Showing papers on "STAR model published in 1997"

Bayesian Estimation of Spatial Autoregressive Models

Abstract: Spatial econometrics has relied extensively on spatial autoregressive models. Anselin (1988) developed a taxonomy of these models using a regression model framework and maximum likelihood estimation methods. A Bayesian approach to estimating these models based on Gibbs sampling is introduced here. It allows for non-constant variance over space taking an unspecified form and outliers in the sample data. In addition, estimates of the non-constant variance at each point in space allow inferences regarding the spatial nature of heteroskedasticity and the position of outliers.

On Fractionally Integrated Autoregressive Moving-Average Time Series Models with Conditional Heteroscedasticity

Abstract: This article considers fractionally integrated autoregressive moving-average time series models with conditional heteroscedasticity, which combines the popular generalized autoregressive conditional heteroscedastic (GARCH) and the fractional (ARMA) models. The fractional differencing parameter d can be greater than 1/2, thus incorporating the important unit root case. Some sufficient conditions for stationarity, ergodicity, and existence of higher-order moments are derived. An algorithm for approximate maximum likelihood (ML) estimation is presented. The asymptotic properties of ML estimators, which include consistency and asymptotic normality, are discussed. The large-sample distributions of the residual autocorrelations and the square-residual autocorrelations are obtained, and two portmanteau test statistics are established for checking model adequacy. In particular, non-stationary FARIMA(p, d, q)-GARCH(r, s) models are also considered. Some simulation results are reported. As an illustration,...

Efficient estimation in nonlinear autoregressive time-series models

Abstract: This paper discusses efficient estimation for a class of nonlinear time-series models with unknown error densities. It establishes local asymptotic normality in this semi-parametric setting. This is then used to describe efficient estimates and to discuss the question of adaptation. Stein's necessary condition for adaptive estimation is satisfied if the error densities are symmetric, but is also satisfied in some models with asymmetric error densities. The paper gives several methods of constructing efficient estimates. These results are then applied to construct efficient estimators in SETAR(2;1,1), EXPAR(1) and ARMA(1,1) models. We observe that adaptation is not possible in the SETAR(2;1,1) model with asymmetric errors while the efficient estimators in the ARMA(1,1) model are adaptive even for asymmetric error densities. Section 8 contains a result that is useful in verifying the continuity of the stationary density with respect to the underlying parameters.

Estimation of Spatial Regression Models with Autoregressive Errors by Two Stage Least Squares Procedures: A Serious Problem

Abstract: Time series regression models that have autoregressive errors are often estimated by two-stage procedures which are based on the Cochrane-Orcutt (1949) transformation. It seems natural to also attempt the estimation of spatial regression models whose error terms are autoregressive in terms of an analogous transformation. Various two-stage least squares procedures suggest themselves in this context, including an analog to Durbin's (1960) procedure. Indeed, these procedures are so suggestive and computationally convenient that they are quite "tempting." Unfortunately, however, as shown in this paper, these two-stage least squares procedures are generally, in a typical cross-sectional spatial context, not consistent and therefore should not be used.

On a multivariate conditional heteroscedastic model

Abstract: Tsay (1987) developed the conditional heteroscedastic autoregressive moving-average model, which includes the conditional heteroscedastic autoregressive and random coefficient autoregressive models as special cases. This paper establishes the multivariate conditional heteroscedastic autoregressive moving-average model, and considers its theoretical properties and applications. Maximum likelihood estimation of the model is discussed in detail. A representation of the information matrix is obtained using the star product. This enhances estimation and statistical inferences procedures. Some simulation results and an application to the volatility of the Standard & Poor's 500 and Sydney's All Ordinaries indices are also considered.

Autoregressive Models with Sample Selectivity for Panel Data

Abstract: The purpose of this paper is to formulate procedures for the analysis of the time series behaviour of micro panel data subject to censoring. We assume an autoregressive model with random effects for a latent variable which is only partly observed due to a selection mechanism. Our methods are based on the observation that the subsamples which only include individuals without censored past observations are exogenously selected for the purpose conditional on its past. We apply these methods to analyze the dynamics of female labour supply and wages using PSID data.

On some simple, autoregression-based estimation and identification techniques for ARMA models

Abstract: SUMMARY We examine simple estimators for general ARMA models and a corresponding identification method. Both estimation and identification are based on a matrix formed from the coefficients of an autoregressive approximation to the process of interest. We show that a zero determinant of this matrix is necessary and sufficient for the existence of a common factor in autoregressive and moving average lag polynomials, and therefore for redundant parameters in the model. Simulation results suggest a close match between the empirical finite-sample distribution of the test statistic for model order reduction and its asymptotic distribution.

Bayesian approach to parameter estimation and interpolation of time-varying autoregressive processes using the Gibbs sampler

Abstract: A nonstationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilise standard analytically defined statistical estimators to parameterise the process. To overcome this difficulty, the time series is considered within a finite time interval and is modelled as a time-varying autoregressive (AR) process. The AR coefficients that characterise this process are functions of time, represented by a family of basis vectors. The corresponding basis coefficients are invariant over the time window and have stationary statistical properties. A method is described for applying a Markov Chain Monte Carlo method known as the Gibbs sampler to the problem of estimating the parameters of such a time-varying autoregressive (TVAR) model, whose time dependent coefficients are modelled by basis functions. The Gibbs sampling scheme is then extended to include a stage which may be used for interpolation. Results on synthetic and real audio signals show that the model is flexible, and that a Gibbs sampling framework is a reasonable scheme for estimating and characterising a time-varying AR process.

The Markov-Switching Vector Autoregressive Model

Abstract: This first chapter is devoted to a general introduction into the Markov-switching vector autoregressive (MS-VAR) time series model. In Section 1.2 we present the fundamental assumptions constituting this class of models. The discussion of the two components of MS-VAR processes will clarify their on time invariant vector auto-regressive and Markov-chain models. Some basic stochastic properties of MS-VAR processes are presented in Section 1.3. Finally, MS-VAR models are compared to alternative non-normal and non-linear time series models proposed in the literature. As most non-linear models have been developed for univariate time series, this discussion is restricted to this case. However, generalizations to the vector case are also considered.

Analyzing X-ray Variability by Linear State Space Models

Abstract: In recent years, autoregressive models have had a profound impact on the description of astronomical time series as the observation of a stochastic process. However, it has to be taken into account that real data always contain observational noise often obscuring the intrinsic time series of the object. We apply the technique of a Linear State Space Model which explicitly models the noise of astronomical data and allows to estimate the hidden autoregressive process. As an example, we have analysed the X-ray flux variability of the Active Galaxy NGC 5506 observed with EXOSAT.

A hybrid model for point rainfall modeling

Abstract: A hybrid point rainfall model, a product of two random processes, is presented. The model uses a jitter model, a general technique for improving the fit of any point process based model. We use the nonrandomized Bartlett-Lewis rectangular pulse and an autoregressive model as a jitter. First, the five parameters of the Bartlett-Lewis model are estimated by the method of moments using the mean of one aggregation level and the dry probabilities of all aggregation levels considered. Second, the parameters of the autoregressive model are derived from the moments of the historical data and those given by the Bartlett-Lewis model, without additional cost in terms of parameter calibration. Using 15-min point rainfall data of Capella, central Queensland, Australia, as a test case, the results of the hybrid model were better than the best results given by the randomized Bartlett-Lewis model. On its own the nonrandomized Bartlett-Lewis model produced very poor results.

Bayesian Models for Non‐linear Autoregressions

Abstract: We discuss classes of Bayesian mixture models for nonlinear autoregressive times series, based on developments in semiparametric Bayesian density estimation in recent years. The development involves formal classes of multivariate discrete mixture distributions, providing flexibility in modeling arbitrary nonlinearities in time series structure and a formal inferential framework within which to address the problems of inference and prediction. The models relate naturally to existing kernel and related methods, threshold models and others, although they offer major advances in terms of parameter estimation and predictive calculations. Theoretic al and computational aspects are developed here, the latter involving efficient simulation of posterior and predictive distributions. Various examples illustrate our perspectives on identification and inference using this mixture approach

Problems Related to Bootstrapping Impulse Responses of Autoregressive Processes

Abstract: Bootstrap confidence intervals for impulse responses computed from autoregressive processes are considered. A detailed analysis of the methods in current use shows that they are not very reliable in some cases. In particular, there are theoretical reasons for them to have actual coverage probabilities which deviate considerably from the nominal level in some situations of practical importance. For a simple case alternative bootstrap methods are proposed which provide correct results asymptotically.

Testing for cyclical non‐stationarity in autoregressive processes

Abstract: This paper deals with the distributions evolving from the likelihood-ratio test for the factor 1 −Bn in the lag polynomial Φ(B) under the basic assumption that the data series is generated by the autoregressive model Φ(B)Xt = et where {et} denotes Gaussian white noise. A characterization of the statistic and its asymptotic properties is given. Asymptotic and finite-sample significance points are tabulated. The test procedure is illustrated by an economics example.

A Bayesian analysis of autoregressive time series panel data

Abstract: We describe a Bayesian hierarchical model to analyze autoregressive time series panel data. We develop two algorithms using Markov-chain Monte Carlo methods, a restricted algorithm that enforces stationarity or nonstationarity conditions on the series and an unrestricted algorithm that does not. Two examples show that restricting stationary series to be stationary provides no new information, but restricting nonstationary series to be stationary leads to substantial differences from the unrestricted case. These examples and a simulation study also show that, compared with inference based on individual series, there are gains in precision for estimation and forecasting when similar series are pooled.

On sequential estimation of an autoregressive parameter

Abstract: We study the estimation problem for the first-order autoregressive model The asymptotic behavior of the classical maximum likelihood estimator (MLE) (when the number of observation n tends to infin...

A unified approach to estimating and modeling linear and nonlinear time series

Abstract: In this article, we propose a unified approach to estimating and modeling univariate time series. The approach applies to both linear and nonlinear time series models and can be used to discriminate non-nested nonlinear models. For example, it can discriminate between threshold autoregressive and bilinear models or between autoregressive and moving average models. It can also be used to estimate and dis- criminate between symmetric and asymmetric conditional heteroscedastic models commonly used in volatility studies of financial time series. The proposed approach is based on Gibbs sampling and may require substantial amounts of computing in some applications. We illustrate the proposed approach by some simulated and real examples. Comparison with other existing methods is also discussed.

Autoregressive models as a tool to discriminate chaos from randomness in geoelectrical time series: an application to earthquake prediction

Abstract: The time dynamics of geoelectrical precursory time series has been investigated and a method to discriminate chaotic behaviour in geoelectrical precursory time series is proposed. It allows us to detect low-dimensional chaos when the only information about the time series comes from the time series themselves. The short-term predictability of these time series is evaluated using two possible forecasting approaches: global autoregressive approximation and local autoregressive approximation. The first views the data as a realization of a linear stochastic process, whereas the second considers the data points as a realization of a deterministic process, supposedly non-linear. The comparison of the predictive skill of the two techniques is a test to discriminate between low-dimensional chaos and random dynamics. The analyzed time series are geoelectrical measurements recorded by an automatic station located in Tito (Southern Italy) in one of the most seismic areas of the Mediterranean region. Our findings are that the global (linear) approach is superior to the local one and the physical system governing the phenomena of electrical nature is characterized by a large number of degrees of freedom. Power spectra of the filtered time series follow a P(f) = F-a scaling law: they exhibit the typical behaviour of a broad class of fractal stochastic processes and they are a signature of the self-organized systems.

Goodness-of-fit tests for autoregressive processes

Abstract: Goodness-of-fit tests for autoregressive processes can be based on the difference betwe en the empirical standardized spectral distribution of an observed time series and the standardized spectral distribution of the autoregressive process with parameters estimated from the series. The asymptotic covariance function of this difference, considered as a stochastic process on [0, π], is found. Methods to compute the asymptotic distribution of the Cramer--von Mises statistic are given.

On the Asymptotic Expectations of Some Unit Root Tests in a First Order Autoregressive Process in the Presence of Trend

Abstract: Estimation in a first order autoregressive process with trend is considered. Integral expressions for the asymptotic bias of the estimator under a unit root and for the expectation of the limit dis ...

Some Simple Remarks on an Autoregressive Scheme and an Implied Problem

Abstract: Nonminimum phase autoregressive schemes are considered in the context of the problem of determining a stationary process that satisfies a possibly nonlinear autoregressive system of equations. It's noted that in most solutions there is an implicit assumption that the independent random variables generating the process are independent of the past of the process. This is not true of the non-minimum phase schemes. A simple scheme that has a characteristic polynomial with roots inside and outside the unit disc in the complex plane is discussed.

On guaranteed estimation of the mean of an autoregressive process

Abstract: This paper considers the problem of sequential point estimation of the mean of a stable autoregressive process with unknown scale and autoregressive parameters. The construction of a sequential procedure makes use of special stopping rules and some modifications of least-squares estimates. The procedure enables estimating the mean with prescribed mean-square accuracy uniformly in nuisance parameters. The uniform asymptotic normality and the asymptotic minimaxity of the sequential estimate are established. The asymptotic formula for the mean sample size is obtained.