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.     

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.     

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.     

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.     

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.     

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。     

Model selection for aqueous slurry coal desulphurization

Simple solid-fluid process models developed for uniform size solid bodies (screened or palletized materials), like the shrinking core model, have been applied to multifraction mixtures of solid bodies usually encountered in processing of ground coal or oil shale. The experimental conversion, measuring total effects on all of the size fractions was recalculated to the conversion of the longest surviving single fraction. The calculations used literature data on coal desulphurization by wet oxidation of pyretic sulphur and results are discussed in terms of rate limiting steps.     

A Bayesian framework for the calibration of cohesive zone models

Adhesively bonded joints are used in several industrial sectors. Cohezive Zone Modes can be used to predict the adhesive mechanical behaviour. This work presents an approach to calibrate Cohesive Zone Models (CZM) by means of Statistical Inverse Analysis. The Bayesian framework for Inverse Problems is used to infer about the CZM model parameters. The solution corresponds to the exploration of the posterior probability density function of the model parameters. The exploration of the posterior density is performed by means of Markov Chain Monte Carlo (MCMC) methods mixing Population-Based MCMC with Adaptive Metropolis (AD) strategies. The assessment of the approach is performed using measured data from a single-lap shear experimental set-up. Measured data from 5 test-specimens is used for calibration and measured data from five other test-specimens is used for model validation. It is proposed a stochastic effective model for the CZM parameters. The predictions of maximum force and maximum displacement that are provided by the effective model are in accordance with measured data that is used for validation.     

ON q-CONDITIONED PARTIAL CORRELATIONS

Abstract. In attempting to develop a procedure for fitting linear multiple autoregressive-moving average models to observed data, perhaps the most difficult problem is to achieve a reasonable initial model selection. A recent paper by Jenkins and Alavi suggests, as one possibility, the examination of so-called q -conditioned partial correlations. We show that the sampling properties of these statistics are such as to render them of dubious value for this purpose.     

Improving prediction capabilities of complex dynamic models via parameter selection and estimation

Many mathematical models describing complex (bio-)chemical reaction networks with a high level of detail are available in the literature. While such detailed models are desirable for investigating the dynamics of a particular component, it is often questionable if it is possible to verify these models due to the limited amount of quantitative data that can be generated. Even if it is not possible to estimate all parameters of these models then one would still be interested in determining which parameters should be estimated.This paper addresses this point and introduces a technique for determining the parameters of a model that should be estimated from experimental data. The focus of this work is on ensuring that the model has good prediction capability as over-fitting the model to noisy experimental data is avoided. Towards this goal, a forward selection approach for selecting a subset of parameters for estimation while taking uncertainty into account is developed to minimize the mean squared prediction error of the model. It is shown that the developed technique is closely related to the often-used orthogonalization method. The technique is applied to a model of the NF-κB signal transduction pathway. The presented method is able to generate a smaller mean squared error than estimation of all parameters and also outperforms the orthogonalization method.     

Validation of continuous-time models with delay

This article is a continuation of an earlier work by Huang [2000. Multivariate model validation in the presence of timevariant disturbance dynamics. Chemical Engineering Science 55, 4583-4595] for validation of discrete time models. We present validation method for continuous-time transfer models with time delay. The proposed procedure is based on the local approach for change detection of model parameters. Both single input single output (SISO) and multiple input multiple output (MIMO) models are considered. The special feature of the proposed algorithm is its ability to detect and isolate changes in the time delay as well as in other parameters. The performance of the proposed method is demonstrated using Monte-Carlo simulations and by application to experimental data from a laboratory scale process.     

选煤厂重介质旋流器的选型

分析了几种常用重介质旋流器选煤工艺的选型计算方法,通过与现场实际使用情况进行对比,表明处理量与旋流器直径D2.5成正比,经适当修正后的庞学诗生产能力计算法更适用于选型;指出了不同类型、产地的旋流器选型应区别对待。     

Automatic identification of seasonal transfer function models by means of iterative stepwise and genetic algorithms

Abstract. In this article, we introduce an automatic identification procedure for transfer function models. These models are commonplace in time‐series analysis, but their identification can be complex. To tackle this problem, we propose to couple a nonlinear conditional least‐squares algorithm with a genetic search over the model space. We illustrate the performances of our proposal by examples on simulated and real data.