Showing papers on "STAR model published in 1985"
TL;DR: In this paper, two structural time series models for annual observations are constructed in terms of trend, cycle, and irregular components, and the models are then estimated via the Kalman filter using data on five U.S. macroeconomic time series.
Abstract: Two structural time series models for annual observations are constructed in terms of trend, cycle, and irregular components. The models are then estimated via the Kalman filter using data on five U.S. macroeconomic time series. The results provide some interesting insights into the dynamic structure of the series, particularly with respect to cyclical behavior. At the same time, they illustrate the development of a model selection strategy for structural time series models.
660 citations
TL;DR: In this paper, various criteria for estimating the order of a vector autoregressive process are compared in a simulation study and Schwarz's BIC criterion chooses the correct order most often and leads to the smallest mean squared forecasting error in samples of the size usually available in practice.
Abstract: . Various criteria for estimating the order of a vector autoregressive process are compared in a simulation study. For the considered processes Schwarz's BIC criterion chooses the correct autoregressive order most often and leads to the smallest mean squared forecasting error in samples of the size usually available in practice.
338 citations
TL;DR: The signal modeling methodology is discussed and experimental results on speaker independent recognition of isolated digits are given and the potential use of the modeling technique for other applications are discussed.
Abstract: In this paper a signal modeling technique based upon finite mixture autoregressive probabilistic functions of Markov chains is developed and applied to the problem of speech recognition, particularly speaker-independent recognition of isolated digits. Two types of mixture probability densities are investigated: finite mixtures of Gaussian autoregressive densities (GAM) and nearest-neighbor partitioned finite mixtures of Gaussian autoregressive densities (PGAM). In the former (GAM), the observation density in each Markov state is simply a (stochastically constrained) weighted sum of Gaussian autoregressive densities, while in the latter (PGAM) it involves nearest-neighbor decoding which in effect, defines a set of partitions on the observation space. In this paper we discuss the signal modeling methodology and give experimental results on speaker independent recognition of isolated digits. We also discuss the potential use of the modeling technique for other applications.
332 citations
TL;DR: In this paper, an autoregressive model of finite order k fitted to a realization of length T is presented, and the consistency and asymptotic normality of the estimated autoregression coefficients are derived.
272 citations
TL;DR: In this paper, simple yet practically efficient conditions for the ergodicity of a Markov chain on a general state space have been developed, and they illustrate their application to non-linear time series models and, in particular, to random coefficient autoregressive models.
Abstract: . Simple yet practically efficient conditions for the ergodicity of a Markov chain on a general state space have recently been developed. We illustrate their application to non-linear time series models and, in particular, to random coefficient autoregressive models.
As well as ensuring the existence of a unique stationary distribution, geometric rates of convergence to stationarity are ensured. Moreover, sufficient conditions for the existence and convergence of moments can be determined by a closely related method. The latter conditions, in particular, are new.
199 citations
TL;DR: In this paper, the second-order moment structure of time series models is used to derive a canonical analysis in time series modelling and a canonical correlation approach for tentative order determination in building autoregressive moving average models is proposed.
Abstract: SUMMARY The second-order moment structure of time series models is used to derive a canonical analysis in time series modelling. Consistency properties of certain canonical correlations and the corresponding eigenvectors are shown. Based on these properties, a canonical correlation approach for tentative order determination in building autoregressivemoving average models is proposed. This approach can handle directly nonstationary as well as stationary processes and it also provides consistent estimates of the autoregressive parameters involved. The asymptotic distribution of the identification statistic is discussed.
119 citations
TL;DR: In this article, it was shown that the likelihood ratio of an autoregressive time series of finite order with a regression trend is asymptotically normal, which is used to derive the power of a test for positive correlation of the residuals under local auto-regression alternatives.
113 citations
TL;DR: In this article, an approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by analysis of a long series of wind velocity data which has first been detrended and then transformed into a stationary series with an exponential marginal distribution.
Abstract: : An approach to modelling and residual analysis of nonlinear autoregressive time series in exponential variables is presented; the approach is illustrated by analysis of a long series of wind velocity data which has first been detrended and then transformed into a stationary series with an exponential marginal distribution The stationary series is modelled with a newly developed type of second order autoregressive process with random coefficients, called the NEAR(2) model; it has a second order autoregressive correlation structure but is nonlinear because its coefficients are random The exponential distributional assumptions involved in this model highlight a very broad four parameter structure which combines five exponential random variables into a sixth exponential random variable; other applications of this structure are briefly considered Dependency in the NEAR(2) process not accounted for by standard autocorrelations is explored by developing a residual analysis for time series having autoregressive correlation structure; this involves defining linear uncorrelated residuals which are dependent, and then assessing this higher order dependence by standard time series computations Application of this residual analysis to the wind velocity data illustrates both the utility and difficulty of nonlinear time series modelling
104 citations
TL;DR: In this article, the effects of misspecification in stationary linear time series models when they fit a pth-order autoregressive model were investigated and the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain.
Abstract: This article investigates major effects of misspecification in stationary linear time series models when we fit a pth-order autoregressive model. The true model can be an autoregressive moving average model. We derive the formulas of bias and mean squared error (MSE) of the least squares estimator and the hth period ahead prediction MSE in the time domain. Contrary to previous studies, the process in estimation is not necessarily independent of the process in prediction, and the distribution of process is not necessarily Gaussian. We examine the effects of this dependence and nonnormality on prediction in misspecified models.
85 citations
TL;DR: In this article, the authors develop methods of objectively choosing a spectrum estimate from a general class C of available estimates, which can simultaneously include Blackman-Tukey and autoregressive estimates, so the statistician no longer need to choose one type or the other arbitrarily.
Abstract: I develop methods of objectively choosing a spectrum estimate from a general class C of available estimates. C can, for example, simultaneously include Blackman—Tukey and autoregressive estimates, so the statistician no longer needs to choose one type or the other arbitrarily. The methods work by extending the applicability of existing cross-validatory techniques through the introduction of generalized leave-out-one spectrum estimates. As special cases, I obtain new objective smoothness parameter selection methods for both autoregressive and Blackman—Tukey estimates. In a Monte Carlo study, I demonstrate the effectiveness of the particular methods that result from generalizing Wahba's CVMSE.
81 citations
TL;DR: A time-series model for Laplace (double-exponential) variables having second-order autoregressive structure (NLAR(2)) is presented and the autocorrelation function for the process is derived as well as third-order moments to further explore dependency in the process.
Abstract: A time-series model for Laplace (double-exponential) variables having second-order autoregressive structure (NLAR(2)) is presented. The model is Markovian and extends the second-order process in exponential variables, NEAR(2), to the case where the marginal distribution is Laplace. The properties of the Laplace distribution make it useful for modeling in some cases where the normal distribution is not appropriate. The time-series model has four parameters and is easily simulated. The autocorrelation function for the process is derived as well as third-order moments to further explore dependency in the process. The model can exhibit a broad range of positive and negative correlations and is partially time reversible. Joint distributions and the distribution of differences are presented for the first-order case NLAR(1).
TL;DR: In this article, Monte Carlo simulations are used to investigate the sampling distribution of the t statistic for the autoregressive parameter when its value is in the neighborhood of unity, and a small sigma asymptotic result is exploited in the construction of exact non-similar tests.
TL;DR: Three criteria for determining the order of autoregressive models are compared and a goodness-of-fit test derived from the runs test judges the adequacy of the autore progressive representation of the spectral structure of EEG data.
Abstract: A parametrization of the spectral structure of time series data is of great interest in many fields of science such as eleetroencephalography (EEG). Autoregressive processes offer such a representation. The problem is to find a parsimonious representation which fits the data well. Three criteria for determining the order of autoregressive models are, therefore, compared. A simulation is done for studying the consistency of these criteria. A goodness-of-fit test derived from the runs test judges the adequacy of the autoregressive representation of the spectral structure of EEG data. For neurophysiological and statistical reasons, autoregressive modeling in a restricted frequency domain is introduced.
TL;DR: It is shown that for Gaussian autoregressive processes, the two types of windows yield approximately the same mean-square error if the windows' parameters are properly chosen.
Abstract: Exact least-squares algorithms for autoregressive signals can be made to track time-varying parameters by using sliding windows on the data. Two common choices for such windows are the exponential one and the rectangular one. In this paper, it is shown that for Gaussian autoregressive processes, the two types of windows yield approximately the same mean-square error if the windows' parameters are properly chosen.
Abstract: SUMMARY Robust analogues of the Wald and the Rao score statistics are presented for testing composite hypotheses in time series models involving dependent observations. Asympto- tic efficiency and empirical power comparisons using moderate size samples are given for first-order autoregressive processes. Our method of robustifying the estimating equation gives a simple and unified approach which is useful in a large class of problems including regression with dependent errors, and autoregressive and moving average processes. Large-sample properties of the robust procedures are given for these processes. Standard methods of estimation and testing based on the likelihood function, least squares and moments are used extensively in the analysis of time series data. The performance of these methods is known to be sensitive to changes in the assumptions regarding the error distribution. Moreover, these procedures are affected adversely by the presence of outliers in the data. Robustified versions of the standard statistical procedures are now well documented in the case of independent observations; see Huber (1981) and references therein. Robust estimation for time series has been considered by several authors. Gastwirth & Rubin (1975) have discussed robust estimation of location parameters in the presence of autoregressive dependence. Denby & Martin (1979) and Martin (1980, 1982) have studied efficiency robustness of M-estimators for autoregressive processes. The recent survey article of Martin & Yohai (1985) gives a good review of the literature on robust estimation for autoregressive and moving average processes, and contains several references to published and as yet unpublished papers. Work on robust tests for time series, on the other hand, appears to be scarce. Large- sample tests based on the score and the Wald statistic for time series using the likelihood framework are well known; see, for example, Basawa, Billard & Srinivasan (1984). Generalizations of the score and the Wald statistics using arbitrary estimating functions in place of the likelihood function were introduced by Basawa (1985). In the present paper we use a similar approach to formulate robustified versions of the score and the Wald statistics in specific time series models. Our main aim is to give a simple general method of constructing robust score functions and robust M-estimators for time series models, and to discuss the efficiency of tests derived from this method. In ?2 we introduce robustified score and Wald statistics, and discuss their limit distributions both under the null and a sequence of alternative hypotheses. We also
TL;DR: In this article, it was shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters.
Abstract: SUMMARY It is shown that any test of normality computed from autoregressive residuals has the same limiting null distribution as for the standard case of independent, identically distributed observations with estimated parameters. Some numerical results are given to indicate that this approximation is acceptable for sample size 20 in first- and second- order models. Limited numerical results are also given to explore the effect of incorrectly specifying the order. It was discovered independently by Mukantseva (1977), Pierce & Kopecky (1979) and Loynes (1980) that any conventional test of normality computed from regression residuals has the same limiting null distribution as for the case of independent, identically distributed observations where only the mean and variance are estimated. It is shown here that the same result holds for such tests when computed from residuals in autoregressive models of any given order. In both the regression and autoregression cases it is necessary, for this result, that the fitting includes estimation of the mean, i.e. a constant term in the model. The results here could be extended, as by Pierce & Kopecky (1979), to tests of distributional form other than normal, but this seems of limited interest for the autoregressive situation. Only asymptotic distribution theory under the null hypothesis of normality is considered here. Some limited numerical results are given to investigate the rate of convergence. These results indicate that for first- and second-order autoregressive models the asymptotic approximation derived here may be adequate for sample sizes as small as 20. There is the practical difficulty that lack of fit indicated by a test of normality of errors for an autoregressive model of specified order may be due to incorrect specification of the order rather than to nonnormality of errors. Some very limited numerical results pertaining to this problem are also given here. Some related theoretical work is given by Moore (1982) and Moore & Gleser (1983). The argument is presented in terms of first-order autoregression, no essential changes being needed for extension to higher-order models. Write the model as
TL;DR: To speed up the response rate of time series tracking an adaptive filter, which is parallel to the Trigg and Leach adaptive forecasting algorithm, is proposed, and results of computer simulations of the first-order autoregressive adaptive model are shown.
Journal Article•
TL;DR: In this paper, the authors present a survey of non-stationary autoregressive time series models and their relation to statistical problems, including the following: Non-Linear Time Series Models and Dynamical Systems (T. Ozaki). Autoregressive Moving Average Models, Intervention Problems and Outlier Detection in Time Series (G.C. Tiao). Robustness in Time series and Estimating ARMA Models (R.D. Jones).
Abstract: Nonstationary Autoregressive Time Series (W.A. Fuller). Non-Linear Time Series Models and Dynamical Systems (T. Ozaki). Autoregressive Moving Average Models, Intervention Problems and Outlier Detection in Time Series (G.C. Tiao). Robustness in Time Series and Estimating ARMA Models (R.D. Martin, V.J. Yohai). Time Series Analysis with Unequally Spaced Data (R.H. Jones). Various Model Selection Techniques in Time Series Analysis (R. Shibata). Estimation of Parameters in Dynamical Systems (L. Ljung). Recursive Identification, Estimation and Control (P. Young). General Structure and Parametrization of ARMA and State-Space Systems and its Relation to Statistical Problems (M.D. Deistler). Harmonizable, Cramer, and Karhunen Classes of Processes (M.M. Rao). On Non-Stationary Time Series (C.S.K. Bhagavan). Harmonizable Filtering and Sampling to Time Series (D.K. Chang). Sampling Designs for Time Series (S. Cambanis). Measuring Attenuation (M.A. Cameron, P.J. Thomson). Speech Recognition Using LPC Distance Measures (P.J. Thomson, P. De Souza). Varying Coefficient Regression (D.F. Nicholls, A.R. Pagan). Small Samples and Large Equation Systems (H. Theil, D.G. Fiebig). Index.
TL;DR: In this paper, confidence bounds for the spectral density of a stationary time series are derived using a unified method that combines the autoregressive spectral estimate with the confidence intervals at single frequencies chosen a priori and a simultaneous confidence band for multiple a posteriori comparisons.
Abstract: . Confidence bounds for the spectral density of a stationary time series are derived. A unified method begins with the autoregressive spectral estimate and produces both confidence intervals at single frequencies chosen a priori and a simultaneous confidence band for multiple a posteriori comparisons. The crux is optimization of a quadratic form subject to the constraint imposed by the F-statistic. An approximate method that may produce tighter bounds is described. The former methods are demonstrated on the Waldmeier annual mean sunspot numbers.
TL;DR: In this article, the relations needed to produce bilateral symmetry using the one-sided autoregressive recursion equations have been attained on the square net and on the isometric lattice by an alternation procedure.
Abstract: The generation of isotropic artificial series in two or three dimensions by the autoregressive process is of considerable interest for the purpose of modeling environmental properties such as ore grade or reservoir porosity. The relations needed to produce bilateral symmetry using the one-sided autoregressive recursion equations have been attained on the square net and on the isometric lattice by an alternation procedure. In the case of the square net, the one-sided autoregressive (AR) process is alternated between the two diagonals of the net, while in three dimensions, the alternation takes place among the four body diagonals of the isometric cell.
TL;DR: In this article, the variance of the generating white noise process is allowed to depend on time, and it is shown that ordinary least squares estimates are strongly consistent and with a proper scaling factor asymptotically normal.
Abstract: . We study nonstationary autoregressive processes, where the variance of the generating white noise process is allowed to depend on time. It is shown that ordinary least squares estimates are strongly consistent and with a proper scaling factor asymptotically normal, but, as can be expected, they are not efficient. Furthermore, AIC type order determination criteria, used as if the underlying process is stationary, are consistent, whereas identification of order in terms of the partial autocorrelation function may lead one astray.
TL;DR: The high-order Yule-Walker equations are used to estimate the autoregressive parameters of an Autoregressive moving-average time series and it is shown that they are asymptotically unbiased and normal, the covariance matrix of the limit distribution is derived.
Abstract: The high-order Yule-Walker equations are used to estimate the autoregressive parameters of an autoregressive moving-average time series. The asymptotic statistical properties of these estimates are derived. It is shown that they are asymptotically unbiased and normal, the covariance matrix of the limit distribution is derived. The special case of estimating the autoregressive parameters of a noise corrupted autoregressive series is also examined.
TL;DR: The proposed estimators, suggested by the form of the Bayesian predictor in autore progressive systems, can be characterized as the average model spectrum and the spectrum corresponding to the "averaged model", with the averages being computed over the set of competetive autoregressive models of different orders.
Abstract: Initially, the problem of estimation of the spectral density function of a stationary multivariate autoregressive Gaussian process of unknown order is considered. Two new solutions to this problem are presented. The proposed estimators, suggested by the form of the Bayesian predictor in autoregressive systems, can be characterized as the average model spectrum and the spectrum corresponding to the "averaged model," with the averages being computed over the set of competitive autoregressive models of different orders and with respect to the sequence of the posterior probabilities of the process order given its observation history. The obtained results are then extended to the case of nonstationary autoregressive processes (identified by means of the exponentially weighted estimators) and more general weighting sequences. Although not Bayesian in the strict sense, the proposed approaches seem to be interesting from the theoretical point of view and give better results than the "classical" one. The efficient computational algorithms are indicated and the results of computer simulations are discussed.
01 Jan 1985
TL;DR: It is shown through simulation that the AR representation yields a mean-square error (MSE) of prediction that is comparable to the nonlinear ARMA models.
Abstract: The idea of using a finite autoregressive (AR) process in conjunction with a Kalman filter, rather than a Box-Jenkins autoregressive moving-average (ARMA) model, to forecast a univariate time series is explored in the context of recursive estimation. It is shown through simulation that the AR representation yields a mean-square error (MSE) of prediction that is comparable to the nonlinear ARMA models. The parameter updating for the AR representation, however, is computationally very simple, whereas the Box-Jenkins method requires all calculations to be repeated when a new piece of data arrives. It is concluded that the simplicity of updating more than compensates for the increase in the MSE of prediction when one is faced with routinely forecasting a large number of variables.
TL;DR: A necessary and sufficient condition for a stationary random field to be described by a finite quarter-plane autoregressive model is derived and the class of stationary image textures that can be represented or approximated by such models is very restricted.
Abstract: A necessary and sufficient condition for a stationary random field to be described by a finite quarter-plane autoregressive model is derived. The result implies that the class of stationary image textures that can be represented or approximated by such models is very restricted.
TL;DR: In this paper, the first and second moments of the OLS estimator of α in the model yt = αyt-1 + ut were derived for the case where ut follows MA(l) (first order moving average) proces with the coefficient different from α.
Abstract: In this paper we have derived the exact first and second moments of the OLS estimator of α in the model yt = αyt-1 + ut. Sawa (1978) has analyzed this model when ut is a white noise. We have extended his analysis to the case where ut follows MA(l) (first order moving average) proces with the coefficient different from α both with and without an intercept term in the model.
TL;DR: In this paper, scores type statistics are proposed to reflect changes in the parameters from their initial values without requiring any input about these values, instead of at restrictive "one point" shift alternatives.
Abstract: Sequential procedures are developed for monitoring the parameters of a time dependent autoregressive model relative to unspecified targets. Such a problem arises when we need to monitor the parameters for changes from their unknown initial values (the unspecified targets), instead of from specified targets. For this purpose, scores type statistics are proposed which: (1) reflect changes in the parameters from their initial values without requiring any input about these values; and (2) are aimed at detecting arbitrary shifts in the parameters, instead of at restrictive "one point" shift alternatives. The procedures developed are capable of monitoring any one of, or any combination of, the mean, variance or correlation structure of an autoregressive sequence of known finite order. Their false signal rates are controlled, and their performance under local shift
TL;DR: In this article, an operational Bayesian approach is described to make inferences for the spectral density function for univariate autoregressive processes and for the AR operator of multivariate AR operators.
Abstract: The article describes an operational Bayesian approach to making inferences for the spectral density function for univariate autoregressive processes and for the AR operator of multivariate autoregressive processes. The derivation of the approach is described. Numerical examples, including the Wolfer Sunspot numbers, are used to demonstrate the practical usefulness of the approach.