Showing papers on "STAR model published in 1993"

Exactly median-unbiased estimation of first order autoregressive /unit root models

Abstract: First-order autoregressive/unit root models with independent identically distributed normal errors are considered, including those without an intercept, those with an intercept, and those with an intercept and time trend. The autoregressive parameter is allowed to lie in the interval (-1, 1], which includes the unit root case. Exactly median-unbiased estimators and exact confidence intervals of the autoregressive parameter are introduced. Corresponding exactly median-unbiased estimators and exact confidence intervals are also provided for the impulse response function, the cumulative impulse response, and the half life of a unit shock. An unbiased model selection procedure is discussed. The introduced procedures are applied to several data series. Copyright 1993 by The Econometric Society.

Bayesian Inference and Prediction for Mean and Variance Shifts in Autoregressive Time Series

Abstract: This article is concerned with statistical inference and prediction of mean and variance changes in an autoregressive time series. We first extend the analysis of random mean-shift models to random variance-shift models. We then consider a method for predicting when a shift is about to occur. This involves appending to the autoregressive model a probit model for the probability that a shift occurs given a chosen set of explanatory variables. The basic computational tool we use in the proposed analysis is the Gibbs sampler. For illustration, we apply the analysis to several examples.

Bayesian threshold autoregressive models for nonlinear time series

Abstract: . This paper provides a Bayesian approach to statistical inference in the threshold autoregressive model for time series. The exact posterior distribution of the delay and threshold parameters is derived, as is the multi-step-ahead predictive density. The proposed methods are applied to the Wolfe's sunspot and Canadian lynx data sets.

On bootstrap predictive inference for autoregressive processes

Abstract: . In this paper we consider bootstrap-based predictive inference for autoregressive processes of order p. We consider both unconditional inference and inference conditional on the last p observed values. We make two contributions. Our first contribution is to point out the best way to apply the bootstrap to unconditional predictive inference when the process is Gaussian. Now, it may be argued that predictive inference for autoregressive processes of order p should be carried out conditional on the last p observed values. When the process is Gaussian, a bootstrap predictive inference conditional on the last p observed values is conveniently computed by ‘running’ the same autoregressive process backwards in time. This procedure is inappropriate for non-Gaussian autoregressive processes. Our second (and more important) contribution is to present a method (which is not computationally burdensome) for the computation of a bootstrap predictive inference for a non-Gaussian autoregressive process of order p conditional on the last p observed values.

Exploring relationships between semi-variogram and spatial autoregressive models

Abstract: This paper seeks to continue the building of a common foundation for spatial statistics and geostatistics. Equations from the conditional autoregressive (CAR) model of spatial statistics for estimating missing geo-referenced data have been found to be exactly those best linear unbiased estimates obtained with the exponential semi-variogram model of kriging, but in terms of the inverse covariance matrix rather than the covariance matrix itself. Further articulation of such relations, between the moving average (MA) and simultaneous autoregressive (SAR) or autoregressive response (AR) models of spatial statistics, and, respectively, the linear and Gaussian semi-variogram models of kriging, is outlined. The exploratory graphical and numerical work summarized in this paper indicates the following: (a) there is evidence to pair the moving average and linear models; (b) the simultaneous autoregressive and autoregressive response model pair with a Bessel function (modified of the second kind and order one) rather than the Gaussian semi-variogram model; (c) both specification error and measurement error can give rise to the nugget effect discussed in geostatistics; (d) restricting estimation to a geographic subregion introduces edge effects that increasingly bias semi-variogram model parameter estimates as the degree of spatial autocorrelation increases toward its upper limit; and (e) the theoretical spectral density function for a simultaneous autoregressive model is a direct extension of that for the conditional autoregressive model.

Modeling exchange rate dynamics: Non-linear dependence and thick tails

Abstract: This paper illustrates a new approach to the statistical modeling of non-linear dependence and leptokurtosis in exchange rate data. The student's t autoregressive model withdynamic heteroskedasticity (STAR) of spanos (1992) is shown to provide a parsimonious and statistically adequate representation of the probabilistic information in exchange rate data. For the STAR model, volatility predictions are formed via a sequentially updated weighting scheme which uses all the past history of the series. The estimated STAR models are shown to statistically dominate alternative ARCH-type formulations and suggest that volatility predictions are not necessarily as large or as variable as other models indicate.

Time series modeling of heart rate dynamics

Abstract: Autoregressive (AR), autoregressive-moving average (ARMA), bilinear (BL), and polynomial autoregressive (PAR) models were fit to heart rate time series obtained from 9 subjects in the supine position. For each data set and model structure, model order was determined by the Akaike Information Criteria (AIC). For all data sets, the nonlinear BL model had a lower residual variance and AIC compared to AR models. In most cases, BL models provided a better fit to the data than either ARMA or PAR models. For most data sets, the nonlinear BL model provides a more accurate representation of HR dynamics compared to the other model structures tested. >

Level : the l-1.4 program for bc-gauheseq regressions - box-cox generalized autoregressive heteroskedastic single equation models

Abstract: L-2.0 is a program designed to deal with the specification of the functional form in the generalized single-equation regression model where the functional form of heteroskedasticity of the residuals, which may also be autocorrelated using an R-Koyck process for each autoregressive order considered, can be estimated. This process is the analog of the usual Koyck transformation on a time series, but extended to a matrix R which is called a contiguity matrix in the context of spatial econometrics and which can be constructed according to any set of rule defined or DIRECTED by the analyst. For each order of correlation l, the R-Koyck process only adds to the usual autoregressive parameter pl a proximity parameter pie-l which measures the relative weight of close and remote neighbors in an infinite distributed lag structure. A maximum likelihood procedure is used to estimate jointly all the parameters including the regression coefficients, the coefficients in the heteroskedasticity function, the autocorrelation and proximity parameters as well as those of the Box-Cox transformations on the dependent, independent and heteroskedasdicity variables.(A)

A note on arma model parameter redundancy

Abstract: . A simple condition expressed directly in terms of the autoregressive moving-average model parameters is given for determining autoregressive moving-average model redundancy.

Identification of Autoregressive Signals Observed in Noise

Abstract: This paper presents an asymptotically unbissed estimator autoregressive parameters from noisy observations. The key ingredient in the present method in that a new and simple scheme for estimation of the variance of the white a measurement noie is developed. This estimated variance is then used in conjunction with the known technique for elimination of the least-squares estimation bias when the noise statistics are known a priori. The properties of the method are illustrated by means of some simulated examples.

Computing Theoretical Autocovariances of Multivariate Autoregressive Moving Average Models by Using a Block Levinson Method

Abstract: A closed form expression relating the theoretical autocovariances of a multivariate autoregressive moving average (ARMA) model to the ARMA parameters in terms of a system of linear equations has been presented recently. Using this result and the special Hankel plus Toeplitz structure of the coefficient matrix obtained after suitable partitioning, this paper presents a method for computing multivariate autocovariance functions that is based on a block Levinson procedure. The method is particularly advantageous for models with high order autoregressive components and/or a large number of variables

Parametric estimate of multivariate autoregressive models with conditional heterocovariance matrix errors

Abstract: This paper establish a class of multiple autoregressive models with conditional hetero-covariance matrix (MARCH) Conditions for the stationariness of the MARCH models arederived The consistency and the asymptotic normality of the least squares (LS) estimatorand the maximum likelihood (ML) estimator are presented

Multivariate autoregressive techniques for constructing confidence regions on the mean vector

Abstract: We develop a method for constructing confidence regions on the mean vectors of multivariate processes that is based on a vector autoregressive VAR representation of the data-generating process. A confidence-region-construction algorithm for a general autoregressive model is given. We establish the asymptotic validity of the confidence-region estimator that is, the exact achievement of nominal coverage probability as the sample size tends to infinity when the output process is a stationary vector autoregressive process of known, finite order. With respect to confidence-region volume, coverage probability, and execution time, we carry out an experimental performance comparison of VAR versus the methods of Bonferroni Batch Means BBM, Multivariate Batch Means MBM, and Multivariate Spectral Analysis SPA. The experimental results indicate that i VAR delivered confidence regions with the smallest volume; ii BBM delivered confidence regions with the largest volume, the highest coverage and the smallest execution time; iii in small samples, all of the methods might yield confidence-region estimators whose coverage differs significantly from the nominal level; and iv in large samples for which the sample autocorrelation function indicates a vector autoregressive dependence structure, VAR is a viable technique for simulation output analysis.

Robust autoregressive modelling through higher order spectral estimation techniques with applications to mammography

Abstract: The research work reported in this paper is concerned with the use of higher order spectral estimation techniques as a means to deriving the parameters of two dimensional autoregressive (AR) models. Image analysis is examined front a higher order statistical perspective and in the context of noise. The objective is to develop analysis techniques through which robust autoregressive parameter estimation is accomplished. The approach taken involves the use of 2-D AR models derived from third order cumulants. The directivity of the cumulant space influences the AR parameter estimation in a decisive manner. The specific application of the developed methods is in mammography, an area in which it is very difficult to discern the appropriate features. The results show significant discriminating gains through such techniques. >

Estimation for regressive and autoregressive models with non‐negative residual errors

Abstract: . The parameter estimation problems for regressive and autoregressive models are investigated. A new procedure is proposed which differs from the least squares method. Theorems relating to the rate of almost sure convergence of the new estimators are formulated. Some simulation results are also shown. With these convergent rates and simulation results a clear comparison of the new estimator with the least squares estimator is obtained.

Bootstrap tests for unit root AR(1) models

Abstract: In this paper, we propose bootstrap tests for unit roots in first-order autoregressive models. We provide the bootstrap functional limit theory needed to prove the asymptotic validity of these tests both for independent and autoregressive errors; in this case, the usual corrections due to innovations dependence can be avoided. We also present a power empirical study comparing these tests with existing alternative methods.

A Note on Prediction and an Autoregressive Sequence

Abstract: Prediction for a first order possibly nonGaus-sian sequence is considered. Remarks are made about prediction with time increasing and with time reversed.

Random coefficient autoregressive loss reserving

Abstract: A wellknown autoregressive model for loss reserving is modified by assuming a random instead of a deterministic coefficient. In the model an optimal method for predicting the loss development is derived.

Recursive estimation in autoregressive models with additive outliers

Abstract: This work deals with recursive robust estimation in autoregressive models that are contaminated by additive outliers. The importance of such procedures in applied time series is obvious: (i) the recursive character of the estimation allows to treat time series in real time (on-line) updating previous estimates by means of simple calculations after delivering new observations; (ii) robustness of the estimation procedures makes them insensitive to outlied observations that can distort significantly results of classical non-robust estimation procedures (the additive outliers have also unpleasant consequences for forecasting, see e.g. [10], [14]). The autoregressive model of the order p with additive outliers denoted as AOAR(p) has the form yt = Xt + Vt, (1A) where xt (pixt-i + ••• + (fpxt-p +£t (1.2)

Non-Gaussian autoregressive moving average processes.

Abstract: Non-Gaussian stationary autoregressive moving average sequences are considered. Under conditions concerning smoothness and positivity of the density function of the independent random variables generating the sequence, asymptotically efficient methods for the estimation of unknown coefficients of the model are described. The main interest is in nonminimum-phase models.