Showing papers on "STAR model published in 1981"

Modeling Multiple Time Series with Applications

Abstract: An approach to the modeling and analysis of multiple time series is proposed. Properties of a class of vector autoregressive moving average models are discussed. Modeling procedures consisting of tentative specification, estimation, and diagnostic checking are outlined and illustrated by three real examples.

Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model

Abstract: SUMMARY The behaviour of nonlinear deterministic vibrations has been studied by many authors, and may typically include such features as jump phenomena and limit cycles. Nonlinear random vibrations in continuous time have also been studied and these may commonly give rise to the phenomenon of amplitude-dependent frequency. A discrete time series model is introduced, which may be demonstrated to have properties similar to those of nonlinear random vibrations. This model is of autoregressive form with amplitudedependent coefficients and may be estimated using an extension of a method for estimating linear time series models. The model is fitted to the Canadian lynx data and demonstrates that it may be possible to regard the periodic behaviour of this series as being generated by some underlying self-exciting mechanism.

A new autoregressive time series model in exponential variables (NEAR(1))

Abstract: : A new time series model for exponential variables having first order autoregressive structure is presented. Unlike the recently studied standard autoregressive model in exponential variables (EAR(1)), runs of constantly scaled values are avoidable, and the two parameter structure allows some adjustment of time nonreversibility effects in sample path behavior. The model is further developed by the use of cross-coupling and antithetic ideas to allow negative dependency. Joint distributions and autocorrelations are investigated. A transformed version of the model has a uniform marginal distribution and its correlation and regression structures are also obtained. Estimation aspects of the models are briefly considered. (Author)

Estimation of Time Series Models in the Presence of Missing Data

Abstract: A method is proposed for the estimation of models for discrete time series in the presence of missing data. Some justification is given for the use of this method over alternatives; the choice of estimator is likely to be governed by the pattern of missing data, the nature of the time series model, and computational considerations. The method's performance in estimating simple models is studied by simulations, and it is applied to a time series of pollution levels containing some missing observations.

A Limit Theorem for the Maximum of Autoregressive Processes with Uniform Marginal Distributions

Abstract: A class of first-order autoregressive processes is given for which the extreme value limit theorems of Loynes and Leadbetter do not apply. A limit theorem is derived for these processes that depends on the parameter $r$, an integer greater than or equal to 2.

Effects of Not Knowing the Order of an Autoregressive Process on the Mean Squared Error of Prediction—I

Abstract: Given a realization of T consecutive observations of an autoregressive process, x, of unknown order m, a process of an arbitrary order p is assumed to be fitted for predicting the future values of another process [xtilde](t), where [xtilde](t) is independent of xt but otherwise has identical probabilistic structure. The mean squared error of prediction when the autoregressive coefficients are estimated by least squares is obtained to terms of order T -1. The bias in estimating the autoregressive coefficients is examined. The results are illustrated for three processes with m = 2 by considering fitting of a process with p = 1.

An Optimal Autoregressive Spectral Estimate

Abstract: An asymptotic lower bound is obtained for the integrated relative squared error of autoregressive spectral estimate when the order of autoregression is selected. The bound is attained in the limit by the same selection as has been proposed for prediction.

Autoregressive Modeling And Spectral Analysis of Array Data in the Plane

Abstract: While a number of efficient statistical techniques exist for analysis of data recorded in time, this is to a lesser degree the case for spatial data such as seismological array data, magnetic data, or gravity data. In this paper we will be concerned with a new type of analysis for spatial variables. We will study autoregressive series F(x1, x2) in the plane defined by a unilateral expansion in the lower left-hand quadrant determined by the point (x1, x2). Using artificial data, we consider the problems of identification, fitting, and estimation for such series. Furthermore, we will indicate how one-quadrant autoregressive models may be used for approximating more general types of spatial data. In this connection we discuss the problem of stability and two criteria for determining the order (p1, p2) of the approximating model. Special consideration is given to the use of autoregressive approximations in spatial spectral density estimation and illustrations are given both for autoregressive series in the plane and for harmonic series. Based on our results we tentatively conclude that, as in the time series case, there are situations for data in the plane where autoregressive procedures are superior to the conventional spectral analysis methods.

Parsimony and Its Importance in Time Series Forecasting

Abstract: The effect of nonparsimonious time series models is studied by deriving the approximate variance of the one-step-ahead forecast error. Also, in a simulation experiment we show the loss in forecast accuracy that can result when a first-order moving-average model is approximated by a nonparsimonious autoregressive model.

Non-linear threshold autoregressive models for non-linear random vibrations

Abstract: Time series models for non-linear random vibrations are discussed from the viewpoint of the specification of the dynamics of the damping and restoring force of vibrations, and a non-linear threshold autoregressive model is introduced. Typical non-linear phenomena of vibrations are demonstrated using the models. Stationarity conditions and some structural aspects of the model are briefly discussed. Applications of the model in the statistical analysis of real data are also shown with numerical results.

Replicated observations of low order autoregressive time series

Abstract: . Independent replicates of first and second order autoregressive stationary time series are considered. Maximum likelihood estimates are studied with special emphasis on asymptotics when the number of replicates tends to infinity and the length of each replicate is fixed.

Properties and applications of Gaussian autoregressive processes in detection theory (Corresp.)

Abstract: A sufficient statistic, having dimension 3p+1 , is constructed for p th order stationary Gaussian autoregressive processes. A computationally efficient discriminator based on the statistic is obtained. A derivation of the whitening filter-correlator detector for known signals in autoregressive noise is presented. A new formula for the signal-to-noise ratio of an optimal detector for a constant signal in stationary correlated Gaussian noise is presented and used to help study the nature of autoregressive approximations to more general processes in this application.

Autoregressive Moving Average Spectral Estimation: A Model Equation Error Procedure

Abstract: A procedure is presented for generating an autoregressive moving average (ARMA) spectral model of a stationary time series based upon a finite set of time series' observations. The ARMA model's autoregressive coefficients are estimated by minimizing a quadratic function of a set of basic error terms. In examples treated to date, this method has demonstrated an exceptional ability in resolving closely spaced narrow band signals in a low signal-to-noise environment where other procedures such as the maximum entropy method often fail. Its effectiveness on other classes of time series also shows promise and a more general evaluation is presently being conducted. With this in mind, the new ARMA procedure promises to be an important spectral estimation tool.

Asymptotic distribution of the order selected by AIC in multivariate autoregressive model fitting

Abstract: First, statistical properties of partial autocorrelation matrices of multivariate autoregressive processes are briefly reviewed. Then, using the result, we derive the asymptotic distribution of the order selected by Akaike's information criterion. Contrary to our intuition, the asymptotic probability of selecting the correct order tends to 1 as the number of the variates becomes large.

On estimating the orders of an autoregressive process

Abstract: A method is proposed for estimating the orders of an autoregressive process. The orders can be estimated by determining whether or not the product of the determinantal ratio of a correlation function matrix and that of another correlation function matrix is 1.

Efficient solution of Lyapunov equation for matrix autoregressive models and its application to the inverse Levinson problem

Abstract: A novel efficient method for solving the discrete Lyapunov equation is presented, for the case where a matrix autoregressive model is assumed. This leads to an efficient procedure for solving the inverse Levinson problem, namely - constructing ladder realizations for given AR models (rather than for given covariance sequences). The method is based on a recently described method of inverting matrices that are sums of block-Toeplitz and block-Hankel matrices. The procedure is then shown to yield a stability test for the given autoregressive model.

Asymptotic Normality of Autoregressive Parameter Estimates for Mixed Time Series

Abstract: : In this report it is shown for mixed time series, a series generated by an autoregressive moving-average (ARMA) process or by an autoregressive process observed in additive white noise (AR+N), that estimates of the autogressive (AR) parameters are asymptotically multivariate jointly normal with zero mean and finite covariance matrix The structure of the asymptotic covariance matrix is evaluated for both types of mixed time series (Author)

On the stationarity of multiple autoregressive approximants: theory and algorithms

Abstract: Numerical methods are presented for determining the stability of a multiple autoregressive scheme. The question of stability is important in prediction theory, and the methods for determining stability are such that they yield information which is very useful for fitting time series models to data.

Identification and spectral estimation of noisy multivariate autoregressive processes

Abstract: Large sample identification spectral estimation problems of a noisy multivariate autoregressive process are solved independent of the probability law governing the observed data. Several different representations of a noisy multivariate autoregressive process are studied and linked to the properties of the block Toeplitz and Hankel matrices derived from the auto-correlation function of the process. Under a simple condition, the parameter estimators for the auto-regressive coefficients and noise statistics derived by solving block Toeplitz and Hankel matrix equations are shown to be strongly consistent. Asymptotic distributions of the parameter estimators are derived and used to compute the confidence bounds of the spectral estimators. For order selection, the Akaike Information Criterion (AIC) is modified into a form independent of the probability law of the observed data.

Comparison of Two Autoregressive Models for Monthly Stream Flow Generation

Abstract: Two autoregressive models for monthly stream flow generation are compared based on the reproduction of the historical record in terms of several important statistics such as the mean, standard deviation, skewness coefficient, correlation coefficient, and the reservoir storage components. In the comparison, both theoretical considerations and practical applications are employed to evaluate the performance of each model.

Computational problems in autoregressive moving average (ARMA) models

Abstract: The choice of the sampling interval and the selection of the order of the model in time series analysis are considered. Band limited (up to 15 Hz) random torque perturbations are applied to the human ankle joint. The applied torque input, the angular rotation output, and the electromyographic activity using surface electrodes from the extensor and flexor muscles of the ankle joint are recorded. Autoregressive moving average models are developed. A parameter constraining technique is applied to develop more reliable models. The asymptotic behavior of the system must be taken into account during parameter optimization to develop predictive models.