Showing papers on "STAR model published in 2009"
TL;DR: In this paper, the authors developed an estimator for higher-order spatial autoregressive panel data error component models, SARAR(R,S), without distributional assumptions.
Abstract: This paper develops an estimator for higher-order spatial autoregressive panel data error component models with spatial autoregressive disturbances, SARAR(R,S). We derive the moment conditions and optimal weighting matrix without distributional assumptions for a generalized moments (GM) estimation procedure of the spatial autoregressive parameters of the disturbance process and define a generalized two-stages least squares estimator for the regression parameters of the model. We prove consistency of the proposed estimators, derive their joint asymptotic distribution, and provide Monte Carlo evidence on their small sample performance.
110 citations
TL;DR: The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper and it is observed that more accurate results are obtained from the proposed hybrid method.
Abstract: In the literature, there have been many studies using fuzzy time series for the purpose of forecasting. The most studied model is the first order fuzzy time series model. In this model, an observation of fuzzy time series is obtained by using the previous observation. In other words, only the first lagged variable is used when constructing the first order fuzzy time series model. Therefore, this model can not be sufficient for some time series such as seasonal time series which is an important class in time series models. Besides, the time series encountered in real life have not only autoregressive (AR) structure but also moving average (MA) structure. The fuzzy time series models available in the literature are AR structured and are not appropriate for MA structured time series. In this paper, a hybrid approach is proposed in order to analyze seasonal fuzzy time series. The proposed hybrid approach is based on partial high order bivariate fuzzy time series forecasting model which is first introduced in this paper. The order of this model is determined by utilizing Box-Jenkins method. In order to show the efficiency of the proposed hybrid method, real time series are analyzed with this method. The results obtained from the proposed method are compared with the other methods. As a result, it is observed that more accurate results are obtained from the proposed hybrid method.
87 citations
TL;DR: In this article, a non-degenerate limiting distribution is given for maximum likelihood estimators of the autoregressive model equation and the parameters of the stable noise distribution, and the behavior of the estimators for finite samples is studied via simulation.
Abstract: We consider maximum likelihood estimation for both causal and noncausal autoregressive time series processes with non-Gaussian $\alpha$-stable noise. A nondegenerate limiting distribution is given for maximum likelihood estimators of the parameters of the autoregressive model equation and the parameters of the stable noise distribution. The estimators for the autoregressive parameters are $n^{1/\alpha}$-consistent and converge in distribution to the maximizer of a random function. The form of this limiting distribution is intractable, but the shape of the distribution for these estimators can be examined using the bootstrap procedure. The bootstrap is asymptotically valid under general conditions. The estimators for the parameters of the stable noise distribution have the traditional $n^{1/2}$ rate of convergence and are asymptotically normal. The behavior of the estimators for finite samples is studied via simulation, and we use maximum likelihood estimation to fit a noncausal autoregressive model to the natural logarithms of volumes of Wal-Mart stock traded daily on the New York Stock Exchange.
79 citations
TL;DR: It is argued that vector error correction models offer a particularly convenient parameterization both for model specification and for using the models for economic analysis.
Abstract: Vector autoregressive (VAR) models for stationary and integrated variables are reviewed. Model specification and parameter estimation are discussed and various uses of these models for forecasting and economic analysis are considered. For integrated and cointegrated variables it is argued that vector error correction models offer a particularly convenient parameterization both for model specification and for using the models for economic analysis.
62 citations
TL;DR: The binomial AR(1) model of McKenzie (1985) for time series of binomial counts has a well-interpretable structure and applies well to several real-world problems as discussed by the authors.
Abstract: The binomial AR(1) model of McKenzie (1985) for time series of binomial counts has a well-interpretable structure and applies well to several real-world problems. After a brief review of important properties of this model, we propose and investigate a new class of pth order autoregressive models, which coincide with the binomial AR(1) model for p = 1. Special cases of this new model family are discussed, each having a different autocorrelation structure. A real-data example demonstrates that these higher-order models have a great potential to be applied in practice.
54 citations
TL;DR: In this paper, the authors introduce a new class of autoregressive models for integer-valued time series using the rounding operator, which have several advantages, such as simple innovation structure, auto-gressive coefficients with arbitrary signs, possible negative values for time series and possible negative value for the autocorrelation function.
Abstract: We introduce a new class of autoregressive models for integer-valued time series using the rounding operator. Compared with classical INAR models based on the thinning operator, the new models have several advantages: simple innovation structure, autoregressive coefficients with arbitrary signs, possible negative values for time series and possible negative values for the autocorrelation function. Focused on the first-order RINAR(1) model, we give conditions for its ergodicity and stationarity. For parameter estimation, a least squares estimator is introduced and we prove its consistency under suitable identifiability condition. Simulation experiments as well as analysis of real data sets are carried out to attest the model performance.
53 citations
TL;DR: In this article, the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes is studied under very weak assumptions on the driven noise of the process.
Abstract: We study the asymptotic behavior of the least squares estimators of the unknown parameters of general pth-order bifurcating autoregressive processes. Under very weak assumptions on the driven noise of the process, namely conditional pair-wise independence and suitable moment conditions, we establish the almost sure convergence of our estimators together with the quadratic strong law and the central limit theorem. All our analysis relies on non-standard asymptotic results for martingales.
53 citations
TL;DR: In this paper, the authors introduce the Student t-mixture autoregressive models for financial time series modelling, which is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal.
Abstract: We introduce the class of Student t-mixture autoregressive models, which is promising for financial time series modelling. The model is able to capture serial correlations, time-varying means and volatilities, and the shape of the conditional distributions can be time varied from short-tailed to long-tailed, or from unimodal to multimodal. The use of t-distributed errors in each component of the model allows conditional leptokurtic distributions that account for the commonly observed excess unconditional kurtosis in financial data. Methods of parameter estimation and model selection are given. Finally, the proposed modelling procedure is illustrated through a real example.
45 citations
TL;DR: The 10th order autoregressive neural network model with extensive input variable selection performs the best among all the competitive models in forecasting the monthly total ozone concentration over the study zone.
40 citations
06 Apr 2009
TL;DR: In this paper, ARCH (Autoregressive Conditional Heteroscedasticity) effects of wind data series are analyzed with Eviews software and results show that ARMA-ARCH model possesses higher accuracy.
Abstract: Short term wind forecasting is a very important work to the operation of wind farms and power systems. In this paper, ARCH (Autoregressive Conditional Heteroscedasticity) effects of wind data series are analyzed with Eviews software. Firstly, an ARMA (Autoregressive Moving Average) model of wind speed time series is built. Secondly, ARCH (Autoregressive Conditional Heteroscedasticity) effect of the residual of ARMA model is tested by Lagrange Multiplier, and the corresponding ARMA-ARCH model is set up. Lastly, forecasting performances of ARMA-ARCH model are compared with ARMA model. Validation of ARMA-ARCH model is proved. And the results show that ARMA-ARCH model possesses higher accuracy.
39 citations
01 Sep 2009
TL;DR: A non-Gaussian autoregressive model with epsilon-skew-normal innovations is introduced and the model is fitted to a real time series.
Abstract: A non-Gaussian autoregressive model with epsilon-skew-normal innovations is introduced. Moments and maximum likelihood estimators of the parameters are proposed and their limit distributions are derived. Monte Carlo simulation results are analysed and the model is fitted to a real time series.
TL;DR: In this article, the authors derived the asymptotic distributions of the least squares estimators of the model parameters in vector periodic autoregressive time series models, allowing the parameters in a given season to satisfy linear constraints.
Abstract: Vector periodic autoregressive time series models (PVAR) form an important class of time series for modelling data derived from climatology, hydrology, economics and electrical engineering, among others. In this article, we derive the asymptotic distributions of the least squares estimators of the model parameters in PVAR models, allowing the parameters in a given season to satisfy linear constraints. Residual autocorrelations from classical vector autoregressive and moving-average models have been found useful for checking the adequacy of a particular model. In view of this, we obtain the asymptotic distribution of the residual autocovariance matrices in the class of PVAR models, and the asymptotic distribution of the residual autocorrelation matrices is given as a corollary. Portmanteau test statistics designed for diagnosing the adequacy of PVAR models are introduced and we study their asymptotic distributions. The proposed test statistics are illustrated in a small simulation study, and an application with bivariate quarterly West German data is presented.
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TL;DR: It is found that one of the factor-augmented models generally outperform the large-scale models in the 20 US states examined in this paper.
Abstract: We implement several Bayesian and classical models to forecast housing prices in 20 US states. In addition to standard vector-autoregressive (VAR) and Bayesian vector autoregressive (BVAR) models, we also include the information content of 308 additional quarterly series in some models. Several approaches exist for incorporating information from a large number of series. We consider two approaches – extracting common factors (principle components) in a Factor-Augmented Vector Autoregressive (FAVAR) or Factor-Augmented Bayesian Vector Autoregressive (FABVAR) models or Bayesian shrinkage in a large-scale Bayesian Vector Autoregressive (LBVAR) models. In addition, we also introduce spatial or causality priors to augment the forecasting models. Using the period of 1976:Q1 to 1994:Q4 as the in-sample period and 1995:Q1 to 2003:Q4 as the out-of-sample horizon, we compare the forecast performance of the alternative models. Based on the average root mean squared error (RMSE) for the one-, two-, three-, and four–quarters-ahead forecasts, we find that one of the factor-augmented models generally outperform the large-scale models in the 20 US states examined in this paper.
TL;DR: A moderate deviation principle for autoregressive processes is established and the moderate deviation estimates of the least square and the Yule-Walker estimators of the parameter of an autore progressive process are provided.
TL;DR: In this paper, a random coefficient autoregressive process for counting data based on a generalized thinning operator is presented and the necessary and sufficient conditions for weak stationarity are the same as those for continuous-valued AR(1) processes.
01 Jan 2009
TL;DR: In this article, the autoregressive conditional duration model was applied to the daily range of the log price of Apple stock and found that adopting the decimal system for the US stock price on January 29, 2001, significantly reduced price volatility.
Abstract: This chapter studies the autoregressive conditional duration model. It discusses properties and statistical inference of the model. It also considers some extensions to handle nonlinear durations and interventions. For applications, we apply the model to daily range of the log price of Apple stock and find that adopting the decimal system for the US stock price on January 29, 2001, significantly reduces price volatility.
TL;DR: A boosting method is proposed that performs model identification and estimation simultaneously within the framework of nonlinear autoregressive time series within which alternative fitting methods fail.
TL;DR: In this paper, a multidimensional diagonalization of the functional parameters (operators) involved in the FAR(p), p < 1, (FAR(p)) formulation is derived.
Abstract: Functional data models provides a suitable framework for the statistical analysis of several environmental phenomena involving continuous time evolution and/or spatial variation. The functional autoregressive model of order p, p ≥ 1, (FAR(p)) extends to the infinite-dimensional space context the classical autoregressive model AR(p) (see, for example, Mourid T (1993) Processus autoregressiifs d’ordre superieur. Acad Sci t.317(Ser. I):1167–1172). In this paper, we derive a multidimensional diagonalization of the functional parameters (operators) involved in the FAR(p), p > 1, formulation. The functional state equation is then transformed into a discrete system of scalar state equations. The decomposition obtained is optimal regarding information on spatiotemporal interaction affecting the evolution of the spatial behavior of the process of interest. For functional prediction and filtering, we implement the Kalman filter equations from the diagonal version derived for FAR(p) models.
TL;DR: The results show that the proposed method consistently outperforms other local time series modelling techniques on a range of performance measures including the mean-square-error, correct trend predication percentage, accumulated profit and model variance.
01 Aug 2009
TL;DR: A structure theory with emphasis on the zeroless case is presented, which is generic in the setting considered and the latent variables are modeled as a possibly singular autoregressive process and (generalized) Yule Walker equations are used for parameter estimation.
Abstract: We consider generalized linear dynamic factor models. These models have been developed recently and they are used for high dimensional time series in order to overcome the “curse of dimensionality”. We present a structure theory with emphasis on the zeroless case, which is generic in the setting considered. Accordingly the latent variables are modeled as a possibly singular autoregressive process and (generalized) Yule Walker equations are used for parameter estimation.
12 Jul 2009
TL;DR: The ability of thespace-time autoregressive models to model the spatial and temporal correlations in the traffic network and show that the space-time model performs well are evaluated.
Abstract: Traffic flow data are in the form of spatial time series and are collected at specific locations at constant intervals of time. Space-time autoregressive time series modeling is a promising inductive method that uses a small number of parameters and can be used for online monitoring and prediction. In this paper, we develop space-time autoregressive models for urban traffic flow network scenarios. We evaluate the ability of the space-time autoregressive models to model the spatial and temporal correlations in the traffic network and show that the space-time model performs well.
TL;DR: A new class of nonlinear autoregressive models for vector time series, where the current vector depends on single‐indexes defined on the past lags and the effects of different lags have an additive form is studied.
Abstract: We study a new class of nonlinear autoregressive models for vector time series, where the current vector depends on single-indexes defined on the past lags and the effects of different lags have an additive form. A sufficient condition is provided for stationarity of such models. We also study estimation of the proposed model using P-splines, hypothesis testing, asymptotics, selec- tion of the order of the autoregression and of the smoothing parameters and nonlinear forecasting. We perform simulation experiments to evaluate our model in various settings. We illustrate our methodology on a climate data set and show that our model provides more accurate yearly forecasts of the El Nino phenomenon, the unusual warming of water in the Pacific Ocean.
TL;DR: In this paper, the authors study the dynamics of the US real effective exchange rate by capturing nonlinearity and long memory features, and use the family of fractionally integrated STAR (FISTAR) models in the case when the transition function is an exponential function.
TL;DR: In this paper, a monitoring procedure for early detection of distributional changes in autoregressive models is proposed, which is based on residuals since the test based on the observations is inappropriate.
Abstract: In this artilce, we develop a monitoring procedure for an early detection of distributional changes in autoregressive models. We design the monitoring procedure based on residuals since the test based on the observations is inappropriate. We verify that under regularity conditions, the stopping rule designed to detect changes behaves asymptotically the same as that in iid samples. Simulation results are provided for illustration.
TL;DR: In this article, the authors derived the local asymptotic normality (LAN) of the log-likelihood for the bifurcating autoregressive model (BAR) for tree structured data where each individual in one generation gives rise to two off-spring in the next generation.
24 Sep 2009
TL;DR: Simulation results show that the performance of the proposed autoregressive channel prediction model based on particle filtering is better than that of Kalman filtering.
Abstract: An autoregressive channel prediction model is presented for cognitive radio systems. This model adopts a second-order AR model and a particle filter. In this paper, an AR model of order p is used to approximate the flat Rayleigh fading channels. Simulation results show that the performance of the proposed autoregressive channel prediction model based on particle filtering is better than that of Kalman filtering.
TL;DR: In this paper, it was shown that the distributions of the multi-step predictors in mixture autoregressive models are also mixtures and specify them analytically using arithmetic manipulation on components' parameters.
TL;DR: This article deals with the adaptive estimation of a periodic autoregressive model, with unspecified innovation density satisfying only some general technical assumptions, and establishes the Local Asymptotic Normality,LAN,LAQ, and the local properties satisfied by its central sequence.
Abstract: This article deals with the adaptive estimation of a periodic autoregressive model, with unspecified innovation density satisfying only some general technical assumptions. We first establish, while verifying the adapted sufficient conditions of Swensen (1985) to our model, the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ), and the Local Asymptotic properties satisfied by its central sequence. Secondly, the Locally Asymptotically Minimax (LAM) estimators are constructed. Using these results, we construct the adaptive estimators of the unknown autoregressive parameters. The performances of the established estimators are shown, via simulation studies.
TL;DR: In this article, the authors developed a switching-regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process, and established stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model.
Abstract: . We develop a switching-regime vector autoregressive model in which changes in regimes are governed by an underlying Markov process. In contrast to the typical hidden Markov approach, we allow the transition probabilities of the underlying Markov process to depend on past values of the time series and exogenous variables. Such processes have potential applications in finance and neuroscience. In the latter, the brain activity at time t (measured by electroencephalograms) will be modelled as a function of both its past values as well as exogenous variables (such as visual or somatosensory stimuli). In this article, we establish stationarity, geometric ergodicity and existence of moments for these processes under suitable conditions on the parameters of the model. Such properties are important for understanding the stability properties of the model as well as for deriving the asymptotic behaviour of various statistics and model parameter estimators.
TL;DR: The restricted likelihood ratio test, RLRT, for the autoregressive coe-cient in auto-gressive models has recently been shown to be second order pivotal when the autOREgressive co-cient is in the interior of the parameter space and so is very well approximated by the ´ 2 distribution.
Abstract: The restricted likelihood ratio test, RLRT, for the autoregressive coe-cient in autoregressive models has recently been shown to be second order pivotal when the autoregressive coe-cient is in the interior of the parameter space and so is very well approximated by the ´ 2 distribution. In this paper, the non-standard asymptotic distribution of the RLRT for the unit root boundary value is obtained and is found to be almost identical to that of the ´ 2 in the right tail. Together, the above two results imply that the ´ 2 distribution approximates the RLRT distribution very well even for near unit root series and transitions smoothly to the unit root distribution.