Showing papers on "STAR model published in 1982"
TL;DR: In this paper, a procedure for making statistical inferences about differences between population means from the output of general circulation model (GCM) climate experiments is presented, yielding a potentially powerful technique for detecting climatic change than the simpler schemes used heretofore.
Abstract: A procedure for making statistical inferences about differences between population means from the output of general circulation model (GCM) climate experiments is presented. A parametric time series modeling approach is taken, yielding a potentially mere powerful technique for detecting climatic change than the simpler schemes used heretofore. The application of this procedure is demonstrated through the use of GCM control data to estimate the variance of winter and summer time averages of daily mean surface air temperature. The test application provides estimates of the magnitude of climatic change that the procedure should be able to detect. A related result of the analysis is that autoregressive processes of higher than first order are needed to adequately model the majority of the GCM time series considered.
78 citations
TL;DR: In this paper, a Bayesian estimator and an ad hoc procedure for the parameters of a first-order spatial autoregressive model are derived, and their small sample properties compared by means of a Monte Carlo simulation experiment.
Abstract: This note considers a Bayesian estimator and an ad hoc procedure for the parameters of a first-order spatial autoregressive model. The approaches are derived, and their small sample properties compared by means of a Monte Carlo simulation experiment.
54 citations
TL;DR: It is shown that the method can often overcome some difficulties inherent in the traditional smoothed periodogram and autoregressive spectral-estimation methods and that additional insights into the structure of a multiple time series can be obtained by using periodic autoregressions.
Abstract: A new method of estimating the spectral density of a multiple time series based on the concept of periodically stationary autoregressive processes is described and illustrated. It is shown that the method can often overcome some difficulties inherent in the traditional smoothed periodogram and autoregressive spectral-estimation methods and that additional insights into the structure of a multiple time series can be obtained by using periodic autoregressions.
36 citations
TL;DR: The autoregressive parameters characterizing the resultant ARMA model estimate can serve the role of decision variables in pattern classification schemes and can be utilized in determining whether or not a member(s) of a given signal class is contained within a noise corrupted measurement signal.
Abstract: A method for efficiently generating a rational model of a wide-sense stationary time series is presented. In this method the autoregressive parameters associated with an ARMA model consisting of q zeros and p poles are optimally chosen with the selection being based on a finite set of time series observations. This selection is made so that a set of Yule-Walker equation approximations are ``best'' satisfied. The resultant autoregressive parameter estimates have the desired statistical feature of being unbiased and consistent. This estimation method has been found to provide a modeling performance which typically equals or exceeds that of contemporary alternatives. Moreover, this method is amenable to a computationally efficient adaptive solution procedure. The autoregressive parameters characterizing the resultant ARMA model estimate can serve the role of decision variables in pattern classification schemes. For example, these parameters can be utilized in determining whether or not a member(s) of a given signal class is contained within a noise corrupted measurement signal. This approach has been found to be particularly effective in Doppler radar and array processing applications in which one is looking for the presence of spectral lines (i.e., sinusoids) in the measurement signal.
29 citations
TL;DR: In this paper, a sequence of "$M$-estimates" for unknown parameters of an autoregressive process of known, finite order which may have heavy-tailed innovations is generated.
Abstract: Stochastic approximation methods are used to generate a sequence of "$M$-estimates" for the unknown parameters of an autoregressive process of known, finite order which may have heavy-tailed innovations. Weak dependence properties, which can be demonstrated for many autoregressive processes, are used in the proof that the sequence converges almost surely to the parameters. A brief Monte Carlo study verifies that bounded influence functions provide protection for recursive procedures against heavy-tailed innovations.
28 citations
TL;DR: Combination of a conceptual model and an autoregressive error model for improving short time forecasting was proposed in this paper, where the authors used a combination of the two models for short-term forecasting.
Abstract: Combination of a conceptual model and an autoregressive error model for improving short time forecasting
25 citations
TL;DR: In this paper, a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process under simple limiting conditions, and the result is discussed in the context of modeling vital rates for biological populations in random environments.
Abstract: Under simple limiting conditions a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process. The result is discussed in the context of modeling vital rates for biological populations in random environments.
25 citations
TL;DR: In this paper, a stepwise procedure is used to estimate time series with an unknown number of deterministic trigonometric components with unknown amplitudes and frequencies, where the frequency of the largest term in the residual series is used as a starting value for finding the best frequency in the least squares sense.
Abstract: Estimation in time series with an unknown number of deterministic trigonometric components with unknown amplitudes and frequencies is considered. A stepwise procedure is used. At each step the frequency of the largest term in the periodogram of the residual series is used as a starting value for finding the best frequency in the least squares sense. The procedure is stopped when there are no further significant harmonic components, when tested by a multiple-test procedure. The fitting procedure is tried on various time series, including the sun-spot series. For long-term prediction the deterministic model does better for the sunspot series than, for example, autoregressive models.
22 citations
TL;DR: In this article, the performance of various types of models for river flows are compared by using a decision rule derived from the Bayes criterion, which has the property that it minimizes the probability of error.
Abstract: The performance of various types of models for river flows are compared by using a decision rule derived from the Bayes criterion. The decision rule has the property that it minimizes the probability of error. The best model among the autoregressive, autoregressive moving average, and moving average models of various orders for the annual flows of about 10 rivers is found by using this decision rule. For the monthly flows, not only the best seasonal autoregressive integrated moving average model but also the best type of transformation is determined. The models for the log transformed monthly data are superior to the models fitted to the observed data without transformation. The variability in the decisions caused by the different prior probability density functions is also discussed.
22 citations
TL;DR: In this paper, the variance of the residual process is modelled by a step function, where the variance depends on the time of the time series and can be estimated using an iterative regression procedure.
Abstract: . We study nonstationary autoregressive time series where the variance of the residual process is allowed to depend on time. In earlier publications the variance has been modelled by a step function. We look at more general classes of functions and propose two estimates of the autoregressive coefficients, both of which are consistent under weak assumptions. We also show how it is possible to obtain an estimate in practice using an iterative regression procedure.
19 citations
TL;DR: In this article, the authors derived a new result in the contiguity framework that leads directly to an expression for the Pitman efficiencies of tests as well as estimators.
Abstract: We considerpth order autoregressive time series where the shocks need not be normal. By employing the concept of contiguity, we obtain the sysmptotic power for tests of hypothesis concerning the autoregressive parameters. Our approach allows consideration of the double exponential and other thicker-tailed distributions for the shocks. We derive a new result in the contiguity framework that leads directly to an expression for the Pitman efficiencies of tests as well as estimators.
TL;DR: In this paper, the Edgeworth distribution of the OLS estimator of the autoregressive parameter of a first-order stochastic difference equation with exogenous variables was obtained.
TL;DR: In this paper, the problem of constructing canonical ladder realizations for vector autoregressive (AR) processes specified by their characteristic matrix polynomials is treated and two efficient procedures for solving this equation are presented, both requiring a number of operations that is proportional to at most the square of the model order.
Abstract: The paper treats the problem of constructing canonical ladder realizations for vector autoregressive (AR) processes specified by their characteristic matrix polynomials. The difficulty of this problem is rooted in the fact that the backward matrix polynomial corresponding to a given vector AR process is a nontrivial function of the forward matrix polynomial. The construction calls for solving a discrete Lyapunov equation in block-controller form. Two efficient procedures for solving this equation are presented, both requiring a number of operations that is proportional to at most the square of the model order. Applications of the new procedures to stability, tests, simulation of AR processes, and model reduction are described.
30 Mar 1982
TL;DR: In this article, an autoregressive spectral estimator for the noise-corrupted case is developed and shown to be consistent, and a least square estimate for the variance of the innovations sequence is also developed.
Abstract: : For the case when the observed series consists of the sum of an autoregressive process of known order and white noise the application of autoregressive spectral estimation methods may not be correct. The presence of the additive noise introduces zeros which are not adequately modeled by an autoregressive model. In this report an autoregressive spectral estimator for the noise-corrupted case is developed and shown to be consistent. The high-order Yule-Walker equations are used to estimate the autoregressive parameters from the noise-corrupted observations. A least squares estimate for the variance of the innovations sequence is also developed and shown to be consistent. These consistent estimates for the autoregressive parameters and the innovations variance are used to form the consistent autoregressive spectral estimates. (Author)
TL;DR: Bayesian decision theory seems a natural approach to this problem and the recent general results of Smith et al. (1981) provide the necessary framework.
Abstract: where p is a 'smooth' function. Suppose that we approximate 4u(x) by 0, a constant, for all x. In subsequent discussion we suppress the argument x whenever this may be done without obscuring the context. Clearly this approximation will incur some errors. On the other hand, as argued by Tong & Lim (1980), we could approximate / arbitrarily closely by a step function. At first sight, it seems that 'this could pose a horrendous computational problem. Indeed, this is the case from a purely deterministic point of view. However, we usually approximate the 'true' model with some purpose in mind, e.g. forecasting, control, filtering. Thus, we should really specify what we mean by approximating ,u arbitrarily closely. Bayesian decision theory seems a natural approach to this problem. In particular, the recent general results of Smith et al. (1981) provide the necessary framework.
01 May 1982
TL;DR: It is shown that if the "higher order" Yule-Walker equations are used to estimate the autoregressive parameters of an autore progressive-moving average process, the estimates are asymptotically jointly multivariate normal.
Abstract: It has been shown that autoregressive spectral estimators can provide very fine spectral resolution estimates for time series which satisfy the all pole assumption. When the observed time series consists of the sum of an auto-regressive process plus white noise, the "all-pole" assumption is no longer valid. The appropriate model is the autoregressive-moving average representation. In this paper, it is shown that if the "higher order" Yule-Walker equations are used to estimate the autoregressive parameters of an autoregressive-moving average process, the estimates are asymptotically jointly multivariate normal. The structure of the asymptotic covariance matrix is evaluated when the process is assumed to be auto-regressive-moving average and for the special case of autoregressive plus noise.
TL;DR: In this paper, a brief account of how the class of threshold autoregressive time series models may be used to make short, medium and long range predictions of cyclical data is given.
Abstract: . We give a brief account of how the class of threshold autoregressive time series models may be used to make short, medium and long range predictions of cyclical data.
Book•
01 Jan 1982
TL;DR: This paper discusses the development of a computer-oriented technique for automatically identifying nonseasonal Box-Jenkins ARIMA (p, d, q) models or multiplicative seasonal Box- Jenkins ARimA∗ (P, D, Q)s models for discrete univariate time series.
Journal Article•
TL;DR: Conditions of stationarity of such a series, its covariance function and spectral density, the inverse of its variance matrix and the best linear prediction are investigated.
Abstract: Autoregressive models with random parameters are natural generalizations of classical autoregressive processes. The problem of stationarity of the autoregressive series with independent random coefficients was solved by Andel (see [1]) and Nicholls and Quinn (see [3]). In some practical situations (for instance in applications to economy) the assumption of independence cannot be accepted and it is suitable to consider some kind of time-dependence among the coefficients. In the simplest case random parameters generate the first-order moving average process. In this paper we investigate conditions of stationarity of such a series, its covariance function and spectral density, the inverse of its variance matrix and we construct the best linear prediction. We shall assume that the first-order autoregressive series with random parameters is generated from a random variable Xx with EXX = 0 and Var Xx = a 2 > 0 by
Posted Content•
TL;DR: In this article, it was shown that the distribution of N samples of a stationary Gaussian autoregressive process admits a sufficient statistic whose dimension is independent of N. This property depends not on the absence of spectral zeros in autoregression models, but rather on the fact that the class of models has a fixed set of spectral zero.
Abstract: . It is known that the distribution of N samples of a stationary Gaussian autoregressive process admits a sufficient statistic whose dimension is independent of N. We show that this property depends not on the absence of spectral zeros in autoregressive models, but rather on the fact that the class of models has a fixed set of spectral zeros.
TL;DR: In this paper, the authors adopt Schmidt's modified polynomial lag models for multiple time series analysis and the resulting method can be regarded as a compromise between modelling pure autoregressive and autooregressive-moving average processes.
Abstract: SUMMARY It is proposed to adopt Schmidt's (1974) modified polynomial lag models for multiple time series analysis. The resulting method can be regarded as a compromise between modelling pure autoregressive and autoregressive-moving average processes. While being as easy to specify and estimate as the former, the resulting class of models avoids some disadvantages that result from fitting pure autoregressive structures. As an example, data of Quenouille (1957) are analysed.
01 Jan 1982
TL;DR: In this paper, a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process under simple limiting conditions, and the result is discussed in the context of modeling vital rates for biological populations in random environments.
Abstract: Under simple limiting conditions a first-order autoregressive process is shown to converge weakly to an Ornstein-Uhlenbeck process. The result is discussed in the context of modeling vital rates for biological populations in random environments.
Book•
01 Jan 1982
TL;DR: The autoregressive method proposed in this paper uses techniques developed for time series analysis to provide both point and interval estimates for parameters associated with the steady-state distribution to get more accurate point estimates along with more precise interval estimates.
Abstract: : As the use of computer simulation becomes more important in the study of complex phenomena, the need to develop theoretically sound and computationally efficient methods for simulation output analysis becomes more pressing. The autoregressive method proposed in this paper uses techniques developed for time series analysis to provide both point and interval estimates for parameters associated with the steady-state distribution. The major advantage of the autoregressive method is obvious. It serves as a black box; users provide the simulation output sequence, the black box will produce results automatically. Furthermore, it seems that the autoregressive method applies to a much broader class of stochastic processes than the regenerative method does. With the generalization to multidimensional processes, the method enables us to apply variance reduction techniques to get more accurate point estimates along with more precise interval estimates. The disadvantages of the autoregressive method are that the covariance matrix obtained by the autoregressive method is just an approximation for the covariance matrix present in the central limit theorem used to construct confidence intervals, and the assumptions put on the system are stricter than we would like.
TL;DR: In this article, under the assumption that subsystems are independent and first order autoregressive, the authors present two methods for estimating the distribution of the subsystem coefficients, assuming that each subsystem is independent.
Abstract: There are many time series applications where an experimenter observes the simultaneous responses of several subsystems over time. In these instances one is often not interested in the parameters of individual subsystems, but rather in an overall characterization of the system in question. Under the assumption that subsystems are independent and first order autoregressive, the present paper presents two methods for estimating the distribution of the subsystem coefficients.
01 Jan 1982
TL;DR: In this paper, the authors make some critical remarks on the method suggested in the above paper for estimating the order of an autoregressive process and an alternative method is then suggested.
Abstract: This correspondence makes some critical remarks on the method suggested in the above paper for estimating the order of an autoregressive process. An alternative method is then suggested.
01 Jul 1982
TL;DR: It is shown how the algorithm provides a unified framework for suggesting robust autoregressive estimators, for finding autoregression diagnostics, and for understanding the Burg algorithm.
Abstract: : An algorithm is presented for efficiently finding the information needed in the modified Gram-Schmidt decomposition of the augmented autoregressive design matrix to find the Yule-Walker estimators of autoregressive parameters for orders 1, 2, ..., M. the algorithm is shown to be slightly slower than Levinson's algorithm and to require slightly more storage but enjoys the superior numerical properties of the modified Gram-Schmidt decomposition algorithm. Further, it is shown how the algorithm provides a unified framework for suggesting robust autoregressive estimators, for finding autoregression diagnostics, and for understanding the Burg algorithm. (Author)
01 Dec 1982
TL;DR: In this article, the authors describe procedures for computing the polynomial defining a backward autoregressive recursion from the one defining a forward autoregression without necessarily using a Levinson-WigginsRobinson type of algorithm.
Abstract: The prime concern of this paper is to describe procedures for computing the polynomial defining a backward autoregressive recursion from the polynomial defining a forward autoregressive recursion without necessarily using a Levinson-Wiggins-Robinson type of algorithm. Two distinct procedures are given, one involving the computation of covariance data, the other not.
01 Jun 1982
TL;DR: Functionals used to describe the probability distributions of time series (both Gaussian and non-Gaussian) are introduced and an approach to empirical spectral analysis is suggested.
Abstract: : Functions used to describe the probability distributions of time series (both Gaussian and non-Gaussian) are introduced. The concept of type of a time series is defined. Autoregressive spectral densities are defined. Order determining criteria are motivated. through the concept of model identification by estimating information. An approach to empirical spectral analysis is suggested. (Author)