Showing papers on "STAR model published in 1994"
TL;DR: In this article, the authors consider the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) models, and consider the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models.
Abstract: This article considers the application of two families of nonlinear autoregressive models, the logistic (LSTAR) and exponential (ESTAR) autoregressive models. This includes the specification of the model based on simple statistical tests: linearity testing against smooth transition autoregression, determining the delay parameter and choosing between LSTAR and ESTAR models are discussed. Estimation by nonlinear least squares is considered as well as evaluating the properties of the estimated model. The proposed techniques are illustrated by examples using both simulated and real time series.
1,883 citations
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TL;DR: In this paper, an experiment was performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability.
Abstract: An experiment is performed to assess the prevalence of instability in univariate and bivariate macroeconomic time series relations and to ascertain whether various adaptive forecasting techniques successfully handle any such instability. Formal tests for instability and out-of-sample forecasts from sixteen different models are computed using a sample of 76 representative U.S. monthly postwar macroeconomic time series, constituting 5700 bivariate forecasting relations. The tests indicate widespread instability in univariate and bivariate autoregressive models. However, adaptive forecasting models, in particular time varying parameter models, have limited success in exploiting this instability to improve upon fixed-parameter or recursive autoregressive forecasts.
814 citations
TL;DR: In this paper, median-unbiased estimators for univariate AR(p) models with time trends with confidence intervals also are considered and the results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest.
Abstract: This article introduces approximately median-unbiased estimators for univariate AR(p) models with time trends. Confidence intervals also are considered. The methods are applied to the Nelson–Plosser macroeconomic data series, the extended Nelson–Plosser macroeconomic data series, and some annual stock-dividend and price series. The results show that most of the series exhibit substantially greater persistence than least squares estimates and some Bayesian estimates suggest. For example, for the extended Nelson–Plosser data set, 8 of the 14 series are estimated to have a unit root, but 6 are estimated to be trend stationary. In contrast, the least squares estimates indicate trend stationarity for all of the series.
478 citations
TL;DR: In this article, the authors present a monograph for students at the graduate level in biostatistics, statistics or other disciplines that collect longitudinal data, focusing on the state space approach that provides a convenient way to compute likelihoods using the Kalman filter.
Abstract: This monograph is written for students at the graduate level in biostatistics, statistics or other disciplines that collect longitudinal data. It concentrates on the state space approach that provides a convenient way to compute likelihoods using the Kalman filter.
344 citations
TL;DR: In this article, the autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms, and it is shown that statistical inference can be performed by reduced rank regression.
Abstract: The autoregressive model for cointegrated variables is analyzed with respect to the role of the constant and linear terms Various models for 1(1) variables defined by restrictions on the deterministic terms are discussed, and it is shown that statistical inference can be performed by reduced rank regression The asymptotic distributions of the test statistics and estimators are found A similar analysis is given for models for 1(2) variables with a constant term
321 citations
Journal Article•
185 citations
TL;DR: It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving-average models.
Abstract: . An overview of model building with periodic autoregression (PAR) models is given emphasizing the three stages of model development:identification, estimation and diagnostic checking. New results on the distribution of residual autocorrelations and suitable diagnostic checks are derived. The validity of these checks is demonstrated by simulation. The methodology discussed is illustrated with an application. It is pointed out that the PAR approach to model development offers some important advantages over the more general approach using periodic autoregressive moving-average models.
137 citations
TL;DR: In this article, the first moment of a time series on lagged information using a step-function-type nonlinear structure is modeled using threshold autoregressive (TAR) models and the statistical estimation and testing procedures are illustrated by modeling the difference between the prices of an index futures contract and the equivalent underlying cash index.
Abstract: Threshold autoregressive (TAR) models condition the first moment of a time series on lagged information using a step-function-type nonlinear structure. TAR techniques are expected to be relevant in financial time-series modeling in situations where deviations of prices from equilibrium values depend on discrete transaction costs and where market regulators follow intervention rules based on threshold values of control variables. an important finance application is in modeling the difference in prices of equivalent assets in the presence of transaction costs. the focus of this paper is on motivating the use of TAR models in this context and on the statistical estimation and testing procedures. the procedures are illustrated by modeling the difference between the prices of an index futures contract and the equivalent underlying cash index. It is found that the hypothesis of linearity is conclusively rejected in favor of threshold nonlinearity and that the estimated thresholds are largely consistent with arbitrage-related transaction costs.
113 citations
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TL;DR: In this paper, the authors assume that the solutions of a set of restrictions on the rational expectations of future values can be represented as a vector autoregressive model, and they study the implied restrictions on coefficients.
Abstract: Assuming that the solutions of a set of restrictions on the rational expectations of future values can be represented as a vector autoregressive model, we study the implied restrictions on the coefficients. Nonstationary behavior of the variables is allowed, and the restrictions on the cointegration relationships are spelled out. In some interesting special cases it is shown that the likelihood ratio statistic can easily be computed.
49 citations
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TL;DR: In this paper, the asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector auto-regression (VAR) representations are derived under the assumption that the auto-gressive order goes to infinity with the sample size.
Abstract: Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the relationships between the variables; therefore, they are important for applied work. Tests for linear restrictions on the coefficients of both the ECM and the pure VAR representation are considered under the present assumptions. It is found that they have limiting x2 distributions. Tests are also derived under the assumption that the number of restrictions goes to infinity with the sample size.
46 citations
TL;DR: In this article, the forward-backward autoregressive model is employed to extrapolate time domain signatures generated by the finite difference time domain algorithm with a view to speeding up the process of obtaining the frequency responses of EM systems.
Abstract: In this paper, the forward-backward autoregressive model is employed to extrapolate time domain signatures generated by the finite difference time domain algorithm with a view to speeding up the process of obtaining the frequency responses of EM systems. It is shown that the present method requires considerably lower-order predictors than those needed in other AR models, e.g, those based on Yule-Walker equations, and is therefore computationally efficient. >
TL;DR: A state-space characterization is used to develop algorithms for modeling and estimating signals as nonlinear autoregressive processes from noise-corrupted measurements, and recursive estimation algorithms for addressing problems of filtering, prediction, and smoothing are based on extended Kalman estimators.
TL;DR: In this article, the Cayley-Hamilton transformation is used to transform the natural parameters of the linear stochastic differential equation describing the process which gives rise to the data, and the new parameter space is identical with that of discrete time autoregressive models.
Abstract: An increasingly valuable tool for modelling irregularly sampled time series data is the continuous time autoregressive model. The natural parameters in this model are the coefficients of the linear stochastic differential equation describing the process which gives rise to the data. A transformation of these parameters is introduced, based on the Cayley-Hamilton transformation. The new parameter space is identical with that of discrete time autoregressive models. The model is also modified by the introduction of prescribed moving average terms. The resulting modelling improvements include rapid and reliable convergence of parameter estimates and the ability to select the model order by testing whether the highest order coefficient is 0
TL;DR: In this article, a model-building approach that consists of model identification, estimation, diagnostic checking, and forecasting is discussed for non-normal stationary first-order autoregressive models.
Abstract: We shall first review some non-normal stationary first-order autoregressive models. The models are constructed with a given marginal distribution (logistic, hyperbolic secant, exponential, Laplace, or gamma) and the requirement that the bivariate joint distribution of the generated process must be sufficiently simple so that the parameter estimation and forecasting problems of the models can be addressed. A model-building approach that consists of model identification, estimation, diagnostic checking, and forecasting is then discussed for this class of models.
TL;DR: In this paper, an expression for the likelihood function of a stationary vector autoregressive-moving average process is developed, which is very efficient numerically and applies to any stationary but not necessarily invertible model.
Abstract: SUMMARY An expression for the likelihood function of a stationary vector autoregressive-moving average process is developed The expression is very efficient numerically and applies to any stationary but not necessarily invertible model In particular, when the multivariate process is autoregressive, the exact likelihood can be evaluated with a small number of operations depending on the order of the autoregressive operator and the process dimension, but not on the size of the observed series The expression also provides an efficient method for the evaluation of the exact likelihood of a partially nonstationary vector autoregressive-moving average process, for which the determinant of the autoregressive operator has at least one unit root and the remaining roots are outside the unit circle This method does not require differencing the series, so that complications caused by over-differencing the series, such as noninvertibility and parameter identifiability problems, are avoided The results for autoregressive models are also applied to testing the stationarity and invertibility of any autoregressive-moving average model with given parameter values
TL;DR: Five classes of stochastic models for analysis and synthesis of gray-scale texture are evaluated; Markov models, autocorrelation and histogram models, linear autoregressive models, fractal models and spectral models.
TL;DR: In this paper, the authors address the problem of estimating vector autoregressive models for nonstationary (integrated) time series, and the main emphasis is upon the estimation of autoregression approximations to stationary processes.
Abstract: This paper addresses the problem of estimating vector autoregressive models. An approach to handling nonstationary (integrated) time series is briefly discussed, but the main emphasis is upon the estimation of autoregressive approximations to stationary processes. Three alternative estimators are considered–the Yule-Walker, least-squares, and Burg-type estimates–and a complete analysis of their asymptotic properties in the stationary case is given. The results obtained, when placed together with those found elsewhere in the literature, lead to the direct recommendation that the less familiar Burg-type estimator should be used in practice when modeling stationary series. This is particularly so when the underlying objective of the analysis is to investigate the interrelationships between variables of interest via impulse response functions and dynamic multipliers.
TL;DR: In this paper, the authors compared the performance of alternative asymptotic tests of linear hypotheses on the cointegration space and the adjustment space and showed that application of simple correction factors typically improves the properties of likelihood ratio test statistics in small-sample situations.
TL;DR: In this paper, the information matrix of the parameters of the multiple-input single-output time series model for correlated and uncorrelated inputs, allowing lags between inputs, is evaluated using algorithms developed for the univariate ARMA model.
Journal Article•
TL;DR: A topology for the set of all autoregressive systems of fixed size and bounded McMillan degree is described and it is shown that this topological space has the structure of a finite CW complex.
TL;DR: The autoregressive-output-analysis method for constructing a confidence interval for the steady-state mean of a simulated process is revisited and updated by using Rissanen's predictive least-squares criterion to estimate the autore progressive order of the process.
Abstract: We revisit and update the autoregressive-output-analysis method for constructing a confidence interval for the steady-state mean of a simulated process by using Rissanen's predictive least-squares criterion to estimate the autoregressive order of the process. This order estimator is strongly consistent when the output is autoregressive. The order estimator is combined with the standard autoregressive-output-analysis method to form a confidence-interval procedure. Alternatives for estimating the degrees of freedom for the procedure are investigated. The main result is an asymptotically valid confidence-interval procedure that, empirically, has good small-sample properties.
TL;DR: In this paper, a test of homogeneity for testing the quality of the parameters in several independent nonlinear autoregressive processes is derived for the case when the number of replications of the realization increases.
TL;DR: In this paper, rank tests for testing the randomness of the regression coefficients in a random coefficient autoregressive model were proposed and asymptotic distributions of these tests were obtained via weak convergence results of a randomly weighted residual empirical process proved by Koul and Ossiander (1993).
Journal Article•
TL;DR: For a continuous time autoregressive model, the rate of exponential convergence of the second kind error of Neyman-Pearson tests was derived when the observation time increases to infinity.
Abstract: For a continuous time autoregressive model, the rate of exponential convergence of the second kind error of Neyman-Pearson tests is derived when the observation time increases to infinity. The assumptions ensure that the Kullback-Leibler information is finite.
TL;DR: A method to distinguish low-dimensional chaos from randomness is presented and the comparison between the predictive skills of the two techniques allows us to gain insight into distinguishing chaos fromrandomness.
Abstract: A method to distinguish low-dimensional chaos from randomness is presented. Autoregressive processes are fitted to the data and forecasts are obtained on the basis of the model selected. Two possible forecasting techniques are distinguished. The global autoregressive approximation views the data as a realization of a linear stochastic process, whereas the local autoregressive approximation views the observations as the realizations of a chaotic process. The comparison between the predictive skills of the two techniques allows us to gain insight into distinguishing chaos from randomness.
TL;DR: A new method is presented which permits one to discriminate low-dimensional chaos from randomness and has been applied to a daily temperature time series recorded in Trieste (Italy) over the past 40 years, giving no evidence for low- dimensional chaos.
Abstract: A new method is presented which permits one to discriminate low-dimensional chaos from randomness. The method consists in fitting autoregressive processes to the data and forecasting future values of the system on the basis of the model selected. We distinguish between 2 possible forecasting techniques of a dynamical system given by experimental series of observations. The “global autoregressive approximation” views the observations as a realization of a stochastic process, whereas the “local autoregressive approximation” views the observations as the realizations of a truly deterministic process. A proper comparison between the predictive skills of the 2 techniques allows us to gain insight into distinguishing low-dimensional chaos from randomness. The procedure has been applied to a daily temperature time series recorded in Trieste (Italy) over the past 40 years (1950–1989). The analysis gives no evidence for low-dimensional chaos, the dynamics being compatible with a limit cycle blurred by red noise. DOI: 10.1034/j.1600-0870.1994.t01-2-00005.x
TL;DR: In this article, an autocorrelation function method was developed for estimating the parameters of autoregressive models, where an ordinary least-squares method was used to optimally determine the parameters by minimizing the sum of the squares of differences between the autocorerelations calculated directly from the observed time series and those from the model-generated streamflow.
Abstract: An autocorrelation function method was developed for estimating the parameters of autoregressive models. For monthly streamflow series, an ordinary least-squares method was used to optimally determine the parameters by minimizing the sum of the squares of differences between the autocorrelations calculated directly from the observed time series and those from the model-generated streamflow. The approach was tested using numerical simulation and historical data. Numerical results showed that for some generated data series the parameters estimated by the new method were closer to their true values than those obtained from the Yule-Walker equations. For monthly streamflow time series of three stations of Yellow River in China, the historical correlation functions were compared with those from data series generated with the AR(2) model. The autocorrelation function estimated from the generated data series was closer to the observed autocorrelation than that obtained from the Yule-Walker equations. This is even more true for the multivariate autoregressive model.
TL;DR: A consistent estimator for the model order of an autoregressive process is derived based on a statistical F test based on its asymptotic properties and found to result in lower model orders in general.
Abstract: A consistent estimator for the model order of an autoregressive process is derived based on a statistical F test. Its asymptotic properties are considered. The procedure is compared with Akaike's information theoretical approach and found to result in lower model orders in general. >