Showing papers on "STAR model published in 2010"

Bayesian Estimation of Limited Dependent Variable Spatial Autoregressive Models

Abstract: A Gibbs sampling (Markov chain Monte Carlo) method for estimating spatial autoregressive limited dependent variable models is presented. The method can accommodate data sets containing spatial outliers and general forms of non-constant variance. It is argued that there are several advantages to the method proposed here relative to that proposed and illustrated in McMillen (1992) for spatial probit models.

Estimation of a Structural Vector Autoregression Model Using Non-Gaussianity

Abstract: Analysis of causal effects between continuous-valued variables typically uses either autoregressive models or structural equation models with instantaneous effects. Estimation of Gaussian, linear structural equation models poses serious identifiability problems, which is why it was recently proposed to use non-Gaussian models. Here, we show how to combine the non-Gaussian instantaneous model with autoregressive models. This is effectively what is called a structural vector autoregression (SVAR) model, and thus our work contributes to the long-standing problem of how to estimate SVAR's. We show that such a non-Gaussian model is identifiable without prior knowledge of network structure. We propose computationally efficient methods for estimating the model, as well as methods to assess the significance of the causal influences. The model is successfully applied on financial and brain imaging data.

Efficient gmm estimation of high order spatial autoregressive models with autoregressive disturbances

Abstract: In this paper, we extend the GMM framework for the estimation of the mixed-regressive spatial autoregressive model by Lee(2007a) to estimate a high order mixed-regressive spatial autoregressive model with spatial autoregressive disturbances. Identification of such a general model is considered. The GMM approach has computational advantage over the conventional ML method. The proposed GMM estimators are shown to be consistent and asymptotically normal. The best GMM estimator is derived, within the class of GMM estimators based on linear and quadratic moment conditions of the disturbances. The best GMM estimator is asymptotically as efficient as the ML estimator under normality, more efficient than the QML estimator otherwise, and is efficient relative to the G2SLS estimator.

Topology Selection in Graphical Models of Autoregressive Processes

Abstract: An algorithm is presented for topology selection in graphical models of autoregressive Gaussian time series. The graph topology of the model represents the sparsity pattern of the inverse spectrum of the time series and characterizes conditional independence relations between the variables. The method proposed in the paper is based on an l1-type nonsmooth regularization of the conditional maximum likelihood estimation problem. We show that this reduces to a convex optimization problem and describe a large-scale algorithm that solves the dual problem via the gradient projection method. Results of experiments with randomly generated and real data sets are also included.

Noncausal autoregressions for economic time series

Abstract: This paper is concerned with univariate noncausal autoregressive models and their potential usefulness in economic applications. In these models, future errors are predictable, indicating that they can be used to empirically approach rational expectations models with nonfundamental solutions. In the previous theoretical literature, nonfundamental solutions have typically been represented by noninvertible moving average models. However, noncausal autoregressive and noninvertible moving average models closely approximate each other, and therefore,the former provide a viable and practically convenient alternative. We show how the parameters of a noncausal autoregressive model can be estimated by the method of maximum likelihood and derive related test procedures. Because noncausal autoregressive models cannot be distinguished from conventional causal autoregressive models by second order properties or Gaussian likelihood, a model selection procedure is proposed. As an empirical application, we consider modeling the U.S. inflation which, according to our results, exhibits purely forward-looking dynamics.

A hybrid of nonlinear autoregressive model with exogenous input and autoregressive moving average model for long-term machine state forecasting

Abstract: This paper presents an improvement of hybrid of nonlinear autoregressive with exogenous input (NARX) model and autoregressive moving average (ARMA) model for long-term machine state forecasting based on vibration data. In this study, vibration data is considered as a combination of two components which are deterministic data and error. The deterministic component may describe the degradation index of machine, whilst the error component can depict the appearance of uncertain parts. An improved hybrid forecasting model, namely NARX-ARMA model, is carried out to obtain the forecasting results in which NARX network model which is suitable for nonlinear issue is used to forecast the deterministic component and ARMA model are used to predict the error component due to appropriate capability in linear prediction. The final forecasting results are the sum of the results obtained from these single models. The performance of the NARX-ARMA model is then evaluated by using the data of low methane compressor acquired from condition monitoring routine. In order to corroborate the advances of the proposed method, a comparative study of the forecasting results obtained from NARX-ARMA model and traditional models is also carried out. The comparative results show that NARX-ARMA model is outstanding and could be used as a potential tool to machine state forecasting.

A Comparison of Methods for Computing Autocorrelation Time

Abstract: This paper describes four methods for estimating autocorrelation time and evaluates these methods with a test set of seven series. Fitting an autoregressive process appears to be the most accurate method of the four. An R package is provided for extending the comparison to more methods and test series.

Detecting Mean Reversion in Real Exchange Rates from a Multiple Regime star Model

Abstract: Recent studies on general equilibrium models with transaction costs show that the dynamics of the real exchange rate are necessarily nonlinear. Our contribution to the literature on nonlinear price adjustment mechanisms is threefold. First, we model the real exchange rate by a Multi-Regime Logistic Smooth Transition Auto Regression (MR-LSTAR), allowing for both ESTAR-type and SETAR-type dynamics. This choice is motivated by the fact that even the theoretical models, which predict a smooth behavior for the real exchange rate, do not rule out the possibility of a discontinuous adjustment as a limit case. Second, we propose two classes of unit-root tests against this MR-LSTAR alternative, based respectively on the likelihood and on an auxiliary model. Their asymptotic distributions are derived analytically. Third, when applied to 28 bilateral real exchange rates, our tests reject the null hypothesis of a unit root for eleven series bringing evidence in favor of the purchasing power parity.

Unit root inference in panel data models where the time-series dimension is fixed: a comparison of different tests

Abstract: Summary The objective of the paper is to investigate and compare the performance of some of the unit root tests in micropanels, which have been suggested in the literature. The framework is a first-order autoregressive panel data model allowing for heterogeneity in the intercept but not in the autoregressive parameter. The tests are all based on usual t-statistics corresponding to least squares estimators of the autoregressive parameter resulting from different transformations of the observed variables. The performance of the tests is investigated and compared by deriving the local power of the tests when the autoregressive parameter is local-to-unity. The results show that the assumption concerning the initial values is extremely important in this matter. The outcome of a simulation experiment demonstrates that the local power of the tests provides a good approximation to their actual power in finite samples.

Forecasting for quantile self-exciting threshold autoregressive time series models

Abstract: Self-exciting threshold autoregressive time series models have been used extensively, and the conditional mean obtained from these models can be used to predict the future value of a random variable. In this paper we consider quantile forecasts of a time series based on the quantile self-exciting threshold autoregressive time series models proposed by Cai and Stander (2008) and present a new forecasting method for them. Simulation studies and application to real time series show that the method works very well.

Parameters estimation for asymmetric bifurcating autoregressive processes with missing data

Abstract: We estimate the unknown parameters of an asymmetric bifurcating autoregressive process (BAR) when some of the data are missing. In this aim, we model the observed data by a two-type Galton-Watson process consistent with the binary tree structure of the data. Under independence between the process leading to the missing data and the BAR process and suitable assumptions on the driven noise, we establish the strong consistency of our estimators on the set of non-extinction of the Galton-Watson, via a martingale approach. We also prove a quadratic strong law and the asymptotic normality.

A representation theory for polynomial cofractionality in vector autoregressive models

Abstract: We extend the representation theory of the autoregressive model in the fractional lag operator of Johansen (2008, Econometric Theory 24, 651–676). A recursive algorithm for the characterization of cofractional relations and the corresponding adjustment coefficients is given, and it is shown under which condition the solution of the model is fractional of order d and displays cofractional relations of order d − b and polynomial cofractional relations of order d − 2b,…, d − cb ≥ 0 for integer c; the cofractional relations and the corresponding moving average representation are characterized in terms of the autoregressive coefficients by the same algorithm. For c = 1 and c = 2 we find the results of Johansen (2008).

Modeling non-Gaussian time-varying vector autoregressive processes by particle filtering

Abstract: We present a novel and general methodology for modeling time-varying vector autoregressive processes which are widely used in many areas such as modeling of chemical processes, mobile communication channels and biomedical signals. In the literature, most work utilize multivariate Gaussian models for the mentioned applications, mainly due to the lack of efficient analytical tools for modeling with non-Gaussian distributions. In this paper, we propose a particle filtering approach which can model non-Gaussian autoregressive processes having cross-correlations among them. Moreover, time-varying parameters of the process can be modeled as the most general case by using this sequential Bayesian estimation method. Simulation results justify the performance of the proposed technique, which potentially can model also Gaussian processes as a sub-case.

Forecasting chaotic time series of exchange rate based on nonlinear autoregressive model

Abstract: Exchange rate time series is often characterized as chaotic in nature. The prediction using conventional statistical techniques and neural network with back propagation algorithm, which is most widely applied, do not give reliable prediction results. Exchange-rate time series is also a dynamic non-linear system, whose characteristics cannot be reflected by the static neutral network. The Nonlinear Autoregressive with eXogenous input (NARX) includes the feedback of the network output, therefore can reflect the dynamic property of the system. This paper proved the chaotic property of the exchange-rate time series, calculated the embedding dimension and time delay of the series, and established the exchange-rate forecast model using the NARX network. The result shows that the NARX network has better short-term forecast effect, comparing to the BP network and the SVM model.

Asymptotic behavior of CLS estimator of autoregressive parameter for nonprimitive unstable INAR(2) models

Abstract: In this paper the asymptotic behavior of conditional least squares estimators of the autoregressive parameter for nonprimitive unstable integer-valued autoregressive models of order 2 (INAR(2)) is described.

Tree-based threshold modeling for short-term forecast of daily maximum ozone level

Abstract: This paper proposes a simple class of threshold autoregressive model for purpose of forecasting daily maximum ozone concentrations in Southern California. Linear time series model has been widely considered in environmental modeling. However, this class of models fails to capture the nonlinearity in ozone process and the complexity of meteorological interactions with ozone. In this article, we used the threshold autoregressive models with two classes of regimes; periodic and meteorological regimes. Days in week were used for the periodic regimes and the regression tree method was used to define the regimes as a function of meteorological variables. As the reference model we used the autoregressive model with lagged ozone and various lagged meteorological variables as the covariates. The proposed models were applied to a 3-year dataset of daily maximum ozone concentrations obtained from five monitoring stations in San Bernardino County, CA and their forecast performances were evaluated using an independent year-long dataset from the same stations. The results showed that the threshold models well capture the nonlinearity in ozone process and remove the nonstationarity in model residuals. The threshold models outperformed the non-threshold autoregressive models in day-ahead forecasts. The tree-based model showed slightly better performance than the periodic threshold model.

Analysis of Non-Stationary Time Series using Wavelet Decomposition

Abstract: The increased computational speed and developments in the area of algorithms have created the possibility for efficiently identifying a well-fitt ing time series model for the given nonstationary-n onlinear time series and use it for prediction. In this pape r a new method is used for analyzing a given nonstationary-nonlinear time series. Based on the M ultiresolution Analysis (MRA) and nonlinear characteristics of the given time series a method f or analyzing the given time series using wavelet decomposition is discussed in this paper. After dec omposing a given nonstationary-nonlinear time series Z t in to a trend series X t and a detail series Y t the trend series and the detail series are separat ely modeled. Model T(t) representing the trend series X t and the Threshold Autoregressive Model of order k (TAR(k)) representing detail series Y t are combined to obtain the Trend and Threshold Aut oregressive(T-TAR) model representing the given nonstationary-nonlinear time series. The scale dependent thresholds for t he T- TAR model are obtained using the detail series and using the trend series. Also simulation studies are done and the results revealed that the developed method could increase the forecasting accuracy. (Nature an d Science 2010;8(1):53-59) ( ISSN: 1545-0740).

M -estimation for a spatial unilateral autoregressive model with infinite variance innovations

Abstract: We study the limiting behavior of the M-estimators of parameters for a spatial unilateral autoregressive model with independent and identically distributed innovations in the domain of attraction of a stable law with index α ∈ (0, 2]. Both stationary and unit root models and some extensions are considered. It is also shown that self-normalized M-estimators are asymptotically normal. A numerical example and a simulation study are also given.

A Time-Varying Threshold STAR Model of Unemployment and the Natural Rate

Abstract: Smooth-transition autoregressive (STAR) models have proven to be worthy competitors of Markov-switching models of regime shifts, but the assumption of a time-invariant threshold level does not seem realistic and it holds back this class of models from reaching their potential usefulness. Indeed, an estimate of a time-varying threshold level of unemployment, for example, might serve as a meaningful estimate of the natural rate of unemployment. More precisely, within a STAR framework, one might call the time-varying threshold the “tipping level”rate of unemployment, at which the mean and dynamics of the unemployment rate shift. In addition, once the threshold level is allowed to be time-varying, one can add an error-correction term— between the lagged level of unemployment and the lagged threshold level— to the autoregressive terms in the STAR model. In this way, the time-varying latent threshold level serves dual roles: as a demarcation between regimes and as part of an error-correction term.

Nonlinear mean-reversion to purchasing power parity: exponential smooth transition autoregressive models and stochastic unit root processes

Abstract: Nonlinear exponential smooth transition autoregressive (ESTAR) models are recently very popular in modelling the deviation from purchasing power parity. This article, shows that there is a close relation between the ESTAR models estimated in Taylor et al. (2001) and stochastic unit root (STUR) processes of Granger and Swanson (1997) and McCabe and Tremayne (1995). Also, for a post-Bretton Woods sample period, the real exchange rates from four major countries are tested if they are better described as I(1), ESTAR or STUR processes.

Characterizing economic trends by Bayesian stochastic model specification search

Abstract: We apply a recently proposed Bayesian model selection technique, known as stochastic model specification search, for characterising the nature of the trend in macroeconomic time series. We illustrate that the methodology can be quite successfully applied to discriminate between stochastic and deterministic trends. In particular, we formulate autoregressive models with stochastic trends components and decide on whether a specific feature of the series, i.e. the underlying level and/or the rate of drift, are fixed or evolutive.

Compative robustness of six tests in repeated measures designs with specified departures from sphericity

Abstract: In this article we examine the behaviour of six univariate statistics for analyzing the data of a Split-plot factorial design. Except for the univariate analysis of variance, which assumes that the dispersion matrix underlying the data is spherical, the other five procedures assume absence of sphericity. However, they do so with a clear distinction between two alternatives, insofar as three of them presuppose an arbitrary correlation between the data and two presuppose serial autocorrelation. These six approaches were compared with regard to their robustness under multivariate normality in the absence of sphericity, both when there was serial autocorrelation and when there was underlying arbitrary correlation. In general, Monte Carlo comparisons show that when underlying the data there is a autoregressive stationary or decreasing structured non-stationary autoregressive process, the Hearne, Clark and Hatch procedure is the most robust. In the rest of the conditions studied, i.e., increasing structured non-stationarity autoregressive and arbitrary non-stationarity (autoregressive and with arbitrary correlation), the Greenhouse-Geisser and Lecoutre statistics display the best behaviour.

Estimation for binary models generated by Gaussian autoregressive processes

Abstract: Regression-type and partial likelihood models are presented for binary data obtained by clipping a Gaussian autoregressive process. Five methods for estimating parameters of the model are proposed and compared via a simulation study. A real data analysis is also presented.