Showing papers on "STAR model published in 2011"

MCMC-based estimation of Markov Switching ARMA–GARCH models

Abstract: Regime switching models, especially Markov Switching (MS) models, are regarded as a promising way to capture nonlinearities in time series. Combining the elements of MS models with full Autoregressive Moving Average–Generalized Autoregressive Conditional Heteroskedasticity (ARMA–GARCH) models poses severe difficulties for the computation of parameter estimators. Existing methods can become completely unfeasible due to the full path dependence of such models. In this article, we demonstrate how to overcome this problem. We formulate a full MS–ARMA–GARCH model and its Bayes estimator. This facilitates the use of Markov Chain Monte Carlo methods and allows us to develop an algorithm to compute the Bayes estimator of the regimes and parameters of our model. The approach is illustrated on simulated data and with returns from the New York Stock Exchange (NYSE). Our model is then compared to other approaches and clearly proves to be advantageous.

Univariate modelling of monthly maximum temperature time series over northeast India: neural network versus Yule–Walker equation based approach

Abstract: The present paper has adopted an autoregressive approach to inspect the time series of monthly maximum temperature (Tmax) over northeast India. Through autocorrelation analysis the Tmax time series of northeast India is identified as non-stationary, with a seasonality of 12 months, and it is also found to show an increasing trend by using both parametric and non-parametric methods. The autoregressive models of the reduced Tmax time series, which has become stationary on removal of the seasonal and the trend components from the original time series, were generated through Yule–Walker equations. The sixth order autoregressive model (AR(6)) is identified as a suitable representative of the Tmax time series based on the Akaike information criteria, and the prediction potential of AR(6) is also established statistically through Willmott's indices. Subsequently, autoregressive neural network models were generated as a multilayer perceptron, a generalized feed forward neural network and a modular neural network. An autoregressive neural network model of order four (AR-NN(4)), in the form of a modular neural network (MNN), has performed comparably well with that of AR(6) based on the high values of Willmott's indices and the low values of the prediction error. Therefore, AR-NN(4)-MNN will be a better option than AR(6) to forecast a time series, i.e. the monthly Tmax time series of northeast India, because AR-NN(4)-MNN requires fewer predictors for a superior forecast of a time series. Copyright © 2010 Royal Meteorological Society

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.

Forecasting Aggregated Time Series Variables: A Survey

Abstract: Aggregated times series variables can be forecasted in different ways. For example, they may be forecasted on the basis of the aggregate series or forecasts of disaggregated variables may be obtained fi rst and then these forecasts may be aggregated. A number of forecasts are presented and compared. Classical theoretical results on the relative effi ciencies of different forecasts are reviewed and some complications are discussed which invalidate the theoretical results. Contemporaneous as well as temporal aggregation are considered. JEL classifi cation : C22, C32 Key Words : Autoregressive moving-average process, contemporaneous aggregation, temporal aggregation, vector autoregressive moving-average process

Estimation and testing for a Poisson autoregressive model

Abstract: This article considers statistical inference for a Poisson autoregressive model. A condition for ergodicity and a necessary and sufficient condition for the existence of moments are given. Asymptotics for maximum likelihood estimator and weighted least squares estimators with estimated weights or known weights of the parameters are established. Testing conditional heteroscedasticity and testing the parameters under a simple ordered restriction are noted. A simulation study is also given.

Stationarity of generalized autoregressive moving average models

Abstract: Time series models are often constructed by combining nonstationary effects such as trends with stochastic processes that are believed to be stationary. Although stationarity of the underlying process is typically crucial to ensure desirable properties or even validity of statistical estimators, there are numerous time series models for which this stationarity is not yet proven. A major barrier is that the most commonly-used methods assume φ-irreducibility, a condition that can be violated for the important class of discrete-valued observation-driven models. We show (strict) stationarity for the class of Generalized Autoregressive Moving Average (GARMA) models, which provides a flexible analogue of ARMA models for count, binary, or other discrete-valued data. We do this from two perspectives. First, we show conditions under which GARMA models have a unique stationary distribution (so are strictly stationary when initialized in that distribution). This result potentially forms the foundation for broadly showing consistency and asymptotic normality of maximum likelihood estimators for GARMA models. Since these conclusions are not immediate, however, we also take a second approach. We show stationarity and ergodicity of a perturbed version of the GARMA model, which utilizes the fact that the perturbed model is φ-irreducible and immediately implies consistent estimation of the mean, lagged covariances, and other functionals of the perturbed process. We relate the perturbed and original processes by showing that the perturbed model yields parameter estimates that are arbitrarily close to those of the original model.

Maximum likelihood parameter estimation algorithm for controlled autoregressive autoregressive models

Abstract: A maximum likelihood parameter estimation algorithm is derived for controlled autoregressive autoregressive (CARAR) models based on the maximum likelihood principle. In this derivation, we use an estimated noise transfer function to filter the input–output data. The simulation results show that the proposed estimation algorithm can effectively estimate the parameters of such class of CARAR systems and give more accurate parameter estimates than the recursive generalized least-squares algorithm.

A p-Order signed integer-valued autoregressive (SINAR(p)) model

Abstract: In this article, we propose an extension of integer-valued autoregressive INAR models. Using a signed version of the thinning operator, we define a larger class of -valued processes, called SINAR, which can have positive as well as negative correlations. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. In particular, it is shown that the autocorrelation function of any real-valued AR process can be recovered with a SINAR process, which improves INAR modeling.

Bayesian Mixtures of Autoregressive Models

Abstract: In this article we propose a class of time-domain models for analyzing possibly nonstationary time series. This class of models is formed as a mixture of time series models, whose mixing weights are a function of time. We consider specifically mixtures of autoregressive models with a common but unknown lag. To make the methodology work we show that it is necessary to first partition the data into small non-overlapping segments, so that all observations within one segment are always allocated to the same component. The model parameters, including the number of mixture components, are then estimated via Markov chain Monte Carlo methods. The methodology is illustrated with simulated and real data. Supplemental materials are available online.

Autoregressive Models for Variance Matrices: Stationary Inverse Wishart Processes

Abstract: We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory The main class of models explored is a novel class of stationary, first-order autoregressive (AR) processes on the cone of positive semi-definite matrices Aspects of the theory and structure of these new models for multivariate "volatility" processes are described in detail and exemplified We then develop approaches to model fitting via Bayesian simulation-based computations, creating a custom filtering method that relies on an efficient innovations sampler An example is then provided in analysis of a multivariate electroencephalogram (EEG) time series in neurological studies We conclude by discussing potential further developments of higher-order AR models and a number of connections with prior approaches

Order selection in arma models using the focused information criterion: arma order selection using fic

Abstract: Summary This paper develops a new approach for order selection in autoregressive moving average models using the focused information criterion. This criterion minimizes the asymptotic mean squared error of the estimator of a parameter of interest. Simulation studies indicate that the suggested criterion is quite effective and comparable to the Akaike information criterion, the corrected Akaike information criterion and the Bayesian information criterion in autoregressive moving average order selection. The use of the focused information criterion for the simultaneous selection of regression variables and order of the error process in a linear regression model with autoregressive moving average errors is also considered.

Modeling and Prediction of Tree Height-Diameter Relationships Using Spatial Autoregressive Models

Abstract: Three spatial autoregressive models were applied to model the tree height-diameter relationship, including spatial lag model (SLM), spatial error model (SEM), and spatial Durbin model (SDM), with ordinary least squares (OLS) as a benchmark. Five spatial weight matrices were used to evaluate the impacts of different weighting schemes on model fitting. It was evident that different schemes of spatial weight matrix strongly affected the model fitting and parameter estimation in these spatial autoregressive models. We found that the variogram or geostatistical weight matrix was superior to other spatial weight matrices such as contiguity, inverse distances, and local G i* statistics. Further, the spatial autoregressive models were used to predict tree heights at unsampled locations. The results showed that the three spatial autoregressive models overperformed the OLS model not only in model fitting and reducing spatial dependence, but also in model predictions. In general, SDM and SEM performed significantly better than SLM, whereas SDM was slightly better than SEM in each aspect of model fitting and prediction. However, if the complexity of the model structure is a concern, SEM with a geostatistical weight matrix is a reasonable choice over SDM because SEM offers the model coefficient estimates close to those of the OLS model, which makes the interpretation and understanding of the model much easier. FOR .S CI. 57(3):252-264.

Beta Autoregressive Transition Markov-switching Models for Business Cycle Analysis

Abstract: We propose a new class of Markov-switching models useful for business cycle analysis, with transition probabilities following independent beta autoregressive processes. We study the effects of the autoregressive dynamics on the regime duration. We propose a full Bayesian inference approach and particular attention is paid to the parameters of the latent beta autoregressive processes. We discuss the choice of the prior distributions and propose a Markov-chain Monte Carlo algorithm for estimating both the parameters and the latent variables. Finally, we provide an application to the Euro area business cycle.

Financial Volatility Forecasting by Nonlinear Support Vector Machine Heterogeneous Autoregressive Model: Evidence from Nikkei 225 Stock Index

Abstract: Support vector machines (SVMs) are new semi-parametric tool for regression estimation. This paper introduced a new class of hybrid models, the nonlinear support vector machines heterogeneous autoregressive (SVM-HAR) models and aimed to compare the forecasting performance with the classical heterogeneous autoregressive (HAR) models to forecast financial volatilities. It was observed through empirical experiment that the newly proposed hybrid (SVM-HAR) models produced higher predicting ability than the classical HAR model.

Periodically correlated autoregressive Hilbertian processes

Abstract: We consider periodically correlated autoregressive processes in Hilbert spaces. Our studies on these processes involve existence, covariance structure, estimation of the covariance operators, strong law of large numbers and central limit theorem.

On the autopersistence functions and the autopersistence graphs of binary autoregressive time series

Abstract: The classical autocorrelation function may not be an effective and informative means in revealing the dependence features of a binary time series {yt}. Recently, the autopersistence functions defined as APF0(k) = P(yt+k = 1 | yt = 0) and APF1(k) = P(yt+k = 1 | yt = 1), k = 1, 2,…, have been proposed as alternatives to the autocorrelation function for binary time series. In this article we consider the theoretical autopersistence functions and their natural sample analogues, the autopersistence graphs, under a binary autoregressive model framework. Some properties of the autopersistence functions and the asymptotic properties of the autopersistence graphs are discussed. The results have potential application in the modelling of binary time series.

Dynamic Simulations of Autoregressive Relationships

Abstract: This postestimation technique produces dynamic simulations of autoregressive ordinary least-squares models.

On non-stationary threshold autoregressive models

Abstract: In this paper we study the limiting distributions of the least-squares estimators for the non-stationary first-order threshold autoregressive (TAR(1)) model. It is proved that the limiting behaviors of the TAR(1) process are very different from those of the classical unit root model and the explosive AR(1).

A semiparametric method for estimating nonlinear autoregressive model with dependent errors

Abstract: The first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function. In the presented model, dependent errors are defined as first-order autoregressive AR(1). The conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment. In this case, some asymptotic behaviors and simulated results for the semiparametric method are presented. Furthermore, the method is applied for the financial data in Iran’s Tejarat-Bank.

Estimating the Order of an Autoregressive Model Using Normalized Maximum Likelihood

Abstract: This paper examines the estimation of the order of an autoregressive model using the minimum description length principle. A closed form for an approximation of the parametric complexity of the autoregressive model class is derived by exploiting a relationship between coefficients and partial autocorrelations. The parametric complexity over the complete parameter space is found to diverge. A model selection criterion is subsequently derived by bounding the parameter space, and simulations suggest that it compares well against standard autoregressive order selection techniques in terms of correct order identification and prediction error.

Generalization error bounds for stationary autoregressive models

Abstract: We derive generalization error bounds for stationary univariate autoregressive (AR) models. We show that imposing stationarity is enough to control the Gaussian complexity without further regularization. This lets us use structural risk minimization for model selection. We demonstrate our methods by predicting interest rate movements.

An extension of max autoregressive models

Abstract: To model clustered maxima behaviors in time series analysis, max-autoregressive (MAR) and moving maxima (MM) processes are naturally adapted from linear autoregressive (AR) and moving average (MA) models. Yet, applications of MAR and MM processes are still sparse due to some difficulties of parameter inference and some abnormality of the processes. Basically, some ratios of observations can take constant values in MAR models. The objective of this present work is to introduce a new model that is closely related to the MAR processes and is free of the aforementioned abnormality. A logarithm transformation of the new model leads to time series models with log-positive alpha stable noises and hidden max Gumbel shocks. Theoretical properties of the new models are derived.

Searching for nonlinearities in real exchange rates

Abstract: A recent innovation in modeling exchange rates has been the use of nonlinear techniques such as threshold autoregressive models and its smooth transition variants. This paper investigates the smooth transition autoregressive (STAR) modeling strategy in an application to real exchange rates. The key findings are as follows. First, using the methodology advocated by Terasvirta (1994), we find evidence of nonlinear dynamics for several of the spot dollar real exchange rates using monthly data on five of the G7 countries. However, once estimated, we find that the STAR specification is appropriate for only one of the three exchange rate series indicated to be an ESTAR process. Moreover, using simulations, we show that the underlying methodology used to detect nonlinearities in the data exhibit substantial size biases, which we attribute to influential observations. We also investigate an alternative nonlinear specification and find that we can model the dollar-sterling and the dollar-lira real exchange rates better as an open-loop TAR process instead of a SETAR process.