Showing papers on "STAR model published in 1996"
TL;DR: In this article, a Lagrange multiplier (LM) test for the hypothesis of no error autocorrelation and LM-type tests for the hypotheses of no remaining nonlinearity and that of parameter constancy are proposed.
596 citations
TL;DR: In this paper, the authors proposed a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments.
Abstract: Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P-ARCH, models is directly related to the class of periodic autoregressive moving average (ARMA) models for the mean. The implicit relation between periodic generalized ARCH (P-GARCH) structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in forecast efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. Two empirical examples with daily bilateral Deutschemark/British pound and intraday Deutschemark/U.S. dollar spot exchange rates highlight the prac...
361 citations
TL;DR: In this article, a class of non-stationary varying-coefficient autoregressive models that allow stochastic variability in the root root is considered and a test of the null hypothesis of a fixed unit root against the alternative of a randomized root with unit mean is presented.
Abstract: This article considers a class of nonstationary varying-coefficient autoregressive models that allow stochastic variability in the autoregressive root It is argued that such models provide a better description of the behavior of macroeconomic variables than fixed-unit-root autoregressive models because they allow more general forms of nonstationarity We construct a test of the null hypothesis of a fixed unit root against the alternative of a randomized root with unit mean and derive its asymptotic distribution The test is applied to several US macroeconomic series generally considered to contain fixed unit roots We find that for about half of the series the fixed-unit-root null is rejected
144 citations
Book•
01 Jan 1996
TL;DR: In this article, the authors provide an up-to-date survey of the recent developments in periodic time series, and present a large number of empirical results, as well as an extensive discussion of deterministic regressors in testing for periodic integration and in forecasting.
Abstract: textThis book considers periodic time series models for seasonal data, characterized by parameters that differ across the seasons, and focuses on their usefulness for out-of-sample forecasting. Providing an up-to-date survey of the recent developments in periodic time series, the book presents a large number of empirical results.
The first part of the book deals with model selection, diagnostic checking and forecasting of univariate periodic autoregressive models. Tests for periodic integration, are discussed, and an extensive discussion of the role of deterministic regressors in testing for periodic integration and in forecasting is provided.
The second part discusses multivariate periodic autoregressive models. It provides an overview of periodic cointegration models, as these are the most relevant. This overview contains single-equation type tests and a full-system approach based on generalized method of moments.
All methods are illustrated with extensive examples, and the book will be of interest to advanced graduate students and researchers in econometrics, as well as practitioners looking for an understanding of how to approach seasonal data.
Provides an up-to-date survey of periodic time series models for seasonal data.
Investigates such areas as seasonal time series; periodic time series models; periodic integration; and periodic cointegration.
Contains many contemporary empirical examples and results.
122 citations
Posted Content•
TL;DR: The emphasis is on the techniques of stationary multivariate time series analysis: autoregressive and moving average representations o f standard microstructure models, vector autore progressive estimation, random-walk decompositions and cointegration.
Abstract: Microstructure data typically consist of trades and bid and offer quotes for financial securities that are collected at fine sampling intervals (often within the day). This paper reviews approaches taken to modeling these data. The emphasis is on the techniques of stationary multivariate time series analysis: autoregressive and moving average representations o f standard microstructure models, vector autoregressive estimation, random-walk decompositions and cointegration. The paper also discusses the challenges posed by irregular observation frequencies, discreteness and nonlinearity.
114 citations
TL;DR: A complete Bayesian treatment of autoregressive model estimation incorporating choice of Autoregressive order, enforcement of stationarity, treatment of outliers, and allowance for missing values and multiplicative seasonality is presented.
111 citations
TL;DR: In this paper, a theoretical explanation of this phenomenon is given, while the 1994 IAEA Benchmark test is presented as a practical example of Yule-Walker yielding poor parameter estimates.
95 citations
TL;DR: In this paper, the effect of parameter uncertainty on impulse response analysis in nonlinear models is investigated and various impulse response functions are defined and applied in a threshold autoregressive model of real US GDP.
85 citations
TL;DR: In this article, the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series are analyzed, and a class of likelihood ratio tests for unit root inference is proposed.
Abstract: text. This paper analyzes the presence and consequences of a unit root in periodic autoregressive models for univariate quarterly time series. First, we consider various representations of such models, including a new parametrization which facilitates imposing a unit root restriction. Next, we propose a class of likelihood ratio tests for a unit root, and we derive their asymptotic null distributions. Likelihood ratio tests for periodic parameter variation are also proposed. Finally, we analyze the impact on unit root inference of misspecifying a periodic process by a constant-parameter model.
83 citations
TL;DR: It is shown that a bootstrap procedure which works by generating time series replicates via an estimated finitek-order vector autoregressive process (k?∞ at an appropriate rate with the sample size) gives asymptotically valid approximations to the joint distribution of the growing set of estimated autore progressive coefficients.
82 citations
TL;DR: In this article, 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.
TL;DR: In this article, a general assumption is made that a finite order VAR model is fitted to a potentially infinite order process, and the order is assumed to increase with the sample size.
Abstract: Tests for Granger-causality have been performed in numerous empirical studies. These tests are usually based on finite order vector autoregressive (VAR) processes, and the assumption is made that the model fitted to the available data corresponds to the true data generating mechanism. In the present study, the more general assumption is made that a finite order VAR model is fitted to a potentially infinite order process. The order is assumed to increase with the sample size. Asymptotic properties of tests for Granger-causality as well as other types of causality concepts are derived. Some limited small sample results are obtained using simulation methods. In the context of multiple time series analysis and dynamic econometric models, different types of causation have been defined and analyzed. Typically, causality analyses have been performed in the framework of vector autoregressive (VAR) or vector autoregressive moving average (VARMA) models. In other words, the restrictions for the parameters of these models characterizing the specific causality concept are derived and then tests of these parameter restrictions are performed. Analyses of Granger's causality concept represent popular examples of this research strategy. Most of these analyses have been based on finite order VAR processes. A main reason for the emphasis on finite order, pure VAR models is that the parameter restrictions implied by different causality concepts are easy to treat under common stationarity assumptions. In contrast, tests for Grangercausality are relatively difficult to execute, for instance, in VARMA models (see, e.g., Eberts and Steece, 1984; Boudjellaba, Dufour, and Roy, 1992;
TL;DR: Linear models of time series are used to describe the sequence of the significant wave heights in two locations of the Portuguese coast and it was found that models with orders up to 20, but without all terms, described well the data.
TL;DR: In this article, a feature extraction scheme for a general type of non-stationary time series is described, where the time series vectors are considered within a finite-time interval and are modeled as time-varying autoregressive (AR) processes.
Abstract: In this paper, a feature extraction scheme for a general type of nonstationary time series is described. A non-stationary time series is one in which the statistics of the process are a function of time; this time dependency makes it impossible to utilize standard globally derived statistical attributes such as autocorrelations, partial correlations, and higher order moments as features. In order to overcome this difficulty, the time series vectors are considered within a finite-time interval and are modeled as time-varying autoregressive (AR) processes. The AR coefficients that characterize the process are functions of time that may be represented by a family of basis vectors. A novel Bayesian formulation is developed that allows the model order of a time-varying AR process as well as the form of the family of basis vectors used in the representation of each of the AR coefficients to be determined. The corresponding basis coefficients are then invariant over the time window and, since they directly relate to the time-varying AR coefficients, are suitable features for discrimination. Results illustrate the effectiveness of the method.
TL;DR: In this paper, a time series of significant wave height measured at the Frigg Platform, in the North Sea is modelled using Box-Jenkins autoregressive models and two different transformations are performed and compared.
Posted Content•
TL;DR: In this article, the research for this paper was carried out within Sonderforschungsbereich 373 at the Humboldt University Berlin and was printed using funds made available by the Deutsche Forschungsgemeinschaft.
Abstract: We are grateful to Bernard Hanzon for helpful comments. The research for this paper was carried out within Sonderforschungsbereich 373 at the Humboldt University Berlin and was printed using funds made available by the Deutsche Forschungsgemeinschaft.
Posted Content•
TL;DR: In this article, the exact expressions for the statistical curvature and related geometric quantities in first order autoregressive models are derived for all sample sizes and covariance matrix for the sufficient statistic is also derived.
Abstract: This paper derives exact expressions for the statistical curvature and related geometric quantities in the first order autoregressive models. We present a method that combines the algebra of differential and difference operators to simplify the problem, and to obtain results valid for all sample sizes. The exact covariance matrix for the sufficient statistic is also derived.
TL;DR: This work presents a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines, which makes it the first exact algorithm for spline smoothing of an additive Autore progressive model which can handle large data sets.
Abstract: . We present a Bayesian approach for estimating nonparametrically an additive autoregressive model with the regression curve estimates cubic smoothing splines. Our approach is robust to innovation outliers; it can handle missing observations and produce multistep ahead forecasts. The computation is carried out using Markov chain Monte Carlo and requires O(nM) operations where n is the sample size and M is the number of Markov chain iterations. This makes it the first exact algorithm for spline smoothing of an additive autoregressive model which can handle large data sets. The properties of the estimates and forecasts are studied empirically using simulated and real data sets.
TL;DR: In this article, the authors considered autoregressive sequences with finite second moment and general order and showed that the best predictor with time reversed is linear if and only if the innovations are Gaussian.
Abstract: Prediction for autoregressive sequences with finite second moment and of general order is considered. It is shown that the best predictor with time reversed is linear if and only if the innovations are Gaussian. The connection to time reversibility is also discussed.
TL;DR: In this article, the authors deal with the estimation of the order, the parameters, and the spectrum of a process modeled by a multivariate autoregressive time series, by minimization of a new criterion function.
TL;DR: The modeling approach, together with the inferential procedures, overcome many of the difficulties encountered in current spectral estimation techniques and enables us to examine a host of issues associated with a practical implementation ofinferential procedures for mixed spectral problems.
Abstract: Statistical inference for mixed spectral problems based on a parametric time series model is studied. The model used is based on the canonical autoregressive decomposition (CARD) and represents the underlying random process as the sum of an autoregressive process and sinusoids. Maximum likelihood estimation of the unknown parameters in the model is considered. The entire estimation problem can be shown to require a numerical maximization with respect to only the sinusoidal frequencies. An iterative algorithm to efficiently implement this maximization is presented. This enables us to examine a host of issues associated with a practical implementation of inferential procedures for mixed spectral problems. Some of the topics are accuracy of parameter estimates, selection of model orders, and sensitivity and robustness of the spectral estimates to modeling inaccuracies. The modeling approach, together with the inferential procedures, overcome many of the difficulties encountered in current spectral estimation techniques.
01 Jan 1996
TL;DR: This articles discusses developments in Bayesian time series modelling and analysis relevant in studies of time series in the physical and engineering sciences.
Abstract: This articles discusses developments in Bayesian time series modelling and analysis relevant in studies of time series in the physical and engineering sciences. With illustrations and references, we discuss: Bayesian inference and computation in various state-space models, with examples in analysing quasi-periodic series; isolation and modelling of various components of error in ime series; decompositions of time series into significant latent subseries; nonlinear time series models based on mixtures of auto-regressions; problems with errors and uncertainties in the timing of observations; and the development of non-linear models based on stochastic deformations of time scales.
01 Mar 1996
TL;DR: In this article, the authors consider model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series [PAR], and compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series.
Abstract: This paper considers model selection and forecasting issues in two closely related models for nonstationary periodic autoregressive time series [PAR]. Periodically integrated seasonal time series [PIAR] need a periodic differencing filter to remove the stochastic trend. On the other hand, when the nonperiodic first order differencing filter can be applied, one can have a periodic model with a nonseasonal unit root [PARI]. In this paper, we discuss and evaluate two testing strategies to select between these two models. Furthermore, we compare the relative forecasting performance of each model using Monte Carlo simulations and some U.K. macroeconomic seasonal time series. One result is that forecasting with PARI models while the data generating process is a PIAR process seems to be worse thanvice versa.
TL;DR: In this paper, the authors introduce a new class of the simultaneous switching autoregressive (SSAR) model, which is a non-linear Markovian switching time series model, and discuss the problems of coherency, ergodicity, the stationary distribution and its moments.
TL;DR: In this article, it was shown that temporally aggregating such a process does not affect the presence of this unit root, i.e. the aggregated series is also periodically integrated.
Posted Content•
TL;DR: A bivariate application of smooth transition models to testing Granger noncausality between variables is presented using two long Swedish macroeconomic time series.
Abstract: This paper considers smooth transition regression models and their univariate counterparts, smooth transition autoregressive models. The model is defined and thereafter, linearity testing, statistical inference in smooth transition models, and areas of application are discussed. A bivariate application of smooth transition models to testing Granger noncausality between variables is presented using two long Swedish macroeconomic time series.
TL;DR: A new approach for time series modeling has been developed that has a neural network structure with three layers: the input, switch, and processing layers that is found to perform as well as or even better than the multilayer perceptron network, the radial basis function network, and the threshold autoregressive model in nonlinear time series modeled experiments.
TL;DR: In this article, the student's t autoregressive model with dynamic heteroscedasticity (STAR) was used to model exchange rate dynamics and showed that the statistical distribution of the sterling-deutschmark exchange rate is leptokurtic in all periods.
TL;DR: In this article, the authors investigated the asymptotic properties of the least squares estimator and the maximum likelihood estimator under the assumption of Gaussian disturbances and showed that due to the specific simultaneity involved in the SSAR model, the least square estimator is badly biased.
Abstract: . The simultaneous switching autoregressive (SSAR) model proposed by Kunitomo and Sato (A non-linearity in economic time series and disequilibrium econometric models. In Theory and Application of Mathematical Statistics (ed. A. Takemura). Tokyo:University of Tokyo Press (in Japanese), 1994; Asymmetry in economic time series and simultaneous switching autoregressive model. Struct. Change Econ. Dyn., forthcoming (1994).) is a Markovian non-linear time series model. We investigate the finite sample as well as the asymptotic properties of the least squares estimator and the maximum likelihood (ML) estimator. Due to a specific simultaneity involved in the SSAR model, the least squares estimator is badly biased. However, the ML estimator under the assumption of Gaussian disturbances gives reasonable estimates.