Showing papers on "STAR model published in 2007"

Introduction to Modern Time Series Analysis

Abstract: This book presents modern developments in time series econometrics that are applied to macroeconomic and financial time series. It attempts to bridge the gap between methods and realistic applications. This book contains the most important approaches to analyse time series which may be stationary or nonstationary. Modelling and forecasting univariate time series is the starting point. For multiple stationary time series Granger causality tests and vector autoregressive models are presented. For real applied work the modelling of nonstationary uni- or multivariate time series is most important. Therefore, unit root and cointegration analysis as well as vector error correction models play a central part. Modelling volatilities of financial time series with autoregressive conditional heteroskedastic models is also treated.

A multiple regime smooth transition heterogeneous autoregressive model for long memory and asymmetries

Abstract: In this paper we propose a flexible model to capture nonlinearities and long-range dependence in time series dynamics. The new model is a multiple regime smooth transition extension of the Heterogenous Autoregressive (HAR) model, which is specifically designed to model the behavior of the volatility inherent in financial time series. The model is able to describe simultaneously long memory, as well as sign and size asymmetries. A sequence of tests is developed to determine the number of regimes, and an estimation and testing procedure is presented. Monte Carlo simulations evaluate the finite-sample properties of the proposed tests and estimation procedures. We apply the model to several Dow Jones Industrial Average index stocks using transaction level data from the Trades and Quotes database that covers ten years of data. We find strong support for long memory and both sign and size asymmetries. Furthermore, the new model, when combined with the linear HAR model, is viable and flexible for purposes of forecasting volatility.

Stochastic simulation model for nonstationary time series using an autoregressive wavelet decomposition: Applications to rainfall and temperature

Abstract: [1] A time series simulation scheme based on wavelet decomposition coupled to an autoregressive model is presented for hydroclimatic series that exhibit band-limited low-frequency variability. Many nonlinear dynamical systems generate time series that appear to have amplitude- and frequency-modulated oscillations that may correspond to the recurrence of different solution regimes. The use of wavelet decomposition followed by an autoregressive model of each leading component is explored as a model for such time series. The first example considered is the Lorenz-84 low-order model of extratropical circulation, which has been used to illustrate how chaos and intransitivity (multiple stable solutions) can lead to low-frequency variability. The central England temperature (CET) time series, the NINO3.4 series that is a surrogate for El Nino–Southern Oscillation, and seasonal rainfall from Everglades National Park, Florida, are then modeled with this approach. The proposed simulation model yields better results than a traditional linear autoregressive (AR) time series model in terms of reproducing the time-frequency properties of the observed rainfall, while preserving the statistics usually reproduced by the AR models.

Forecasting with Smooth Transition Autoregressive Models

Abstract: This paper considers the use of smooth transition autoregressive models for forecasting. First, the modelling of time series with these nonlinear models is discussed. Techniques for obtaining multiperiod forecasts are presented. The usefulness of forecast densities in the case of nonlinear models is considered and techniques of graphically displaying such densities demonstrated. The paper ends with an empirical example of forecasting two quarterly unemployment series.

Autoregressive approximation in nonstandard situations: the fractionally integrated and non-invertible cases

Abstract: Autoregressive models are commonly employed to analyze empirical time series. In practice, however, any autoregressive model will only be an approximation to reality and in order to achieve a reasonable approximation and allow for full generality the order of the autoregression, h say, must be allowed to go to infinity with T, the sample size. Although results are available on the estimation of autoregressive models when h increases indefinitely with T such results are usually predicated on assumptions that exclude (1) non-invertible processes and (2) fractionally integrated processes. In this paper we will investigate the consequences of fitting long autoregressions under regularity conditions that allow for these two situations and where an infinite autoregressive representation of the process need not exist. Uniform convergence rates for the sample autocovariances are derived and corresponding convergence rates for the estimates of AR(h) approximations are established. A central limit theorem for the coefficient estimates is also obtained. An extension of a result on the predictive optimality of AIC to fractional and non-invertible processes is obtained.

Order Estimation and Discrimination Between Stationary and Time-Varying (TVAR) Autoregressive Models

Abstract: For a set of T independent observations of the same N-variate correlated Gaussian process, we derive a method of estimating the order of an autoregressive (AR) model of this process, regardless of its stationary or time-varying nature. We also derive a test to discriminate between stationary AR models of order m,AR(m), and time-varying autoregressive models of order m,TVAR(m). We demonstrate that within this technique the number T of independent identically distributed data samples required for order estimation and discrimination just exceeds the maximum possible order mmax, which in many cases is significantly fewer than the dimension of the problem N

Quantile self-exciting threshold autoregressive time series models

Abstract: In this paper we present a Bayesian approach to quantile self-exciting threshold autoregressive time series models The simulation work shows that the method can deal very well with nonstationary time series with very large, but not necessarily symmetric, variations The methodology has also been applied to the growth rate of US real GNP data and some interesting results have been obtained

Switching Varma Term Structure Models - Extended Version

Abstract: The purpose of the paper is to propose a global discrete-time modeling of the term structure of interest rates able to capture simultaneously the following important features: (i) an historical dynamics of the factor driving term structure shapes involving several lagged values, and switching regimes; (ii) a specification of the stochastic discount factor (SDF) with time-varying and regime dependent risk-premia; (iii) explicit or quasi explicit formulas for zero-coupon bond and interest rate derivative prices; (iv) the positivity of the yields at each maturity. The first family of models we develop is given by the Switching Autoregressive Normal (SARN) and the Switching Vector Autoregressive Normal (SVARN) Factor-Based Term Structure Models of order p. The second family of models we study is given by the Switching Autoregressive Gamma (SARG) and the Switching Vector Autoregressive Gamma (SVARG) Factor-Based Term Structure Models of order p. Regime shifts are described by a Markov chain with (historical) non-homogeneous transition probabilities.

Detrended fluctuation analysis of autoregressive processes

Abstract: Autoregressive processes (AR) have typical short-range memory. Detrended Fluctuation Analysis (DFA) was basically designed to reveal long-range correlations in non stationary processes. However DFA can also be regarded as a suitable method to investigate both long-range and short-range correlations in non stationary and stationary systems. Applying DFA to AR processes can help understanding the non-uniform correlation structure of such processes. We systematically investigated a first order autoregressive model AR(1) by DFA and established the relationship between the interaction constant of AR(1) and the DFA correlation exponent. The higher the interaction constant the higher is the short-range correlation exponent. They are exponentially related. The investigation was extended to AR(2) processes. The presence of an interaction between distant terms with characteristic time constant in the series, in addition to a near by interaction will increase the correlation exponent and the range of correlation while the effect of a distant negative interaction will significantly decrease the range of interaction, only. This analysis demonstrate the possibility to identify an AR(1) model in an unknown DFA plot or to distinguish between AR(1) and AR(2) models.

Stability of mixtures of vector autoregressions with autoregressive conditional heteroskedasticity

Abstract: This paper gives necessary and sucien t conditions for stationarity and existence of second moments in mixtures of linear vector autoregressive models with autoregressive conditional heteroskedasticity. Sucien t conditions are also provided for a more general model in which the mixture components are permitted to exhibit limited forms of nonlinearity. When specialized to the corresponding non-mixture case these sucien t conditions improve on their previous counterparts obtained for nonlinear autoregressions with nonlinear conditional heteroskedasticity. In this context, a previous conjecture is also disproved. The results of the paper are proved by using the stability theory of Markov chains. Stationarity, existence of second moments of the stationary distribution, and -mixing are obtained by establishing an appropriate version of geometric ergodicity.

Why does the standard garch(1, 1) model work well?

Abstract: The AutoRegressive Conditional Heteroskedasticity (ARCH) and its generalized version (GARCH) family of models have grown to encompass a wide range of specifications, each of them is designed to enhance the ability of the model to capture the characteristics of stochastic data, such as financial time series. The existing literature provides little guidance on how to select optimal parameters, which are critical in efficiency of the model, among the infinite range of available parameters. We introduce a new criterion to find suitable parameters in GARCH models by using Markov length, which is the minimum time interval over which the data can be considered as constituting a Markov process. This criterion is applied to various time series and its results support the known idea that GARCH(1, 1) model works well.

Threshold variable determination and threshold variable driven switching autoregressive models

Abstract: In this paper we propose a new class of nonlinear time series models, the threshold variable driven switching autoregressive models. It is a hierarchical model that combines two important nonlinear time series models, the threshold autoregressive (AR) models and the random switching AR models. The underlying time series process switches between two (or more) dieren t linear models. The switching dynamics relies on an observable threshold variable (up to certain es- timable parameters) as used in a threshold model, hence reveals the true nature of the switching mechanism. It also allows certain randomness in the switching proce- dure similar to that in a random switching model, hence provides some exibilit y. Furthermore, we propose a model building procedure that concentrates on a fast determination of an appropriate threshold variable among a large set of candidates (and linear combinations of them). This procedure is applicable to the new models as well as the classical threshold models. A simulation study and two data examples are presented.

A New Method of Load Forecasting Based on Generalized Autoregressive Conditional Heteroscedasticity Model

Abstract: The generalized autoregressive conditional heteroscedasticity (GARCH) model has the ability to describe the volatility of time series. A feasible approach to short-term load forecasting based on GARCH methodology is given. By analyzing the random disturbance series of the classical time series model, the existence of autoregressive conditional heteroscedasticity (ARCH) effect is demonstrated by the Lagrange multiplier (LM) test, and the non-satisfaction of homoscedasticity of the classical model is discussed. Furthermore, an improved autoregressive moving average (ARMA)-GARCH model is built, in which the conditional variance equation is included and the estimation of model parameters is obtained by maximum likelihood estimation (MLE). A comparison between the improved model and the classical ARMA model is made by taking into account the actual forecasting effect. The results show that the new model has more practical preconditions and better forecasting performance.

Forecasting the Unknown Dynamics in NN3 Database Using a Nonlinear Autoregressive Recurrent Neural Network

Abstract: In this paper, a nonlinear autoregressive (NAR) recurrent neural network is used for the prediction of the next 18 data samples of each time series in a set of 11 unknown dynamics in NN3 Database. The models are built on the reconstructed state spaces of data and no other domain knowledge is available to be used. Here, we clarify that the employed method is in part similar to a superior subclass of recurrent neural network, namely the nonlinear autoregressive model with exogenous inputs (NARX). Using the extensive available research about NARX networks, we briefly explain that our model is preferred to the both non-recursive and even other recurrent predictors, because of its intrinsic ability for learning long term dependencies in time series. As the desired values of the predicted time series are not available yet, no analysis have been performed on the presented results.

Higher-order Autoregressive Models for Dynamic Textures

Abstract: Dynamic textured sequences are characterized by the interactions between many particles or objects in the scene. Based on earlier work the images of the sequence are interpreted as the output of a linear autoregressive process driven by white Gaussian noise. We extend earlier work by increasing the amount temporal information included when learning the motion in the scene, allowing the models to capture complex motion patterns which extend over multiple frames, thereby increasing the perceptual accuracy of the synthesized results. To overcome problems of dynamic model stability, we apply Burg’s Maximum Entropy Spectral Analysis technique f or parameter estimation, which is found to be reliably stable on smaller samples of training data, even with higher-order dynamics.

Threshold variable selection using nonparametric methods

Abstract: Selecting the threshold variable is a key step in building a generalized threshold autoregressive (TAR) model. This paper proposes a semi-parametric method for this purpose that is based on a single-index functional coecien t model. The asymptotic distribution of the estimator is obtained. A simple algorithm is given and its convergence is proved. Some simulations are reported. Two data sets are analyzed, one of which gives strong statistical support for ratio-dependent predation in Ecology.

Autoregressive spectral analysis based on statistical autocorrelation

Abstract: The autoregressive method of spectral analysis is widely used in diverse areas for its solid theoretical foundation. Various aspects of its statistical performance have been investigated. People assume the times series xn to be samples from a zero-mean distribution whose variance remains constant in time. However, it is not available in fact. In this paper, by formulating the resolution event in the framework of statistical autocorrelation theory and directly determining its value from its center-autocorrelation function and statistical autocorrelation function, we obtain a power spectral density formula for the statistical resolution. On this basis, we determine the limiting resolving behavior of the sample autoregressive spectrum and develop the corresponding statistical insight in the time series. Simulation results are also presented to confirm and illustrate the effectiveness of the theory.

Clues for discriminating between moving average and autoregressive models in spatial processes

Abstract: In this paper we try to provide additional insight into the problem of how to discriminate between the two most common spatial processes: the autoregressive and the moving average. This problem, whose analogous time series is apparently simple, acquires a certain complexity when it is considered in an irregular system of spatial units, mainly because there are few tools to carry out this discussion. Nevertheless, even with this lack, we believe that it is possible to make some progress using the methods available at present. In this paper we discuss the advantages and inconveniences of the different techniques that can help us to discriminate between both processes. We finish off the examination with a Monte Carlo exercise, and an application to the European regional income, which has enabled us to better understand the performance of several proposals such as the Lagrange Multipliers, the so-called Variance criterion and the tests of Vuong and Clarke.

SVM-based time series prediction with nonlinear dynamics methods

Abstract: A key problem in time series prediction using autoregressive models is to fix the model order, namely the number of past samples required to model the time series adequately. The estimation of the model order using cross-validation is a long process. In this paper we explore faster alternative to cross-validation, based on nonlinear dynamics methods, namely Grassberger-Procaccia, Kegl and False Nearest Neighbors algorithms. Once the model order is obtained, it is used to carry out the prediction, performed by a SVM. Experiments on three real data time series show that nonlinear dynamics methods have performances very close to the cross-validation ones.