Showing papers on "STAR model published in 2005"
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TL;DR: In medical investigations, it is not uncommon to record observations on two or more time series, such as blood pressure and weight, and the individual time series may be analyzed by methods appropriate for univariate series, but this article concentrates on methods of analysis that help in understanding the system that gives rise to the data.
Abstract: In medical investigations, it is not uncommon to record observations on two or more time series For example, blood pressure and weight may be regularly monitored on a sample of patients The individual time series may be analyzed by methods appropriate for univariate series, but this article concentrates on methods of analysis that help in understanding the system that gives rise to the data
Keywords:
time series;
fast Fourier transformation;
autoregressive moving average;
vector models
289 citations
TL;DR: The authors examined the forecast accuracy of linear autoregressive, smooth transition auto-regression (STAR), and neural network (NN) time series models for 47 macroeconomic variables of the G7 economies.
277 citations
TL;DR: In this article, the authors show that combining many models for forecasting gives better estimates than single time series models, and that the combined forecast can underperform significantly compared to its constituents' performances.
179 citations
TL;DR: In this paper, the authors proposed an econometric model with this structure, where the distribution of each price change is a multinomial, conditional on past information and the time interval between the transactions.
Abstract: Financial transaction prices typically lie on a discrete grid of values and arrive at random times. This paper proposes an econometric model with this structure. The distribution of each price change is a multinomial, conditional on past information and the time interval between the transactions. The proposed autoregressive conditional multinomial (ACM) model is not restricted to be Markov or symmetric in response to shocks; however, such restrictions can be imposed. The duration between trades is modeled as an autoregressive conditional duration (ACD) model following Engle and Russell (1998). Maximum likelihood estimation and testing procedures are developed. The model is estimated with 12 months of tick data on a moderately frequently traded NYSE stock, Airgas. The preferred model is estimated, with three lags for the ACM model and two lags for the ACD model. Both price returns and squared returns influence future durations and present and past durations affect price movements. The model exhibits revers...
144 citations
TL;DR: In this article, a multi-level smooth transition model for a panel of time series is introduced, which can be used to examine the presence of common nonlinear business cycle features across many variables.
Abstract: We introduce a multi-level smooth transition model for a panel of time series, which can be used to examine the presence of common nonlinear business cycle features across many variables. The model is positioned in between a fully pooled model, which imposes such common features, and a fully heterogeneous model, which allows for unrestricted nonlinearity. We introduce a second-stage model linking the parameters that determine the timing of the switches between business cycle regimes to observable explanatory variables, thereby allowing for lead–lag relationships across panel members. We discuss representation, estimation by concentrated simulated maximum likelihood and inference. We illustrate our model using quarterly industrial production in 19 US manufacturing sectors, and document that there are subtle differences across sectors in leads and lags for switches between business cycle recessions and expansions. Copyright © 2005 John Wiley & Sons, Ltd.
135 citations
TL;DR: In this article, an ARMA-GARCH error model is proposed to capture the ARCH effect present in daily streamflow series, as well as to preserve seasonal variation in variance in the residuals.
Abstract: Conventional streamflow models operate under the assumption of constant variance or season-dependent variances (e.g. ARMA (AutoRegressive Moving Average) models for deseasonalized streamflow series and PARMA (Periodic AutoRegressive Moving Average) models for seasonal streamflow series). However, with McLeod-Li test and Engle's Lagrange Multiplier test, clear evidences are found for the existence of autoregressive conditional heteroskedasticity (i.e. the ARCH (AutoRegressive Conditional Heteroskedasticity) effect), a nonlinear phenomenon of the variance behaviour, in the residual series from linear models fitted to daily and monthly streamflow processes of the upper Yellow River, China. It is shown that the major cause of the ARCH effect is the seasonal variation in variance of the residual series. However, while the seasonal variation in variance can fully explain the ARCH effect for monthly streamflow, it is only a partial explanation for daily flow. It is also shown that while the periodic autoregressive moving average model is adequate in modelling monthly flows, no model is adequate in modelling daily streamflow processes because none of the conventional time series models takes the seasonal variation in variance, as well as the ARCH effect in the residuals, into account. Therefore, an ARMA-GARCH (Generalized AutoRegressive Conditional Heteroskedasticity) error model is proposed to capture the ARCH effect present in daily streamflow series, as well as to preserve seasonal variation in variance in the residuals. The ARMA-GARCH error model combines an ARMA model for modelling the mean behaviour and a GARCH model for modelling the variance behaviour of the residuals from the ARMA model. Since the GARCH model is not followed widely in statistical hydrology, the work can be a useful addition in terms of statistical modelling of daily streamflow processes for the hydrological community.
111 citations
TL;DR: In this paper, the authors introduce a class of autoregressive gamma processes with conditional distributions from the family of noncentered gamma (up to a scale factor) and provide the stationarity and ergodicity conditions for ARG processes of any order p, including long memory, and closed-form expressions of conditional moments.
Abstract: We introduce a class of autoregressive gamma processes with conditional distributions from the family of noncentered gamma (up to a scale factor). The paper provides the stationarity and ergodicity conditions for ARG processes of any autoregressive order p, including long memory, and closed-form expressions of conditional moments. The nonlinear state space representation of an ARG process is used to derive the filtering, smoothing and forecasting algorithms. The paper also presents estimation and inference methods, illustrated by an application to interquote durations data on an infrequently traded stock listed on the Toronto Stock Exchange (TSX).
98 citations
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TL;DR: In this article, the authors established unified sufficient conditions for geometric ergodicity of autoregressive models and showed that there is a close relationship between geometric erodicity and mixing properties.
Abstract: In this paper we attempt to establish unified sufficient conditions for geometric ergodicity of autoregressive models. It is shown that there is a close relationship between geometric ergodicity and mixing properties. The case of nonstationary time series is incorporated into the investigations. Several time series models including threshold and EXPARCH-models are examined with respect to geometric ergodicity. In some cases we obtain regions of geometric ergodicity in the parameter space, which are larger than that known from the literature.
84 citations
01 Apr 2005
TL;DR: In this article, the performance of moment-based estimators, regression-and least square estimators and likelihood-based estimation methods for a Poisson marginal model using backcasting is investigated.
Abstract: We consider estimation in the class of first order conditional linear autoregressive models with discrete support that are routinely used to model time series of counts. Various groups of estimators proposed in the literature are discussed: moment-based estimators; regression-based estimators; and likelihood-based estimators. Some of these have been used previously and others not. In particular, we address the performance of new types of generalized method of moments estimators and propose an exact maximum likelihood procedure valid for a Poisson marginal model using backcasting. The small sample properties of all estimators are comprehensively analyzed using simulation. Three situations are considered using data generated with: a fixed autoregressive parameter and equidispersed Poisson innovations; negative binomial innovations; and, additionally, a random autoregressive coefficient. The first set of experiments indicates that bias correction methods, not hitherto used in this context to our knowledge, are some-times needed and that likelihood-based estimators, as might be expected, perform well. The second two scenarios are representative of overdispersion. Methods designed specifically for the Poisson context now perform uniformly badly, but simple, bias-corrected, Yule-Walker and least squares estimators perform well in all cases.
77 citations
TL;DR: If the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, this formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models.
Abstract: We consider a flexible smooth transition autoregressive (STAR) model with multiple regimes and multiple transition variables. This formulation can be interpreted as a time varying linear model where the coefficients are the outputs of a single hidden layer feedforward neural network. This proposal has the major advantage of nesting several nonlinear models, such as, the self-exciting threshold autoregressive (SETAR), the autoregressive neural network (AR-NN), and the logistic STAR models. Furthermore, if the neural network is interpreted as a nonparametric universal approximation to any Borel measurable function, our formulation is directly comparable to the functional coefficient autoregressive (FAR) and the single-index coefficient regression models. A model building procedure is developed based on statistical inference arguments. A Monte Carlo experiment showed that the procedure works in small samples, and its performance improves, as it should, in medium size samples. Several real examples are also addressed.
75 citations
TL;DR: In this article, the authors studied analogies of Granger's representation theorem in the context of a general nonlinear vector autoregressive error correction model and developed a useful transformation which shows how the NER model can be transformed to a nonlinear VAR model so that available results on the stationarity or nonstationarity of the latter can be used for the former.
TL;DR: In this article, the stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes and an adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions.
Abstract: This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong to appropriate smoothness classes. An adequate normalization for the correction term used in the recursive estimation procedure allows for very mild assumptions on the innovations distributions. The rate of convergence of the pointwise estimates is shown to be minimax in β-Lipschitz classes for 0 < β ≤ 1. For 1 < β ≤ 2, this property no longer holds. This can be seen by using an asymptotic expansion of the estimation error. A bias reduction method is then proposed for recovering the minimax rate.
TL;DR: In this article, it was shown that when the autoregressive parameter p is invariant over time and lies between - 1 and 1, it can be shown that these models are algebraically equivalent.
Abstract: Curran and Bollen combined two models for longitudinal panel data: the latent growth curve model and the autoregressive model. In their model, the autoregressive relationships are modeled between the observed variables. This is a different model than a latent growth curve model with autoregressive relationships between the disturbances. However when the autoregressive parameter p is invariant over time and lies between - 1 and 1, it can be shown that these models are algebraically equivalent. This result can be shown to generalize to the multivariate case. When the autoregressive parameters in the autoregressive latent trajectory model vary over time, the equivalence between the autoregressive latent trajectory model and a latent growth curve model with autoregressive disturbances no longer holds. However, a latent growth curve model with time-varying autoregressive parameters for the disturbances could be considered an interesting alternative to the autoregressive latent trajectory model with time-varying autoregressive parameters.
TL;DR: The switching autoregressive model outperformed the linear predictive model in a digit recognition task and provided comparable performance to a cepstral-based recognizer.
Abstract: Linear predictive hidden Markov modeling is compared with a simple form of the switching autoregressive process. The latter process captures existing signal correlation during transitions of the Markov chain. Parameter estimation is described using naturally stable forward-backward recursions. The switching autoregressive model outperformed the linear predictive model in a digit recognition task and provided comparable performance to a cepstral-based recognizer.
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TL;DR: In this article, a model-based method is proposed for detecting the presence of additive or innovational outliers when the series is generated by a general nonlinear model, which is applied for detecting outliers in the Canadian lynx trappings and in the sunspot numbers data.
Abstract: The problem of identifying the time location and estimating the amplitude of outliers in nonlinear time series is addressed. A model-based method is proposed for detecting the presence of additive or innovational outliers when the series is generated by a general nonlinear model. We use this method for identifying and estimating outliers in bilinear, self-exciting threshold autoregressive and exponential autoregressive models. A simulation study is performed to test the proposed procedures and comparing them with the methods based on linear models and linear interpolators. Finally, our results are applied for detecting outliers in the Canadian lynx trappings and in the sunspot numbers data.
TL;DR: In this article, a wavelet-based estimator of the Hurst parameter was proposed for long-range dependent FARIMA time series with symmetric α-stable innovations.
Abstract: . Methods for parameter estimation in the presence of long-range dependence and heavy tails are scarce. Fractional autoregressive integrated moving average (FARIMA) time series for positive values of the fractional differencing exponent d can be used to model long-range dependence in the case of heavy-tailed distributions. In this paper, we focus on the estimation of the Hurst parameter H = d + 1/α for long-range dependent FARIMA time series with symmetric α-stable (1 < α < 2) innovations. We establish the consistency and the asymptotic normality of two types of wavelet estimators of the parameter H. We do so by exploiting the fact that the integrated series is asymptotically self-similar with parameter H. When the parameter α is known, we also obtain consistent and asymptotically normal estimators for the fractional differencing exponent d = H − 1/α. Our results hold for a larger class of causal linear processes with stable symmetric innovations. As the wavelet-based estimation method used here is semi-parametric, it allows for a more robust treatment of long-range dependent data than parametric methods.
TL;DR: This work constructs models that parallel existing structures, namely state-space models, autoregressive conditional heteroscedasticity (ARCH) models, and generalized ARCH models, that perform well compared with competing methods for the applications considered, count models and volatility models.
Abstract: Here we present a novel method for modeling stationary time series. Our approach is to construct the model with a specified marginal family and build the dependence structure around it. We show that the resulting time series is linear with a simple autocorrelation structure. We construct models that parallel existing structures, namely state-space models, autoregressive conditional heteroscedasticity (ARCH) models, and generalized ARCH models. We use Bayesian techniques to estimate the resulting models. We also demonstrate that the models perform well compared with competing methods for the applications considered, count models and volatility models.
TL;DR: The autoregressive Hilbertian with exogenous variables model (ARHX) as mentioned in this paper takes into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions.
Abstract: We present the autoregressive Hilbertian with exogenous variables model (ARHX) which intends to take into account the dependence structure of random curves viewed as H-valued random variables, where H is a Hilbert space of functions, under the influence of explanatory variables. Limit theorems and consistent estimators are derived from an autoregressive representation. A simulation study illustrates the accuracy of the estimation by making a comparison on forecasts with other functional models.
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TL;DR: In this paper, the authors derived exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregression process with exponential innovations and unified the limit distributions for the stationary, critical and explosive cases via a single pivot using a random normalization.
Abstract: Exact and asymptotic distributions of the maximum likelihood estimator of the autoregressive parameter in a first-order bifurcating autoregressive process with exponential innovations are derived. The limit distributions for the stationary, critical and explosive cases are unified via a single pivot using a random normalization. The pivot is shown to be asymptotically exponential for all values of the autoregressive parameter.
TL;DR: A methodology for analyzing bivariate time series with missing data is presented and it is assumed that there is a dynamical nonlinear relationship between the two time series, which is described by a threshold autoregressive (TAR) model.
Abstract: In this article, a methodology for analyzing bivariate time series with missing data is presented. It is assumed that there is a dynamical nonlinear relationship between the two time series, which is described by a threshold autoregressive (TAR) model. The time series analysis consists in the identification and estimation of the model in the presence of missing data. As a main result, the model parameters and the missing observations are estimated jointly. The TAR model analysis is accomplished by means of Markov Chain Monte Carlo (MCMC) and Bayesian approaches.
TL;DR: The authors presented and evaluated alternative methods for multi-step forecasting using univariate and multivariate functional coefficient autoregressive (FCAR) models, including a simple plug-in approach, a bootstrap-based approach, and a multi-stage smoothing approach, where the functional coefficients are updated at each step to incorporate information from the time series captured in previous predictions.
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TL;DR: This paper proposes a method for determining the number of regimes in threshold autoregressive models using smooth transition autoregression as a tool and finds that it works reasonably well for both single and multiple threshold models.
Abstract: In this paper we propose a method for determining the number of regimes in threshold autoregressive models using smooth transition autoregression as a tool. As the smooth transition model is just an approximation to the threshold autoregressive one, no asymptotic properties are claimed for the proposed method. Tests available for testing the adequacy of a smooth transition autoregressive model are applied sequentially to determine the number of regimes. A simulation study is performed in order to find out the finite-sample properties of the procedure and to compare it with two other procedures available in the literature. We find that our method works reasonably well for both single and multiple threshold models.
TL;DR: A number of stationary INAR ( p ) processes with specific marginals are presented and are shown to generalize several existing models.
Abstract: The purpose of this paper is to introduce and develop a family of
ℤ + -valued autoregressive processes of order p ( INAR ( p ) ) by
using the generalized multiplication ⊙ F of van Harn and
Steutel (1982). We obtain various distributional and regression
properties for these models. A number of stationary INAR ( p ) processes with specific marginals are presented and are shown to
generalize several existing models.
TL;DR: A French discourse analysis model is introduced, e.g. the ‘star model’, initiated by the LAA team led by Robert Vion in Aix-en-Provence, to English-speaking researchers to offer a unified and comprehensive view of such heterogeneous phenomena in constant interconnection.
Abstract: This article is aimed at introducing a French discourse analysis model, e.g. the ‘star model’, initiated by the LAA team led by Robert Vion in Aix-en-Provence, to English-speaking researchers. It will be argued that language activity is multi-dimensional and can be traced at various heterogeneous levels of speech productions belonging to macro as well as micro orders. Speakers achieve different varieties of positioning which result in negotiating an interactional space within a pre-given situation. The model is precisely designed to offer a unified and comprehensive view of such heterogeneous phenomena in constant interconnection. In this study, we also intend to illustrate our approach through the analysis of two different corpora. Speakers’ strategies under extreme conditions will be analysed; the various sequences used were taken from a special corpus which we were asked to study as part of a national research programme. In order to illustrate interactional space shifts, we will also use the transcript...
TL;DR: The proposed global standardized partial autocorrelation (SPAC) method tests whether the spatial profile of partial autcorrelations at a certain lag is random, and uses random field theory to account for the spatial correlations typical for fMRI data.
TL;DR: Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed, based on the bootstrap technique, which take into account the uncertainty associated with the estimation of the model order and parameters.
Abstract: Two new methods for improving prediction regions in the context of vector autoregressive (VAR) models are proposed These methods, which are based on the bootstrap technique, take into account the uncertainty associated with the estimation of the model order and parameters In particular, by exploiting an independence property of the prediction error, we will introduce a bootstrap procedure that allows for better estimates of the forecasting distribution, in the sense that the variability of its quantile estimators is substantially reduced, without requiring additional bootstrap replications The proposed methods have a good performance even if the disturbances distribution is not Gaussian An application to a real data set is presented
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TL;DR: In this paper, the authors introduced the Bi-parameter Smooth Transition Autoregressive (BSTAR) model that generalizes the LSTR2 model, which is characterized by the asymmetric transition function which implies different local dynamics in the neighborhood of the respective location parameters.
Abstract: The present paper introduces the Bi-parameter Smooth Transition Autoregressive (BSTAR) model that generalizes the LSTR2 model, see Terasvirta (1998). In contrast to the LSTR2 model, which features the symmetric transition function, the BSTAR model is characterized by the asymmetric transition function which implies different local dynamics in the neighborhood of the respective location parameters. An empirical example using the time series of the annual growth rates of the Italian industrial production index is provided.
01 Jan 2005
TL;DR: For a set of T independent N-variate Gaussian training samples, maximum the likelihood estimate of its time-varying autoregressive model of order m is derived, and the TVAR(m) model parameters are used to calculate the ML time-frequency spectrum estimate.
Abstract: For a set of T independent N-variate Gaussian training samples (T < N), we derive maximum the likelihood (ML) estimate of its time-varying autoregressive model of order m, TVAR(m), and method to estimate the order of an autoregressive (AR) model, regardless of its stationary or time-varying nature. For the estimated order m, we then use the TVAR(m) model parameters to calculate the ML time-frequency spectrum estimate
TL;DR: The forecasting procedure can be used to obtain approximate m-step-ahead predictive probability density functions, predictive distribution function, predictive mean and variance, etc. for a range of nonlinear autoregressive time series models.
Abstract: Forecasting for nonlinear time series is an important topic in time series analysis. Existing numerical algorithms for multi-step-ahead forecasting ignore accuracy checking, alternative Monte Carlo methods are also computationally very demanding and their accuracy is difficult to control too. In this paper a numerical forecasting procedure for nonlinear autoregressive time series models is proposed. The forecasting procedure can be used to obtain approximate m-step-ahead predictive probability density functions, predictive distribution functions, predictive mean and variance, etc. for a range of nonlinear autoregressive time series models. Examples in the paper show that the forecasting procedure works very well both in terms of the accuracy of the results and in the ability to deal with different nonlinear autoregressive time series models. Copyright © 2005 John Wiley & Sons, Ltd.
01 Jan 2005
TL;DR: The Generalized Mixture of AR-ARCH model (GMAR-ARCH) is defined which is an extension of the classical ARCH model to suit to model with dynamical changes and derives the consistency and asymptotic normality of the parameter estimates.
Abstract: The problem of structural changes (variations) play a central role in many scientific fields. One of the most current debates is about climatic changes. Further, politicians, environmentalists, scientists, etc. are involved in this debate and almost everyone is concerned with the consequences of climatic changes. However, in this thesis we will not move into the latter direction, i.e. the study of climatic changes. Instead, we consider models for analyzing changes in the dynamics of observed time series assuming these changes are driven by a non-observable stochastic process. To this end, we consider a first order stationary Markov Chain as hidden process and define the Generalized Mixture of AR-ARCH model(GMAR-ARCH) which is an extension of the classical ARCH model to suit to model with dynamical changes. For this model we provide sufficient conditions that ensure its geometric ergodic property. Further, we define a conditional likelihood given the hidden process and a pseudo conditional likelihood in turn. For the pseudo conditional likelihood we assume that at each time instant the autoregressive and volatility functions can be suitably approximated by given Feedfoward Networks. Under this setting the consistency of the parameter estimates is derived and versions of the well-known Expectation Maximization algorithm and Viterbi Algorithm are designed to solve the problem numerically. Moreover, considering the volatility functions to be constants, we establish the consistency of the autoregressive functions estimates given some parametric classes of functions in general and some classes of single layer Feedfoward Networks in particular. Beside this hidden Markov Driven model, we define as alternative a Weighted Least Squares for estimating the time of change and the autoregressive functions. For the latter formulation, we consider a mixture of independent nonlinear autoregressive processes and assume once more that the autoregressive functions can be approximated by given single layer Feedfoward Networks. We derive the consistency and asymptotic normality of the parameter estimates. Further, we prove the convergence of Backpropagation for this setting under some regularity assumptions. Last but not least, we consider a Mixture of Nonlinear autoregressive processes with only one abrupt unknown changepoint and design a statistical test that can validate such changes.