk management Volatility measures the size of the errors made in modeling returns and other financial variables It was discovered that, for vast classes of models, the average size of volatility is not constant but changes with time and is predictable Autoregressive conditional heteroskedasticity (ARCH), generalized autoregressive conditional heteroskedasticity (GARCH) models and stochastic volatility models are the main tools used to model and forecast volatility Moving from single assets to portfolios made of multiple assets, we find that not only idiosyncratic volatilities but also correlations and covariances between assets are time varying and predictable Multivariate ARCH/GARCH models and dynamic factor models, eventually in a Bayesian framework, are the basic tools used to forecast correlations and covariances
Keywords:
autoregressive conditional duration;
ACD-GARCH;
autoregressive conditional heteroskedasticity (ARCH);
autoregressive models;
conditional autoregressive value at risk (CAViaR);
dynamic factor models;
generalized autoregressive conditional heteroskedasticity (GARCH);
exponential GARCH (EGARCH);
F-GARCH;
GARCH-M;
heteroskedasticity;
high-frequency data;
homoskedasticity;
integrated GARCH (IGARCH);
MGARCH;
threshold ARCH (TARCH);
temporal aggregation;
ultra-high-frequency data;
value at risk (VaR);
VEC;
volatility
TL;DR: In this paper, an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors was developed, where a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoreskasticity (GARCH(1,1)) model was considered.
Abstract: This paper develops an asymptotic estimation theory for nonlinear autoregressive models with conditionally heteroskedastic errors. We consider a functional coefficient autoregression of order p (AR(p)) with the conditional variance specified as a general nonlinear first order generalized autoregressive conditional heteroskedasticity (GARCH(1,1)) model. Strong consistency and asymptotic normality of the global Gaussian quasi maximum likelihood (QML) estimator are established under conditions comparable to those recently used in the corresponding linear case. To the best of our knowledge, this paper provides the first results on consistency and asymptotic normality of the QML estimator in nonlinear autoregressive models with GARCH errors.
TL;DR: A functional autoregressive model is used as a robust predictor of the cash flow and intensity of transactions in a credit card payment systems and two linear wavelet methods are compared for the prediction problem of a continuous-time stochastic process on an entire time interval.
SIDI1
TL;DR: New method based on wavelet decomposition combined with autoregressive models to analyse time series is exposed, essentially applied for the prediction of time series among approximation and modelisation.
01 Aug 2008
TL;DR: This work proposes to estimate the vector autoregressive model by using a multivariate least trimmed squares estimator, and shows how the order of the autore progressive model can be determined in a robust way.
Abstract: The vector autoregressive model is very popular for modeling multiple time series Estimation of its parameters is typically done by a least squares procedure However, this estimation method is unreliable when outliers are present in the data, and therefore we propose to estimate the vector autoregressive model by using a multivariate least trimmed squares estimator We also show how the order of the autoregressive model can be determined in a robust way The robust procedure is illustrated on a real data set
TL;DR: It is shown that the integration of autoregressive (simplex) structures and latent trajectories rests on the strong assumption that neither the AR part nor the LGC part contains any misspecification, but in practice this assumption is often violated, rendering any substantive interpretation of parameter estimates virtually impossible.
Abstract: The simultaneous estimation of autoregressive (simplex) structures and latent trajectories, so called ALT (autoregressive latent trajectory) models, is becoming an increasingly popular approach to the analysis of change. Although historically autoregressive (AR) and latent growth curve (LGC) models have been developed quite independently from each other, the underlying pattern of change is often highly similar. In this article it is shown that their integration rests on the strong assumption that neither the AR part nor the LGC part contains any misspecification. In practice, however, this assumption is often violated due to nonlinearity in the LGC part. As a consequence, the autoregressive (simplex) process incorrectly accounts for part of this nonlinearity, thus rendering any substantive interpretation of parameter estimates virtually impossible. Accordingly, researchers are advised to exercise extreme caution when using ALT models in practice. All arguments are illustrated by empirical data on skill ac...
TL;DR: This paper attempts to carry over intuitions from the estimation procedure of smooth transition autoregressive (STAR) models by introducing the following three stochastic optimization algorithms: Simulated Annealing, Threshold Accepting, and Differential Evolution.
Abstract: It has been shown in the literature that the task of estimating the parameters of nonlinear models may be tackled with optimization heuristics Thus, we attempt to carry these intuitions over to the estimation procedure of smooth transition autoregressive (STAR, Terasvirta, 1994) models by introducing the following three stochastic optimization algorithms: Simulated Annealing, (Kirkpatrick, Gelatt, and Vecchi, 1983), Threshold Accepting (Dueck and Scheuer, 1990) and Differential Evolution (Storn and Price, 1995, 1997) Besides considering the performance of these heuristics in estimating STAR model parameters, our paper additionally picks up the problem of identifying redundant parameters which, according to our view, has not been addressed in a satisfactory way by now The resulting findings of our simulation studies seem to argue for an implementation of heuristic approaches within the STAR modeling cycle In particular for the case of STAR model specification, an application of these heuristics might offer valuable information to empirical researchers
TL;DR: An infinite mixture of autoregressive models is developed, one main feature of which is the generalization of a finite mixture model by having the number of components unspecified.
TL;DR: The FitAR R (R Development Core Team 2008) package that is available on the Comprehensive R Archive Network is described and a new improved extended {BIC} criterion, {UBIC}, developed by Chen and Chen (2008) is implemented for subset model selection.
Abstract: The FitAR R (R Development Core Team 2008) package that is available on the Comprehensive R Archive Network is described. This package provides a comprehensive approach to fitting autoregressive and subset autoregressive time series. For long time series with complicated autocorrelation behavior, such as the monthly sunspot numbers, subset autoregression may prove more feasible and/or parsimonious than using AR or ARMA models. The two principal functions in this package are SelectModel and FitAR for automatic model selection and model fitting respectively. In addition to the regular autoregressive model and the usual subset autoregressive models (Tong 1977), these functions implement a new family of models. This new family of subset autoregressive models is obtained by using the partial autocorrelations as parameters and then selecting a subset of these parameters. Further properties and results for these models are discussed in McLeod and Zhang (2006). The advantages of this approach are that not only is an efficient algorithm for exact maximum likelihood implemented but that efficient methods are derived for selecting high-order subset models that may occur in massive datasets containing long time series. A new improved extended {BIC} criterion, {UBIC}, developed by Chen and Chen (2008) is implemented for subset model selection. A complete suite of model building functions for each of the three types of autoregressive models described above are included in the package. The package includes functions for time series plots, diagnostic testing and plotting, bootstrapping, simulation, forecasting, Box-Cox analysis, spectral density estimation and other useful time series procedures. As well as methods for standard generic functions including print, plot, predict and others, some new generic functions and methods are supplied that make it easier to work with the output from FitAR for bootstrapping, simulation, spectral density estimation and Box-Cox analysis.
TL;DR: In this paper, an extension of the Autoregressive Conditional Duration (ACD) model was proposed by adopting a mixture of distribution approach with time-varying weights, and the model lends itself to some structural interpretation related to price formation and information diffusion in the market.
Abstract: Financial market price formation and exchange activity can be investigated by means of ultra-high frequency data. In this article, we investigate an extension of the Autoregressive Conditional Duration (ACD) model of Engle and Russell (1998) by adopting a mixture of distribution approach with time-varying weights. Empirical estimation of the Mixture ACD model shows that the limitations of the standard base model and its inadequacy of modelling the behavior in the tail of the distribution are suitably solved by our model. When the weights are made dependent on some market activity data, the model lends itself to some structural interpretation related to price formation and information diffusion in the market.
TL;DR: In this article, a parameter constancy test of a stationary vector autoregressive model against the hypothesis that the parameters of the model change smoothly over time is proposed, and a single structural break is contained in this alternative hypothesis as a special case.
Abstract: In this article we derive a parameter constancy test of a stationary vector autoregressive model against the hypothesis that the parameters of the model change smoothly over time. A single structural break is contained in this alternative hypothesis as a special case. The test is a generalization of a single-equation test of a similar hypothesis proposed in the literature. An advantage here is that the asymptotic distribution theory is standard. The performance of the tests is compared to that of generalized Chow-tests and found satisfactory in terms of both size and power.
TL;DR: In this paper, a first-order observation-driven integer-valued autoregressive model is introduced and the performance of the model is compared to a real data set via simulation.
TL;DR: A model composed of AR* and GRNN is proposed to take advantage of their feathers in linear and nonlinear modeling and provides an effective way to improve forecasting performance which can be achieved by either of the models used separately.
Abstract: AR* models contain Autoregressive Moving Average and Generalized Autoregressive Conditional Heteroscedastic class model which are widely used in time series. Recent researches in forecasting with Generalized Regression Neural Network (GRNN) suggest that GRNN can be a promising alternative to the linear and nonlinear time series models. In this paper, a model composed of AR* and GRNN is proposed to take advantage of their feathers in linear and nonlinear modeling. In the AR*-GRNN model, AR* modeling improves the forecasting performance of the combined model by capturing statistical and volatility information from the time series. The relative experiments testify that the combined model provides an effective way to improve forecasting performance which can be achieved by either of the models used separately.
TL;DR: In this article, a new algorithm for the identification of AR plus noise models that is characterized by a very good compromise between accuracy and efficiency is presented, taking advantage of both low and high-order Yule-Walker equations, also guarantees the positive definiteness of the autocorrelation matrix of the estimated process and allows to estimate the equation error and observation noise variance.
Abstract: A common approach in modeling signals in many engineering applications consists in adopting autoregressive (AR) models, consisting in filters with transfer functions having a unitary numerator, driven by white noise. Despite their wide application, these models do not take into account the possible presence of errors on the observations and cannot prove accurate when these errors are significant. AR plus noise models constitute an extension of AR models that consider also the presence of an observation noise. This paper describes a new algorithm for the identification of AR plus noise models that is characterized by a very good compromise between accuracy and efficiency. This algorithm, taking advantage of both low and high-order Yule–Walker equations, also guarantees the positive definiteness of the autocorrelation matrix of the estimated process and allows to estimate the equation error and observation noise variances. It is also shown how the proposed procedure can be used for estimating the order of the AR model. The new algorithm is compared with some traditional algorithms by means of Monte Carlo simulations. Copyright © 2007 John Wiley & Sons, Ltd.
TL;DR: This paper used tests developed from time-varying smooth transition autoregressive (TV-STAR) models to re-examine dollar-based rates and found that structural change is an important feature of the data.
TL;DR: In this article, the forecasting performance of Bayesian autoregressive and vector auto-regression models can be improved by incorporating prior beliefs on the steady state of the time series.
Abstract: This paper investigates whether the forecasting performance of Bayesian autoregressive and vector autoregressive models can be improved by incorporating prior beliefs on the steady state of the tim ...