Showing papers on "STAR model published in 1998"

A Generalized Spatial Two-Stage Least Squares Procedure for Estimating a Spatial Autoregressive Model with Autoregressive Disturbances

Abstract: Cross-sectional spatial models frequently contain a spatial lag of the dependent variable as a regressor or a disturbance term that is spatially autoregressive. In this article we describe a computationally simple procedure for estimating cross-sectional models that contain both of these characteristics. We also give formal large-sample results.

Limiting properties of the least squares estimator of a continuous threshold autoregressive model

Abstract: The continuous threshold autoregressive model is a sub-class of the threshold autoregressive model subject to the requirement that the piece-wise linear autoregressive function be continuous everywhere. In contrast with the discontinuous case, it is shown that, under suitable regularity conditions, the conditional least squares estimator of the parameters including the threshold parameter is root-n consistent and asymptotically normally distributed. The theory is illustrated by a simulation study and is applied to the quarterly U.S. unemployment rates.

A comparison of the forecast performance of Markov-switching and threshold autoregressive models of US GNP

Abstract: While there has been a great deal of interest in the modelling of non-linearities in economic time series, there is no clear consensus regarding the forecasting abilities of non-linear time-series models. We evaluate the performance of two leading non-linear models in forecasting post-war US GNP, the self-exciting threshold autoregressive model and the Markov-switching autoregressive model. Two methods of analysis are employed: an empirical forecast accuracy comparison of the two models, and a Monte Carlo study. The latter allows us to control for factors that may otherwise undermine the performance of the non-linear models.

On unified model selection for stationary and nonstationary short- and long-memory autoregressive processes

Abstract: SUMMARY The question of model choice for the class of stationary and nonstationary, fractional and nonfractional autoregressive processes is considered. This class is defined by the property that the dth difference, for -2 < d < oo, is a stationary autoregressive process of order p0 < 00. A version of the Akaike information criterion, AIC, for determining an appropriate autoregressive order when d and the autoregressive parameters are estimated simultaneously by a maximum likelihood procedure (Beran, 1995) is derived and shown to be of the same general form as for a stationary autoregressive process, but with d treated as an additional estimated parameter. Moreover, as in the stationary case, this criterion is shown not to provide a consistent estimator of p0. The corresponding versions of the BIC of Schwarz (1978) and the HIC of Hannan & Quinn (1979) are shown to yield consistent estimators of po. The results provide a unified treatment of fractional and nonfractional, stationary and integrated nonstationary autoregressive models.

Existence and Stochastic Structure of a Non‐negative Integer‐valued Autoregressive Process

Abstract: A simple criterion is given for the existence of a generalized integer-valued autoregressive (GINAR(p)) process. We show that the GINAR(p) process is nothing but an AR(p) process. The spectral density gives a good insight into the stochastic structure of a GINAR(p) model. The spectral representation of the process is explicitly given. The estimation of parameters of the process is also discussed and clarifies some results presented by Du and Li (The integer-valued autoregressive (INAR(p)) model. J. Times Ser. Anal., 12 (1991), 129--42). Finally, we describe the number of seizures of an epileptic patient using a model of this class.

Diagnosing Shocks in Time Series

Abstract: Efficient means of modeling aberrant behavior in times series are developed. Our methods are based on state-space forms and allow test statistics for various interventions to be computed from a single run of the Kalman filter smoother. The approach encompasses existing detection methodologies. Departures commonly observed in practice, such as outlying values, level shifts, and switches, are readily dealt with. New diagnostic statistics are proposed. Implications for structural models, autoregressive integrated moving average models, and models with explanatory variables are given.

Limiting distributions of maximum likelihood estimators for unstable autoregressive moving-average time series with general autoregressive heteroscedastic errors

Abstract: This paper investigates the maximum likelihood estimator (MLE) for unstable autoregressive moving-average (ARMA) time series with the noise sequence satisfying a general autoregressive heteroscedastic (GARCH) process. Under some mild conditions, it is shown that the MLE satisfying the likelihood equation exists and is consistent. The limiting distribution of the MLE is derived in a unified manner for all types of characteristic roots on or outside the unit circle and is expressed as a functional of stochastic integrals in terms of Brownian motions. For various types of unit roots, the limiting distribution of the MLE does not depend on the parameters in the moving-average component and hence, when the GARCH innovations reduce to usual white noises with a constant conditional variance, they are the same as those for the least squares estimators (LSE) for unstable autoregressive models given by Chan and Wei (1988). In the presence of the GARCH innovations, the limiting distribution will involve a sequence of independent bivariate Brownian motions with correlated components. These results are different from those already known in the literature and, in this case, the MLE of unit roots will be much more efficient than the ordinary least squares estimation.

A subspace approach to estimation of autoregressive parameters from noisy measurements

Abstract: This correspondence describes a method for estimating the parameters of an autoregressive (AR) process from a finite number of noisy measurements The method uses a modified set of Yule-Walker (YW) equations that lead to a quadratic eigenvalue problem that, when solved, gives estimates of the AR parameters and the measurement noise variance

Modelling economic high-frequency time series with STAR-STGARCH models

Abstract: In this paper we introduce the STAR-STGARCH model that can characterize nonlinear behaviour both in the conditional mean and the conditional variance A modelling cycle for this family of models, consisting of specification, estimation, and evaluation stages is constructed Misspecification tests for the estimated model are obtained using standard asymptotic distribution theory We illustrate the actual modelling by applying the STAR-STGARCH model family to two series of daily observations, the Swedish OMX index and the exchange rate JPY-USD

A reversible jump sampler for autoregressive time series

Abstract: We use reversible jump Markov chain Monte Carlo (MCMC) methods to address the problem of model order uncertainty in autoregressive (AR) time series within a Bayesian framework. Efficient model jumping is achieved by proposing model space moves from the the full conditional density for the AR parameters, which is obtained analytically. This is compared with an alternative method, for which the moves are cheaper to compute, in which proposals are made only for new parameters in each move. Results are presented for both synthetic and audio time series.

Consistent Estimation of Linear and Non‐linear Autoregressive Models with Markov Regime

Abstract: An autoregressive process with Markov regime is an autoregressive process for which the regression function at each time-point is given by a (non-observable) Markov chain. We examine maximum likelihood estimation for such models and show consistency of a conditional maximum likelihood estimator. Also identifiability issues are discussed

On the Optimal Segment Length for Parameter Estimates for Locally Stationary Time Series

Abstract: We discuss the behaviour of parameter estimates when stationary time series models are fitted locally to non-stationary processes which have an evolutionary spectral representation. A particular example is the estimation for an autoregressive process with time-varying coefficients by local Yule–Walker estimates. The bias and the mean squared error for the parameter estimates are calculated and the optimal length of the data segment is determined.

Ergodicity of Autoregressive Processes with Markov-Switching and Consistency of the Maximum-Likelihood Estimator

Abstract: An autoregressive model with Markov-switching assumes a sequence of random vectors to be a non linear autoregressive model given a sequence of non observed state variables which forms a Markov chain. A particular case of this model is the hidden Markov model. In this paper conditions for the existence of an ergodic stationary solution are given and consistency of the maximum likelihood estimator is proved.

Prediction of Continuous Time Processes by C[0,1]‐Valued Autoregressive Process

Abstract: In order to predict a continuous time process on an entire‐time interval, we introduce the C[0,1]‐valued autoregressive process of first order. We show, under mild regularity conditions the convergence almost sure of the predictor. We propose an estimator of the dimension of the projecting space of observations and illustrate the results by a numerical example.

Autoregressive model order selection by a finite sample estimator for the Kullback-Leibler discrepancy

Abstract: The finite sample information criterion (FSIC) is introduced as an estimator for the Kullback-Leibler discrepancy of an autoregressive time series. It is derived especially for order selection in finite samples, where model orders are greater than one tenth of the sample size. It uses a theoretical expression for the ratio between the squared prediction error and the residual variance its the penalty factor for additional parameters in a model. This ratio can be found with the finite sample theory for autoregressive estimation, which is based on empirical approximations for the variance of parameters. It takes into account the different number of degrees of freedom that are available effectively in the various algorithms for autoregressive parameter estimation. The performance of FSIC has been compared with existing order selection criteria in simulation experiments using four different estimation methods. In finite samples, the FSIC selects model orders with a better objective quality for all estimation methods.

Semiparametric Regression Smoothing of Non‐linear Time Series

Abstract: In this paper, we consider using a semiparametric regression approach to modelling non-linear autoregressive time series. Based on a finite series approximation to non-parametric components, an adaptive selection procedure for the number of summands in the series approximation is proposed. Meanwhile, a large sample study is detailed and a small sample simulation for the Mackey-Glass system is presented to support the large sample study.

Some Inference Results for Causal Autoregressive Processes on a Plane

Abstract: We investigate the causal autoregressive process on a plane pioneered by Whittle (On stationary processes on the plane. Biometrika 41 (1954), 434–49) and further studied by Besag (Spatial interaction and statistical analysis of lattice systems. J. R. Stat. Soc. Ser. B 36 (1974), 192–236). We develop test statistics to test composite hypotheses about the parameters and to test if the process is separable. Also, when some data points are missing, we develop a computational procedure obtained by combining the EM algorithm and bootstrap procedures to find estimates of the parameters and hence the distribution of these estimates.

Stationarity and Stability of Autoregressive Neural Network Processes

Abstract: We analyze the asymptotic behavior of autoregressive neural network (AR-NN) processes using techniques from Markov chains and non-linear time series analysis. It is shown that standard AR-NNs without shortcut connections are asymptotically stationary. If linear shortcut connections are allowed, only the shortcut weights determine whether the overall system is stationary, hence standard conditions for linear AR processes can be used.

Consistent Estimation of the Number of Cointegration Relations in a Vector Autoregressive Model

Abstract: A class of criteria is developed which estimate the cointegration rank of a vector autoregressive (VAR) model consistently. It turns out that the usual consistent criteria for lag length selection can be adapted for the present purpose. However, alternative criteria may be advantageous. The small sample relevance of the asymptotic results is demonstrated by a small simulation study.

Non-Linear Time-Series Models of Ethernet Traffic

Abstract: In this paper non-linear threshold autoregressive models are examined for use in modeling the temporal variation in the byte-rate in Ethernet traffic The model is comprised of a number of autoregressive processes each of which is to be used in a specified range of amplitude of the byte-rate The local dynamics within each threshold range are captured by an autoregressive process The switching between each submodel is conditioned on the amplitude of a lagged value of the time-series To dev elop the model the Bellcore Ethernet LAN data is used It is shown that non-linear threshold autoregressive processes can be used to capture the dynamics of Ethernet LAN traffic This model also provides for both short and longterm prediction capability and allows us to quantitatively identify the sources of long-range-dependence features in the traffic When the aggregate traffic is partitioned into classes based on packet sizes, certain classes of traffic follow deterministic cyclical patterns These periodic components arise from the process switching between different amplitude regimes Superposed on this fundamental period are longer cycles that can be localized either below or above the mean byte-rate By constructing amplitude thresholds associated with a finite set of delay parameters, the dynamics within each threshold are captured by locally linear autoregressive processes The aggregate process is globally nonlinear This model is shown to provide good agreement with the marginal distributions and the correlation functions derived from the Ethernet traffic data In addition, simulation experiments demonstrate that the loss statistics observed in finite buffer queues agree favorably with those generated by the measurements

Modelling macroeconomic time series with smooth transition autoregressions

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.

Nonlinear Dynamics and European GNP Data

Abstract: The aim of this paper is to assess whether the data-generation process of the GDP can be interpreted by means of a nonlinear model instead of a linear one. We model the first differences of logarithmic real GDP data with constant parameters for those European countries (France, Germany, Italy, U.K., Denmark, Sweden, and Norway) which have long-term time series. Since the linear autoregressive model is rejected, an alternative nonlinear model has been specified: it turns out that the annual European GDPs can adequately be described by means of a nonlinear model with constant parameters.

Stabilization of stationary and time-varying autoregressive models

Abstract: A method for the stabilization of stationary and time-varying autoregressive models is presented. The method is based on the hyperstability constrained LS-problem with nonlinear constraints. The problems are solved iteratively with Gauss-Newton type algorithm that sequentially linearizes the constraints. The proposed method is applied to simulated data in the stationary case and to real EEG data in the time-varying case.

Bayesian Analysis of Autoregressive Time Series with Change Points

Abstract: The paper deals with the identification of a stationary autoregressive model for a time series and the contemporary detection of a change in its mean. We adopt the Bayesian approach with weak prior information on the parameters of the models under comparison and an exact form of the likelihood function. When necessary, we resort to fractional Bayes factors to choose between models, and to importance sampling to solve computational issues.

A parametric characterization of integrated vector autoregressive (var) processes

Abstract: This paper provides a polynomial factorization theorem that is then used to extend the characterization parts of the parametric representation theorems of Johansen (1992, Econometric Theory 8, 188–202) for vector autoregressive processes integrated of up to order 2. A characterization theorem is provided in the general case of an I(d) process. For the discussion of the complicated polynomial cointegration properties of such processes, the case of an I(3) process is considered as an example.