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.     

Bayesian Subset Model Selection for Time Series

Abstract.  This paper considers the problem of subset model selection for time series. In general, a few lags which are not necessarily continuous, explain lag structure of a time-series model. Using the reversible jump Markov chain technique, the paper develops a fully Bayesian solution for the problem. The method is illustrated using the self-exciting threshold autoregressive (SETAR), bilinear and AR models. The Canadian lynx data, the Wolfe's sunspot numbers and Series A of Box and Jenkins (1976) are analysed in detail.     

Bayesian Model Uncertainty In Smooth Transition Autoregressions

Abstract. In this paper, we propose a fully Bayesian approach to the special class of nonlinear time‐series models called the logistic smooth transition autoregressive (LSTAR) model. Initially, a Gibbs sampler is proposed for the LSTAR where the lag length, k, is kept fixed. Then, uncertainty about k is taken into account and a novel reversible jump Markov Chain Monte Carlo (RJMCMC) algorithm is proposed. We compared our RJMCMC algorithm with well‐known information criteria, such as the Akaikes? information criteria, the Bayesian information criteria (BIC) and the deviance information criteria. Our methodology is extensively studied against simulated and real‐time series.     

Estimation of stationary autoregressive models with the Bayesian LASSO

This article explores the problem of estimating stationary autoregressive models from observed data using the Bayesian least absolute shrinkage and selection operator (LASSO). By characterizing the model in terms of partial autocorrelations, rather than coefficients, it becomes straightforward to guarantee that the estimated models are stationary. The form of the negative log‐likelihood is exploited to derive simple expressions for the conditional likelihood functions, leading to efficient algorithms for computing the posterior mode by coordinate‐wise descent and exploring the posterior distribution by Gibbs sampling. Both empirical Bayes and Bayesian methods are proposed for the estimation of the LASSO hyper‐parameter from the data. Simulations demonstrate that the Bayesian LASSO performs well in terms of prediction when compared with a standard autoregressive order selection method.     

Bayesian analysis of switching ARCH models

We consider a time series model with autoregressive conditional heteroscedasticity that is subject to changes in regime. The regimes evolve according to a multistate latent Markov switching process with unknown transition probabilities, and it is the constant in the variance process of the innovations that is subject to regime shifts. The joint estimation of the latent process and all model parameters is performed within a Bayesian framework using the method of Markov chain Monte Carlo (MCMC) simulation. We perform model selection with respect to the number of states and the number of autoregressive parameters in the variance process using Bayes factors and model likelihoods. To this aim, the model likelihood is estimated by the method of bridge sampling. The usefulness of the sampler is demonstrated by applying it to the data set previously used by Hamilton and Susmel (1994 ) who investigated models with switching autoregressive conditional heteroscedasticity using maximum likelihood methods. The paper concludes with some issues related to maximum likelihood methods, to classical model selection, and to potential straightforward extensions of the model presented here.     

Efficient order selection algorithms for integer-valued ARMA processes

Abstract.  We consider the problem of model (order) selection for integer-valued autoregressive moving-average (INARMA) processes. A very efficient reversible jump Markov chain Monte Carlo (RJMCMC) algorithm is constructed for moving between INARMA processes of different orders. An alternative in the form of the EM algorithm is given for determining the order of an integer-valued autoregressive (INAR) process. Both algorithms are successfully applied to both simulated and real data sets.     

A note on the corrected Akaike information criterion for threshold autoregressive models

A bias-corrected Akaike information criterion AIC_C is derived for self-exciting threshold autoregressive (SETAR) models. The small sample properties of the Akaike information criteria (AIC, AIC_C) and the Bayesian information criterion (BIC) are studied using simulation experiments. It is suggested that AIC_C performs much better than AIC and BIC in small samples and should be put in routine usage.     

A new Bayesian approach to quantile autoregressive time series model estimation and forecasting

This paper proposes a Bayesian approach to quantile autoregressive (QAR) time series model estimation and forecasting. We establish that the joint posterior distribution of the model parameters and future values is well defined. The associated Markov chain Monte Carlo algorithm for parameter estimation and forecasting converges to the posterior distribution quickly. We also present a combining forecasts technique to produce more accurate out‐of‐sample forecasts by using a weighted sequence of fitted QAR models. A moving window method to check the quality of the estimated conditional quantiles is developed. We verify our methodology using simulation studies and then apply it to currency exchange rate data. The results obtained show that an unequally weighted combining method performs better than other forecasting methodology.     

Bayesian analysis of multivariate Gaussian hidden Markov models with an unknown number of regimes

Multivariate Gaussian hidden Markov models with an unknown number of regimes are introduced here in the Bayesian setting and new efficient reversible jump Markov chain Monte Carlo algorithms for estimating both the dimension and the unknown parameters of the model are presented. Hidden Markov models are an extension of mixture models that can be applied to time series so as to classify the observations in a small number of groups, to understand when change points occur in the dynamics of the series and to model data heterogeneity through the switching among subseries with different means and covariance matrices. These aims can be achieved by assuming that the observed phenomenon is driven by a latent, or hidden, Markov chain. The methodology is illustrated through two different examples of multivariate time series.     

The effect of observations on Bayesian choice of an autoregressive model

Abstract. We consider the effect, on a Bayes factor, of omitting observations in time‐series models. In particular, we study a Bayes factor for deciding between autoregressive models of different orders. Throughout we use Gibbs sampling to estimate the parameters of the models and the marginal densities. We illustrate the methods using data generated from an autoregressive model and some data on bag snatching in the Hyde Park area of Chicago.     

A Bayesian nonlinearity test for threshold moving average models

We propose a Bayesian test for nonlinearity of threshold moving average (TMA) models. First, we obtain the marginal posterior densities of all parameters, including the threshold and delay, of the TMA model using Gibbs sampler with the Metropolis–Hastings algorithm. And then, we adopt reversible‐jump Markov chain Monte Carlo methods to calculate the posterior probabilities for MA and TMA models. Posterior evidence in favour of the TMA model indicates threshold nonlinearity. Simulation experiments and a real example show that our method works very well in distinguishing MA and TMA models.     

Generalized autoregressive moving average models with GARCH errors

One of the important and widely used classes of models for non-Gaussian time series is the generalized autoregressive model average models (GARMA), which specifies an ARMA structure for the conditional mean process of the underlying time series. However, in many applications one often encounters conditional heteroskedasticity. In this article, we propose a new class of models, referred to as GARMA-GARCH models, that jointly specify both the conditional mean and conditional variance processes of a general non-Gaussian time series. Under the general modeling framework, we propose three specific models, as examples, for proportional time series, non-negative time series, and skewed and heavy-tailed financial time series. Maximum likelihood estimator (MLE) and quasi Gaussian MLE are used to estimate the parameters. Simulation studies and three applications are used to demonstrate the properties of the models and the estimation procedures.     

Estimation in nonstationary random coefficient autoregressive models

Abstract.  We investigate the estimation of parameters in the random coefficient autoregressive (RCA) model X _k  = ( φ  +  b _k ) X _{k −1} +  e _k , where ( φ ,  ω ²,  σ ²) is the parameter of the process,     ,     . We consider a nonstationary RCA process satisfying E  log | φ  +  b ₀| ≥ 0 and show that σ ² cannot be estimated by the quasi-maximum likelihood method. The asymptotic normality of the quasi-maximum likelihood estimator for ( φ ,  ω ²) is proven so that the unit root problem does not exist in the RCA model.     

A simple procedure for computing improved prediction intervals for autoregressive models

Abstract.  This article concerns the construction of prediction intervals for time series models. The estimative or plug-in solution is usually not entirely adequate, since the (conditional) coverage probability may differ substantially from the nominal value. Prediction intervals with improved (conditional) coverage probability can be defined by adjusting the estimative ones, using rather complicated asymptotic procedures or suitable simulation techniques. This article extends to Markov process models a recent result by Vidoni, which defines a relatively simple predictive distribution function, giving improved prediction limits as quantiles. This new solution is fruitfully considered in the challenging context of prediction for time-series models, with particular regard to AR and ARCH processes.     

Bayesian analysis of autoregressive fractionally integrated moving-average processes

For the autoregressive fractionally integrated moving-average (ARFIMA) processes which characterize both long-memory and short-memory behavior in time series, we formulate Bayesian inference using Markov chain Monte Carlo methods. We derive a form for the joint posterior distribution of the parameters that is computationally feasible for repetitive evaluation within a modified Gibbs sampling algorithm that we employ. We illustrate our approach through two examples.     

一种基于经验知识和信息熵的阈值选择策略

针对高炉料面温度场红外图像的特征提取问题,提出一种基于经验知识和信息熵的图像分割阈值选择策略。该方法首先利用双峰法、最大方差法和一致性准则法分别对图像进行区域分割,再根据图像目标大小,运用知识规则制定判断图像质量的信息熵评价准则,选择合适的分割阈值,获得对判断料面温度分布最有利的图像区域特征。实际运行结果表明图像分割结果和期望的图像特征一致,符合实际工业应用要求,有利于操作人员判断炉况。     

Consistent estimation and order selection for nonstationary autoregressive processes with stable innovations

Abstract. A possibly nonstationary autoregressive process, of unknown finite order, with possibly infinite‐variance innovations is studied. The ordinary least squares autoregressive parameter estimates are shown to be consistent, and their rate of convergence, which depends on the index of stability, α, is established. We also establish consistency of lag‐order selection criteria in the nonstationary case. A small experiment illustrates the relative performance of different lag‐length selection criteria in finite samples.     

On the three-step non-Gaussian quasi-maximum likelihood estimation of heavy-tailed double autoregressive models

This note considers a three-step non-Gaussian quasi-maximum likelihood estimation (TS-NGQMLE) of the double autoregressive model with its asymptotics, which improves efficiency of the GQMLE and circumvents inconsistency of the NGQMLE when the innovation is heavy-tailed. Under mild conditions, the estimator not only can achieve consistency and asymptotic normality regardless of density misspecification of the innovation, but also outperforms the existing estimators, such as the GQMLE and the (weighted) least absolute deviation estimator, when the innovation is indeed heavy-tailed.     

地下矿山设备选择专家系统

按照全国磷矿资源开发系统研究的要求,开发了地下矿山设备选择专家系统,该系统包括坑内运输、提升、排水和压气设备的选择四个子系统。系统的主要目标是在很短时间内提供决策支持系统所必须的技术经济、概算、文字报告和设备清单等准确数据,以适应方案比较和优化。