Showing papers on "STAR model published in 2002"
TL;DR: This paper reviewed econometric methods for dynamic panel data models, and presented examples that illustrate the use of these procedures for the analysis of large number of individuals or firms observed for a small number of time periods.
Abstract: This paper reviews econometric methods for dynamic panel data models, and presents examples that illustrate the use of these procedures The focus is on panels where a large number of individuals or firms are observed for a small number of time periods, typical of applications with microeconomic data The emphasis is on single equation models with autoregressive dynamics and explanatory variables that are not strictly exogenous, and hence on the Generalised Method of Moments estimators that are widely used in this context Two examples using firm-level panels are discussed in detail: a simple autoregressive model for investment rates; and a basic production function
2,200 citations
TL;DR: This paper surveys recent developments related to the smooth transition autoregressive (STAR) time series model and several of its variants, putting emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting.
Abstract: This paper surveys recent developments related to the smooth transition autoregressive (STAR) time series model and several of its variants. We put emphasis on new methods for testing for STAR nonlinearity, model evaluation, and forecasting. Several useful extensions of the basic STAR model, which concern multiple regimes, time-varying non-linear properties, and models for vector time series, are also reviewed.
1,120 citations
TL;DR: In this article, the authors provide sufficient conditions for β-mixing and finite higher order moments for various linear and nonlinear GARCH(1,1), linear and power GARCH (p,q), stochastic volatility, and autoregressive conditional duration models.
Abstract: This paper first provides some useful results on a generalized random coefficient autoregressive model and a generalized hidden Markov model. These results simultaneously imply strict stationarity, existence of higher order moments, geometric ergodicity, and β-mixing with exponential decay rates, which are important properties for statistical inference. As applications, we then provide easy-to-verify sufficient conditions to ensure β-mixing and finite higher order moments for various linear and nonlinear GARCH(1,1), linear and power GARCH(p,q), stochastic volatility, and autoregressive conditional duration models. For many of these models, our sufficient conditions for existence of second moments and exponential β-mixing are also necessary. For several GARCH(1,1) models, our sufficient conditions for existence of higher order moments again coincide with the necessary ones in He and Terasvirta (1999, Journal of Econometrics 92, 173–192).
596 citations
TL;DR: In this paper, the authors show that in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can even be asymptotically efficient relative to some other estimators.
Abstract: Least squares estimation has casually been dismissed as an inconsistent estimation method for mixed regressive, spatial autoregressive models with or without spatial correlated disturbances. Although this statement is correct for a wide class of models, we show that, in economic spatial environments where each unit can be influenced aggregately by a significant portion of units in the population, least squares estimators can be consistent. Indeed, they can even be asymptotically efficient relative to some other estimators. Their computations are easier than alternative instrumental variables and maximum likelihood approaches.
251 citations
TL;DR: It was found that all the four criteria underestimate the true AR order; specifying a fixed model order was looked at and it was recommended that an AR order not less than p = 16, should be used for spectral analysis of short segments of tachograms.
Abstract: Heart rate variability (HRV) has been used as a non-invasive marker of the activity of the autonomic nervous system and its spectrum analysis gives a measure of the sympatho-vagal balance. If short segments are used in an attempt to improve temporal resolution, autoregressive spectral estimation, where the mode] order must be estimated, is preferred. In this paper we compare four criteria for the estimation of the 'optimum' model order for an autoregressive (AR) process applied to short segments of tachograms used for HRV analysis. The criteria used were Akaike's final prediction error, Akaike's information criterion, Parzen's criterion of autoregressive transfer function and Rissanen's minimum description length method, and they were first applied to tachograms to verify (i) the range and distribution of model orders obtained and (ii) if the different techniques suggest the same model order for the same frames. The four techniques were then tested using a true AR process of known order p = 6; this verified the ability of the criteria to estimate the correct order of a true AR process and the effect, on the spectrum, of choosing a wrong model order was also investigated. It was found that all the four criteria underestimate the true AR order; specifying a fixed model order was then looked at and it is recommended that an AR order not less than p = 16, should be used for spectral analysis of short segments of tachograms.
217 citations
TL;DR: In this article, the smooth transition autoregression (STAR) model is used to model the transition between the extreme regimes of a time series, where the transition is assumed to be characterized by a bounded continuous function of a transition variable.
Abstract: Among the parametric nonlinear time series model families, the smooth transition regression (STR) model has recently received attention in the literature. The considerations in this dissertation focus on the univariate special case of this model, the smooth transition autoregression (STAR) model, although large parts of the discussion can be easily generalised to the more general STR case. Many nonlinear univariate time series models can be described as consisting of a number of regimes, each one corresponding to a linear autoregressive parametrisation, between which the process switches. In the STAR models, as opposed to certain other popular models involving multiple regimes, the transition between the extreme regimes is smooth and assumed to be characterised by a bounded continuous function of a transition variable. The transition variable, in turn, may be a lagged value of the variable in the model, or another stochastic or deterministic observable variable. A number of other commonly discussed nonlinear autoregressive models can be viewed as special or limiting cases of the STAR model.The applications presented in the first two chapters of this dissertation,Chapter I: Another look at Swedish Business Cycles, 1861-1988Chapter II: Modelling asymmetries and moving equilibria in unemployment rates, make use of STAR models.In these two studies, STAR models are used to provide insight into dynamic properties of the time series which cannot be be properly characterised by linear time series models, and which thereby may be obscured by estimating only a linear model in cases where linearity would be rejected if tested. The applications being of interest in their own right, an important common objective of these two chapters is also to develop, suggest, and give examples of various methods that may be of use in discussing the dynamic properties of estimated STAR models in general.Chapter III, Testing linearity against smooth transition autoregression using a parametric bootstrap, reports the result of a small simulation study considering a new test of linearity against STAR based on bootstrap methodology.
177 citations
TL;DR: In this article, the structural and statistical properties of the STAR-GARCH model and the finite sample properties of maximum likelihood estimation (MLE) of the estimators of the model were investigated.
Abstract: Theoretical and practical interest in non-linear time series models, particularly regime switching models, have increased substantially in recent years Given the abundant research activity in analysing time-varying volatility through Generalized Autoregressive Conditional Heteroscedasticity (GARCH) processes (see Engle, 1982; Bollerslev, 1986), it is important to analyse regime switching models with GARCH errors A popular specification in this class is the (stationary) Smooth Transition Autoregressive–GARCH (STAR-GARCH) model Little is presently known about the structure of the model, or the consistency, asymptotic normality and finite sample properties of the estimators The paper develops the structural and statistical properties of the STAR-GARCH model, and investigates the finite sample properties of maximum likelihood estimation (MLE) of STAR and STAR-GARCH models through numerical simulation The effects of fixing the threshold value and/or the transition rate for the STAR model, misspecification of the conditional mean and the transition function of the STAR-GARCH model, and the finite sample properties of the MLE for the STAR-GARCH model, are also examined These numerical results are used as a guide in empirical research, with an application to Standard and Poor's Composite 500 Index returns for alternative STAR-GARCH models Copyright © 2002 John Wiley & Sons, Ltd
79 citations
TL;DR: A unifying stochastic model reproducing correlations for all time scales is proposed, an extension of a first-order autoregressive model with power-law correlated noise.
Abstract: Classical spectral, Hurst, and detrended fluctuation analysis have been revealed asymptotic power-law correlations for daily average temperature data. For short-time intervals, however, strong correlations characterize the dynamics that permits a satisfactory description of temperature changes as a low order linear autoregressive process (dominating the texts on climate research). Here we propose a unifying stochastic model reproducing correlations for all time scales. The concept is an extension of a first-order autoregressive model with power-law correlated noise. The inclusion of a nonlinear "atmospheric response function" conveys the observed skew for the amplitude distribution of temperature fluctuations. While stochastic models cannot help to understand the physics behind atmospheric processes, they are capable to extract useful features promoting to benchmark physical models, an example is shown. Possible applications for other systems of strong short-range and asymptotic power-law correlations are discussed.
78 citations
01 Apr 2002
TL;DR: In this paper, an interpretable class of models called AutoRegressive Tree models, or ART models, were proposed for continuous valued time-series data that are useful for data mining in that they can be learned efficiently from data, support accurate predictions, and are easy to interpret.
Abstract: The analysis and modeling of time-series data is an important area of research for many communities. In this paper, our goal is to identify models for continuous valued time-series data that are useful for data mining in that they (1) can be learned eficiently from data, (2) support accurate predictions, and (3) are easy to interpret. To these ends, we describe an interpretable class of models that we call AutoRegressive Tree models, or ART models, that are a generalization of standard autoregressive (AR) models. We describe learning methods for ART models and compare these methods to those for alternative models. Our experiments, performed on 2,494 time-series data sets from the International Institute of Forecasters, demonstrate that ART models provide superior predictive accuracy. We concentrate on the problem of modeling the evolution of values of a continuous variable over time; that is, we model a univariate time series. The generalization to multivariate time-series analysis is straightforward and is discussed in Section 6.
73 citations
TL;DR: A variational Bayesian algorithm for the estimation of a multivariate autoregressive model with time-varying coefficients that adapt according to a linear dynamical system and is especially suited to the analysis of event-related data.
Abstract: We describe a variational Bayesian algorithm for the estimation of a multivariate autoregressive model with time-varying coefficients that adapt according to a linear dynamical system. The algorithm allows for time and frequency domain characterization of nonstationary multivariate signals and is especially suited to the analysis of event-related data. Results are presented on synthetic data and real electroencephalogram data recorded in event-related desynchronization and photic synchronization scenarios.
60 citations
TL;DR: In this article, first order stationary autoregressive (AR(1)) models are introduced for which there exists a linear relation between the expectations of the observations, and where it is readily possible to arrange the marginal distributions to be other than normal.
Abstract: First order stationary autoregressive (AR(1)) models are introduced for which there exists a linear relation between the expectations of the observations, and where it is readily possible to arrange the marginal distributions to be other than normal.
TL;DR: A conceptual approach and algorithm for the generation of surrogate data is proposed, called the statically transformed autoregressive process (STAP), which identifies a normal autore progressive process and a monotonic static transform, so that the transformed realizations of this process fulfill exactly both conditions and do not suffer from bias in autocorrelation as the surrogate data generated by other algorithms.
Abstract: The key feature for the successful implementation of the surrogate data test for nonlinearity on a scalar time series is the generation of surrogate data that represent exactly the null hypothesis (statically transformed normal stochastic process), i.e., they possess the sample autocorrelation and amplitude distribution of the given data. A conceptual approach and algorithm for the generation of surrogate data is proposed, called the statically transformed autoregressive process (STAP). It identifies a normal autoregressive process and a monotonic static transform, so that the transformed realizations of this process fulfill exactly both conditions and do not suffer from bias in autocorrelation as the surrogate data generated by other algorithms. The appropriateness of STAP is demonstrated with simulated and real world data.
TL;DR: In this article, the goodness of fit test of the errors of autoregressive models using the kernel estimate of the marginal density function based on residuals was considered and the test statistic is based on the integrated squared error of the nonparametric density estimate and a smoothed version of the parametric fit of the density.
TL;DR: This paper addresses parameter estimation of time-varying non-Gaussian autoregressive processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights.
Abstract: Parameter estimation of time-varying non-Gaussian autoregressive processes can be a highly nonlinear problem. The problem gets even more difficult if the functional form of the time variation of the process parameters is unknown. In this paper, we address parameter estimation of such processes by particle filtering, where posterior densities are approximated by sets of samples (particles) and particle weights. These sets are updated as new measurements become available using the principle of sequential importance sampling. From the samples and their weights we can compute a wide variety of estimates of the unknowns. In absence of exact modeling of the time variation of the process parameters, we exploit the concept of forgetting factors so that recent measurements affect current estimates more than older measurements. We investigate the performance of the proposed approach on autoregressive processes whose parameters change abruptly at unknown instants and with driving noises, which are Gaussian mixtures or Laplacian processes.
TL;DR: A program is presented for generating multivariate autoregressive data with a shift in the mean vector of the noise series that can be used to compare the shift detection properties of multivariate control chart methods.
Abstract: The comparison of out-of-control performance of multivariate control chart methods on autoregressive processes requires a consistent method of generating a multivariate process shift. By applying t...
TL;DR: In this article, the relative performance of some popular nonlinearity tests when applied to time series generated by Markov switching autoregressive models is examined, including RESET-type tests, the Keenan test, the Tsay test, McLeod-Li test, and neural network test.
Abstract: This paper examines the relative performance of some popular nonlinearity tests when applied to time series generated by Markov switching autoregressive models. The nonlinearity tests considered include RESET-type tests, the Keenan test, the Tsay test, the McLeod-Li test, the BDS test, the White dynamic information matrix test, and the neural network test. Applications to economic time series are also considered.
TL;DR: The task of finding multivariate thresholds as a combinatorial optimization problem is formulated and an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem is developed.
Abstract: Over recent years, several nonlinear time series models have been proposed in the literature. One model that has found a large number of successful applications is the threshold autoregressive model (TAR). The TAR model is a piecewise linear process whose central idea is to change the parameters of a linear autoregressive model according to the value of an observable variable, called the threshold variable. If this variable is a lagged value of the time series, the model is called a self-exciting threshold autoregressive (SETAR) model. In this article, we propose a heuristic to estimate a more general SETAR model, where the thresholds are multivariate. We formulate the task of finding multivariate thresholds as a combinatorial optimization problem. We develop an algorithm based on a greedy randomized adaptive search procedure (GRASP) to solve the problem. GRASP is an iterative randomized sampling technique that has been shown to quickly produce good quality solutions for a wide variety of optimization pro...
TL;DR: The Cramer-Rao bound for the parameters of a general time series model whose parameterization is dependent upon an unknown integer model order is derived.
Abstract: We derive the Cramer-Rao bound for the parameters of a general time series model whose parameterization is dependent upon an unknown integer model order. To illustrate the usefulness of the theoretical results, the example of autoregressive spectral density estimation using Akaike (1974) order selection criterion is presented.
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TL;DR: The authors developed a time series model which allows long-term disequilibria to have epochs of nonstationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship.
Abstract: In this paper we develop a time series model which allows long-term disequilibriums to have epochs of non-stationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship. This autoregressive root model is shown to be ergodic and covariance stationary under some rather general conditions. We study how this model can be estimated and tested, developing appropriate asymptotic theory for this task. Finally we apply the model to assess the purchasing power parity relationship.
01 Jan 2002
TL;DR: This paper examines the estimation method proposed by Haggan and Ozaki, Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model, and forms a generalization of the EXPAR model to both achieve parsimony in model specification and allow for more flexibility.
Abstract: The exponential autoregressive (EXPAR) models attracted much interest because they are able to account for amplitude-dependent frequency, jump phenomena, and limit cycles. In this paper we examine the estimation method proposed by Haggan and Ozaki, Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model, Biometrika, 68, 1981, 189-196. We are trying to improve their grid search procedure by using a genetic algorithm. Further, two entirely different procedures are presented based on indirect inference. The first one implements the calibration step by using the Gauss-Newton algorithm, the second one by using a genetic algorithm. The relative merits of the procedures are investigated by means of a simulation study. This latter shows that implementing the Haggan-Ozaki’s method by means of the genetic algorithm performs better than all other procedures. Then, two well-known real data sets are considered, the Canadian lynx data and the sunspot numbers. We attempt to formulate a generalization of the EXPAR model in order to both achieve parsimony in model specification and allow for more flexibility. The estimation procedure makes use of the genetic algorithm. Both parameter estimates and multi-step out-of-sample forecasts are performed for comparison purpose.
TL;DR: In this article, a weaker second-order stationarity assumption is proposed, in the framework of Markov-switching first-order autoregressions, and the authors discuss the stationarity conditions proposed by M. Yang (2000, Econometric Theory 16, 23, 23 and 43).
Abstract: This paper discusses the stationarity conditions proposed by M. Yang (2000, Econometric Theory 16, 23–43), in the framework of Markov-switching first-order autoregressions. A weaker second-order stationarity assumption is proposed.
TL;DR: In this article, the authors study Bayesian inference procedures to commonly used time series models, in particular, the dynamic or state-space models, the time-varying vector autoregressive model and the structural vector auto-regression model.
Abstract: This paper is concerned with the study of Bayesian inference procedures to commonly used time series models. In particular, the dynamic or state-space models, the time-varying vector autoregressive model and the structural vector autoregressive model are considered in detail. Inference procedures are based on a hybrid integration scheme where state parameters are analytically integrated and hyperparameters are integrated by Markov chain Monte Carlo methods. Credibility regions for forecasts and impulse responses are then derived. The procedures are illustrated in real data sets.
TL;DR: The process feedback nonlinear autoregressive (PFNAR) model may reveal the nonlinear dynamic system for pseudo-periodic biomedical oscillation generated by complex physiological phenomena and be applied to determine the mechanisms of phenomena fed back to the data processes within a certain system.
TL;DR: In this paper, the relevance of the P-star model to the Malaysian experience is analyzed and an extension to the original model, following a generalized monetary approach to the balance of payments and which allows the evaluation of the exchange rate regime's influence on inflation, is also tested.
Abstract: Introduced in 1989, the P -star model draws on the quantity theory of money. Money plays a central role in determining the long-termprice level. The model has been applied to various industrialized countries. Its advantage is in providing a consistent framework for analysing short-term monetary policy setting against the prospects of achieving a longer-term price stability objective. Hence its adoption greatly assists policy-makers in overcoming the 'time-inconsistency' problem by taking a forward-looking approach to policy. This article analyses the relevance of the P -star model to the Malaysian experience. An extension to the original P -star model, following a generalized monetary approach to the balance of payments and which allows the evaluation of the exchange rate regime's influence on inflation, is also tested. It is found that the original P -star model fits the Malaysian case well although the extended model cannot be rejected. The results strongly support the view that inflation in Malaysia is...
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TL;DR: This article developed a time series model which allows long-term disequilibria to have epochs of nonstationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship.
Abstract: In this paper we develop a time series model which allows long-term disequilibriums to have epochs of non-stationarity, giving the impression that long term relationships between economic variables have temporarily broken down, before they endogenously collapse back towards their long term relationship. This autoregressive root model is shown to be ergodic and covariance stationary under some rather general conditions. We study how this model can be estimated and tested, developing appropriate asymptotic theory for this task. Finally we apply the model to assess the purchasing power parity relationship.
TL;DR: The purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models, via a new martingale approach, with asymptotic results for the standard least squares estimator of the unknown model parameter.
Abstract: The purpose of this note is to investigate the stability and the optimality of the adaptive tracking for a wide class of parametric nonlinear autoregressive models, via a new martingale approach. Several asymptotic results for the standard least squares estimator of the unknown model parameter, such as a central limit theorem, a law of iterated logarithm, and strong laws of large numbers are also provided.
TL;DR: The finite sample formulae in this paper provide a more accurate description of the behavior of vector autoregressive estimators than asymptotic theory or the exact Cramer-Rao lower bound.
Abstract: In vector autoregressive modeling, the order selected with the Akaike Information Criterion tends to be too high. This effect is called overfit. Finite sample effects are an important cause of overfit. By incorporating finite sample effects, an order selection criterion for vector AR models can be found with an optimal trade-off of underfit and overfit. The finite sample formulae in this paper provide a more accurate description of the behavior of vector autoregressive estimators than asymptotic theory or the exact Cramer-Rao lower bound. A comparison of estimators in simulations as well as experimental data shows that the Nuttall-Strand estimator is more accurate than the least-squares estimator for high-order models. With the extension to channel prediction, the finite sample theory can also be used in order selection for autoregressive models with exogeneous input (ARX models) in system identification.
10 Dec 2002
TL;DR: This paper looks at the possibility of modelling MPEG4 traffic at the group of picture (GoP) level with autoregressive models, and found that the mean, variance and autocorrelation structure could be matched closely provided the right order autore progressive model was used.
Abstract: This paper looks at the possibility of modelling MPEG4 traffic at the group of picture (GoP) level with autoregressive models. Even though these models are short-range dependent the autocorrelation structure of the traffic can be matched up to an arbitrary lag by using the right order of the autoregressive process. No attempt is made to capture the long-range dependence in the traffic. A procedure to build such an autoregressive model of any order is described. Koenen (see ISO/IEC 14496, May/June 2000) found that the autocorrelation structure of GoPs decays almost exponentially for certain MPEG-4 traffic traces. Consequently, the use of autoregressive models for such traces seemed appropriate. It was found that the mean, variance and autocorrelation structure could be matched closely provided the right order autoregressive model was used. However, the empirical distribution function could not be matched closely. A distortion of the marginal distribution function was required to match that of the empirical sequence. A gamma distribution approximation was used. As this was not very successful the empirical distribution function itself was used to distort the marginal distribution.
TL;DR: In this paper, a stationary uniform autoregressive process of second order is introduced, and the unknown parameters of this model are estimated by the conditional least squares. Spectral density, autocovariance and autocorrelation functions are derived.