Showing papers on "STAR model published in 1991"

Estimation of the arrival times of seismic waves by multivariate time series model

Abstract: A computationally efficient procedure was developed for the fitting of many multivariate locally stationary autoregressive models. The details of the Householder method for fitting multivariate autoregressive model and multivariate locally stationary autoregressive model (MLSAR model) are shown. The proposed procedure is quite efficient in both accuracy and computation. The amount of computation is bounded by a multiple of Nm 2 with N being the data length and m the highest model order, and does not depend on the number of models checked. This facilitates the precise estimation of the change point of the AR model. Based on the AICs' of the fitted MLSAR models and Akaike's definition of the likelihood of the models, a method of evaluating the posterior distribution of the change point of the AR model is also presented. The proposed procedure is, in particular, useful for the estimation of the arrival time of the S wave of a microearthquake. To illustrate the usefulness of the proposed procedure, the seismograms of the foreshocks of the 1982 Urakawa-Oki Earthquake were analyzed. These data sets have been registered to AISM Data Library and the readers of this Journal can access to them by the method described in this issue.

On the Ergodicity of Tar(1) Processes

Abstract: This paper establishes a necessary and sufficient condition for geometrical ergodicity for the general first-order threshold autoregressive processes. This is achieved by investigating the nonlinear dynamic behavior generated by the delay parameter of a threshold model. The ergodic region turns out to be unbounded which is different from that of a linear process.

Estimating Orthogonal Impulse Responses via Vector Autoregressive Models

Abstract: Impulse response functions from time series models are standard tools for analyzing the relationship between economic variables. The asymptotic distribution of orthogonalized impulse responses is derived under the assumption that finite order vector autoregressive (VAR) models are fitted to time series generated by possibly infinite order processes. The resulting asymptotic distributions of forecast error variance decompositions are also given.

Levinson-Durbin-type algorithms for continuous-time autoregressive models and applications

Abstract: Different forms of Levinson-Durbin-type algorithms, which relate the coefficients of a continuous-time autoregressive model to the residual variances of certain regressions or their ratios, are derived. The algorithms provide parametrizations of the model by a finite set of positive numbers. They can be used for computing the covariance structure of the process, for testing the validity of such a structure, and for stability testing.

Convergence of Moments of Least Squares Estimators for the Coefficients of an Autoregressive Process of Unknown Order

Abstract: Given a realization of $T$ consecutive observations of a stationary autoregressive process of unknown, possibly infinite, order $m$, it is assumed that a process of arbitrary finite order $p$ is fitted by least squares. Under appropriate conditions it is known that the estimators of the autoregressive coefficients are asymptotically normal. The question considered here is whether the moments of the (scaled) estimators converge, as $T \rightarrow \infty$, to the moments of their asymptotic distribution. We establish a general result for stationary processes (valid, in particular, in the Gaussian case) which is sufficient to imply this convergence.

Spectral analysis based on the canonical autoregressive decomposition

Abstract: Time series modeling as the sum of an autoregressive (AR) process and sinusoids is proposed. When the AR model order is infinite, it is called the canonical autoregressive decomposition and is equivalent to the Wold decomposition. Maximum likelihood estimation of the sinusoidal and AR parameters is shown to require minimization with respect to only the unknown frequencies. Although the estimation problem is nonlinear in the sinusoidal amplitudes and AR parameters, it is reduced to a linear least-squares problem by using a nonlinear parameter transformation. Similar results are derived for AR processes in polynomial or polynomial-times-exponential signals. Applications include frequency estimation/transient analysis in unknown colored noise. >

Texture model validation using higher-order statistics

Abstract: Higher-than-second-order statistics are used to derive and implement 2-D Gaussianity and linearity tests which validate the assumptions of random models which characterize texture analysis and synthesis in terms of first- and second-order statistics. The non-redundant region of the 2-D cumulant sequence and its Fourier transform, the bispectrum, are correctly defined and proven. General non-minimum phase and asymmetric non-causal AR (autoregressive) and ARMA (autoregressive moving average) models of textures are derived using cumulant statistics. Parameter estimators are obtained both by solving a set of linear equations and by minimizing a cumulant-matching criterion. Simulations on synthetic data are performed and the results of the higher-order analysis on real textures are reported. >

Threshold Autoregressive Modeling in continuous-time

Abstract: We have developed a procedure for identifying continuous time, self-exciting, threshold, autoregressive models and applied the procedure to several real data sets. The performance of the fitted threshold models to real data is discussed and compared with that of the fitted linear models.

A methodology for selecting subset autoregressive time series models

Abstract: . In time series modelling, subset models are often desirable, especially when the data exhibit some form of periodic behaviour with a range of different natural periods in terms of days, weeks, months and years. Recently, Hokstad proposed a method based on personal judgement for selecting the first tentative model to obtain the best subset autoregressive model. The subjective approach adopted in the Hokstad method is a disadvantage in building up a computer program which could automatically select the appropriate model of a given time series. In this paper, we propose overcoming this disadvantage by employing the inverse autocorrelation function to select the first tentative model. In addition to sets of synthetic data, some well-known real series such as the D, E and F series of Box and Jenkins and the Canadian lynx data are analysed to validate the proposed method. The results indicate that the method can successfully detect the true model for a given time series.

Stable Vector Autoregressive Processes

Abstract: In this chapter, the basic, stationary finite order vector autoregressive (VAR) model will be introduced. Some important properties will be discussed. The main uses of vector autoregressive models are forecasting and structural analysis. These two uses will be considered in Sections 2.2 and 2.3. Throughout this chapter, the model of interest is assumed to be known. Although this assumption is unrealistic in practice, it helps to see the problems related to VAR models without contamination by estimation and specification issues. The latter two aspects of an analysis will be treated in detail in subsequent chapters.

Shape recognition using a nonstationary autoregressive hidden Markov model

Abstract: An autoregressive hidden Markov model (ARHMM) is introduced for the analysis and classification of shape boundaries. The principal features of this model are: an autoregressive shape representation that is invariant to scaling, rotation and translation; a nonstationary contour characterization providing descriptions of abrupt and gradual changes in complex boundaries typical in image analysis; and a hidden Markov model (HMM) for description of such changes. An experimental study is presented which demonstrates the model's effectiveness. >

Almost sure convergence analysis of autoregressive spectral estimation in additive noise

Abstract: The almost sure convergence properties of autoregressive spectral estimates from noisy observations are derived. Sharp rates of almost sure convergence are established for the estimates of the autoregressive parameters, innovation variance, and spectral density function of the signal process. The distributions of the signal and noise processes are arbitrary. >

Model order estimation of 2D autoregressive processes

Abstract: The work on model order estimation by Bayesian predictive densities of 1-D real autoregressive processes is extended to 2-D complex autoregressive processes. According to the procedure, the best model is the one which most accurately predicts the data yet to be observed and whose parameters are estimated from the data already observed. The derivation steps of the algorithm are demonstrated and verified by computer simulations. The computer simulations show that the algorithm based on this approach yields good results. >

Measuring Influence in Dynamic Regression Models

Abstract: This article presents a methodology for building measures of influence in regression models with time series data. We introduce statistics that measure the influence of each observation on the parameter estimates and on the forecasts. These statistics take into account the autocorrelation of the sample. The first statistic can be decomposed to measure the change in the univariate autoregressive integrated moving average parameters, the transfer-function parameters, and the interaction between both. For independent data, they reduced to the D statistic considered by Cook in the standard regression model. These statistics can be easily computed using standard time series software. Their performance is analyzed in an example in which they are shown to be useful in identifying important events, such as additive outliers and trend shifts, in time series data.

Identification of Autoregressive Process Model by the Extended Kalman Filter

Abstract: Much attention has been paid by many researchers to stochastic time domain models such as autoregressive and moving average (ARMA), autoregressive (AR) or moving average (MA) models that can be used in the idealization of earthquake ground motions, since by these models not only sample input waves but also response waves may be recursively simulated and consequently it has been found that they are effective models used in the field of stochastic dynamics [1]~ [9]

Robust estimation of a change point in the properties of autoregressive 'sequences

Abstract: The problem of determination of a change point in the properties of autoregressive sequences with unknown distri­ bution is analysed Two robust algorithms for the estimation of a change point when the distribution is symmetric and asymmetric are presented

Detecting abrupt changes in ARMA signals

Abstract: The authors describe a novel method for detecting changes in time series represented by autoregressive moving average models, based on a method by Nikiforov (see I.V. Nikiforov, 1986, I.V. Nikiforov and I.N. Tikhohov, 1986, and A.F. Kushnin et al., 1983). They review previous work by Nikiforov, describing a derivation of the sequential change detection method. The application of Nikiforov's method to autoregressive models and its extension to ARMA models are described. Examples of the algorithm's performance are given. >

Two-dimensional boundary inspection using autoregressive model

Abstract: In this paper a new procedure is presented which extracts two dimensional " time" series data containing maximum information about a closed boundary. The " time" series data is used for estimation of autoregressive model parameters. The extracted data makes autoregressive parameters to lie in closer space partitions. The use of two dimensional data overcomes the limitation of loss of phase information faced in one dimensional autoregressive models. A bivanate circular autoregressive model is used to represent the closed boundary data. The parameter extraction of the model is camed out by residual method which produces a stationary estimation. The model parameters are invariant to rotation translation scaling and choice of starting point on the boundary. The maximum information about the closed boundary and model parameters invariant to said transformations makes the procedure effective for inspection of planar objects.© (1991) COPYRIGHT SPIE--The International Society for Optical Engineering. Downloading of the abstract is permitted for personal use only.