Showing papers on "STAR model published in 1990"

Comparing Information in Forecasts from Econometric Models

Abstract: The information contained in one model's forecast compared to that in another can be assessed from a regression of actual values on predicted values from the two models. The authors do this for forecasts of real GNP growth rates for different pairs of models. The models include a structural model (the Fair model), various versions of the vector autoregressive model, and various versions of a model the authors call the "autoregressive components" model. The authors' procedure requires that forecasts make no use of future information and they have been careful to try to insure this, including using the version of the Fair model that existed in 1976, the beginning of their test period. Copyright 1990 by American Economic Association.

Asymptotic Distributions of Impulse Response Functions and Forecast Error Variance Decompositions of Vector Autoregressive Models

Abstract: In recent years, vector autoregressive models have become standard tools for economic analyses. Impulse response functions and forecast error variance decompositions are usually computed from these models in order to investigate the interrelationships within the system. However, sometimes no measures of estimation uncertainty are provided by authors. One reason may be that the relevant asymptotic distribution theory is distributed over various publications. In this article, the available results are summarized and the missing links are provided in order to facilitate the computation of standard errors and test statistics. Copyright 1990 by MIT Press.

First-order autoregressive models for gamma and exponential processes

Abstract: In this paper we propose an autoregressive representation for a particular type of stationary Gamma(θ –1, v) process whose n-dimensional joint distributions have Laplace transform |In + θSnVn | –v , where Sn = diag(s 1, · ··, sn ), Vn is an n × n positive definite matrix with elements υ ij = p|i–j|i 2, i, j = 1, ···, n and p is the lag-1 autocorrelation of the gamma process. We also generalize the two-parameter NEAR(1) model of Lawrance and Lewis (1981) to an exponential first-order autoregressive model with three parameters. The correlation structure and higher-order properties of the two proposed models are also given.

A general approach to the limiting distribution for estimators in time series regression with nonstable autoregressive errors

Abstract: We consider the time series regression model where the error term follows a nonstable autoregressive process, and present a general approach for deriving the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads us to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. Our methodology is illustrated and percent points are tabulated. The present approach produces a good approximation method for the finite sample distribution and also provides an accurate evaluation of the limiting powers of some unit root tests under a sequence of local alternatives.

Repeated Time Series Analysis of ARIMA–Noise Models

Abstract: This article develops a theory and methodology for repeated time series (RTS) measurements on autoregressive integrated moving average–noise (ARIMAN) process. The theory enables us to relax the normality assumption in the ARIMAN model and to identify models for each component series of the process. We discuss the properties, estimation, and forecasting of RTS ARIMAN models and illustrate with examples.

Gamma‐Autoregressive Models for Stream‐Flow Simulation

Abstract: Since hydrologic time series in general, and stream‐flow series, in particular, are dependent and not normally distributed, use of the classical autoregressive and moving average (ARMA) models to represent such series requires transformation of the original series into normal before applying the model. On the other hand, gamma‐autoregressive (GAR) models assume that the underlying series is dependent with a gamma marginal distribution and the models do not require variable transformation. However, the models require the estimation of certain statistics generally leading to biased estimates of the model parameters. This paper presents a procedure for bias correction, based on computer simulation studies, applicable for estimating parameters of GAR(l) models. Applications of the proposed procedure to annual stream‐flow series of several rivers are included. The GAR(l) model, when used in conjunction with the proposed estimation procedure, is an attractive alternative for synthetic stream‐flow simulation, is...

The growth curve model with an autoregressive covariance structure

Abstract: The growth curve model with an autoregressive covariance structure is considered. An iterative algorithm for finding the MLE's of the parameters in the model is presented, based on the modified likelihood equations. Asymptotic distributions of the MLE's are obtained when the sample size is large. A likelihood ratio statistic for testing the autoregressive covariance structure is presented.

Efficient computation of autoregressive estimates through a sufficient statistic

Abstract: It is shown that various time reversible methods, in particular, Burg's algorithm, for autoregressive model estimation may be performed through the use of a simple sufficient statistic. This provides more efficient computation of the estimators. >

Bayesian forecasting for AR(1) models with normal coefficients

Abstract: This paper presents a Bayesian solution to the problem of time series forecasting, for the case in which the generating process is an autoregressive of order one, with a normal random coefficient. The proposed procedure is based on the predictive density of the future observation. Conjugate priors are used for some parameters, while improper vague priors are used for others.

Sequential estimation of the mean of a first-order autoregressive process

Abstract: This paper considers the problem of sequential point estimation, under an appropriate loss function, of the location parameter when the errors form an autoregressive process with unknown scale and autoregressive parameters, A sequential procedure is developed and an asymptotic second order expansion is provided for the difference between expected stopping time and the optimal fixed sample size procedure. Also, the asymptotic normality of the stopping time is proved. Though the procedure Is asymptotically risk efficient, it. Is not clear whether it has bounded regret.

Simultaneous confidence bands for the spectral estimate of two-channel autoregressive processes

Abstract: . In this paper we derive simultaneous confidence bands for the maximum entropy method spectral estimate of two-channel autoregressive (AR) processes by using the asymptotic theory of the estimation of periodic AR processes.

Reversed residuals in autoregressive time series analysis

Abstract: Both linear and non-linear time series can have directional features which can be used to enhance the modelling and investigation of linear or non-linear autoregressive statistical models For this purpose, reversed pth-order residuals are introduced Cross-correlations of residuals and squared reversed residuals allow extensions of current model identification ideas Quadratic types of partial autocorrelation functions are introduced to assess dependence associated with non-linear models which nevertheless have linear autoregressive correlation structures The use of these residuals and their cross-correlation functions is exemplified empirically on some deseasonalized river flow data for which a first-order autoregressive model is a satisfactory second-order fit Parallel theoretical computations are undertaken for the non-linear first-order random coefficient autoregressive model and comparisons are made While the data are shown to be strongly non-linear, their correlational signatures are found to be convincingly different from those of a first-order autoregressive model with random coefficients

Hypothesis testing for nearly nonstationary autoregressive models

Abstract: In this paper, a new asymptotic theory is developed for nearly nonstationary autoregressive processes of first and second order A general model is investigated and a hypothesis testing method is proposed for it In important special cases the limit distribution of the test statistic can be expressed in terms of functionals of simple diffusion processes

Selecting order for general autoregressive models by minimum description length

Abstract: . In this paper we put forward some criteria for estimating the order for general autoregressive (AR) models (i.e. AR models without any constraint about the roots of the characteristic polynomial) according to the minimum description length. Different criteria are given for different kinds of AR models because the convergence rates are different. It is proved that all the estimates for the order are strongly consistent.

Identification of an autoregressive model for multivariate one-dimensional nonstationary gaussian random processes

Abstract: Identification problems on coefficient matrices of an autoregressive model for multivariate and one-dimensional nonstationary Gaussian random processes are investigated, by appling the Kalman filter incorporated with a weighted global iteration.The major contributions of the paper are the use of Kalman filter for estimating time varying model parameters and the development of an effective method in terms of computer time.The results indicate that the coefficients of this recursive equation are identified extremely well at the stage of their stable convergency to optimal ones.

A note on square root filtering for vector autoregressive moving‐average models

Abstract: . A simplified version of the square root Kalman filter is obtained for a vector autoregressive moving-average (VARMA) model. The algorithm is computationally more efficient that the standard square root algorithm and its output can be used to compute the likelihood of a VARMA model accurately.

On bates of convergence in the central limit theorem for parameter estimation in general autoregressive model

Abstract: This paper explores the rate at which the estimates of the unknown parameters in an autoregressive process converge in distribution to the normal variate

Bias of Autoregressive Spectral Estimators

Abstract: Bias of the least squares estimator of the log of the spectral density of an autoregression attenuates the peaks of the estimator. Under the assumption of an autoregressive generating process of known finite order, we obtain an expression for the order 1/T bias, where T is the sample length of the observed series. This approximation is a sum of several simple functions of the unknown coefficients. When the spectral density has sharp peaks, one of these functions dominates the bias. The attenuation from this dominant component can be substantial when the spectral peak is well defined, and several examples illustrate this effect. Since the integral of the order 1/T bias components that are frequency dependent is 0, unbiased estimation of entropy to this order is possible for autoregressive processes. These bias expressions extend to autoregressive models in which the mean is a polynomial function of time. Similar results obtain for the log of the Yule-Walker spectral estimator, for which the order ...

Nonminimum phase non-Gaussian autoregressive processes.

Abstract: The structure of non-Gaussian autoregressive schemes is described. Asymptotically efficient methods for the estimation of the coefficients of the models are described under appropriate conditions, some of which relate to smoothness and positivity of the density function f of the independent random variables generating the process. The principal interest is in nonminimum phase models.

Further comments on nonstationarity identification problems for autoregressive models

Abstract: Nonstationarity for autoregressive models is identified by giving the necessary and sufficient conditions for autoregressive models to be oscillatory. The criteria previously proposed to identify autoregressive models to be asymptotically stationary or nonstationary are improved and extended to general multidimensional autoregressive models. >

Modeling of random natural textures using a spatially variant multiplicative autoregressive model

Abstract: A spatially variant seasonal multiplicative autoregressive model which treats an image as an inhomogeneous random process with a nonstationary mean and possibly nonstationary covariance is introduced. The principal features of this model are the ability to guarantee stability online, efficient one-dimensional recursive parameter estimation and explicit coefficient representation necessary for classification and synthesis applications