A Novel Particle Filter Aided by Interval Analysis Approach

This paper addresses the issue of state estimation in nonlinear systems in the presence of non-Gaussian and bounded noises, under which the interval analysis based estimation is introduced as an auxiliary approach of generic particle filter (PF). This yields the so-called Set-Membership aided particle filter (SMPF). Unlike the mature alternatives of generic particle filter, the proposal distribution of SMPF approximates the posterior probability density function (PDF), not only on the numerical value but also on the definition-domain, and the performance analysis on the proposed alternative is proven through detailed formulations. In addition, contrasting simulations under SMPF and other mature alternatives also validate the effectiveness of SMPF.     

基于辅助粒子滤波的DSGE模型识别方法及应用

动态随机一般均衡模型中涵盖无法直接观测的变量,同时跨方程约束涉及复杂的非线性关系使方程的解析估计难以实现。在贝叶斯框架下识别动态随机一般均衡模型,基于状态空间方法建立度量方程和状态转移方程,采用辅助粒子滤波预测条件后验分布,建立贝叶斯误差带描述宏观经济变量脉冲响应函数的动态特征。实际数据分析验证了贝叶斯识别方法的有效性。     

An On-Line Estimation Algorithm for Periodic Autoregressive Models

This paper develops an on-line estimation algorithm for periodic autoregressive models (PAR). Indeed, we provide an adaptation of the well known recursive least squares algorithm (RLS), which has been successfully applied to classical autoregressive models (AR), to deal with PAR models. The obtained estimators are shown to be asymptotically efficient under mild conditions. Moreover, the performance of the periodic least squares algorithm (PRLS) is assessed via an intensive simulation study.     

Empirical Likelihood for an Autoregressive Model with Explanatory Variables

In this article, we use the empirical likelihood method to construct the confidence region for parameters in autoregressive model with martingale difference error. It is shown that the empirical log-likelihood ratio at the true parameter converges to the standard chi-square distribution. The simulation results suggest that the empirical likelihood method outperforms the normal approximation based method in terms of coverage probability.     

Bayesian Analysis of Two-Regime Threshold Autoregressive Moving Average Model with Exogenous Inputs

We consider Bayesian analysis of threshold autoregressive moving average model with exogenous inputs (TARMAX). In order to obtain the desired marginal posterior distributions of all parameters including the threshold value of the two-regime TARMAX model, we use two different Markov chain Monte Carlo (MCMC) methods to apply Gibbs sampler with Metropolis-Hastings algorithm. The first one is used to obtain iterative least squares estimates of the parameters. The second one includes two MCMC stages for estimate the desired marginal posterior distributions and the parameters. Simulation experiments and a real data example show support to our approaches.     

A NOTE ON ‘A COMPARISON OF BAYES AND MAXIMUM LIKELIHOOD ESTIMATION OF THE INTRACLASS CORRELATION COEFFICIENT’

Palmer and Broemeling [1] Palmer, J. L. and Broemeling, L. D. 1990. A Comparison of Bayes and Maximum Likelihood Estimation of the Intraclass Correlation Coefficient. Comm. Statist.-Theory Meth, 19: 953–975. [Taylor & Francis Online], [Web of Science ®] , [Google Scholar] compare Bayes and maximum likelihood estimates of the intraclass correlation (ICC). The prior information in their derivation of the Bayes estimator is placed on the variance components instead of the ICC itself. This paper finds a Bayes estimator of the ICC with the prior placed on the ICC. Bayes estimates based on three different priors are then compared to method of moments estimate.     

Density-Tempered Marginalized Sequential Monte Carlo Samplers

We propose a density-tempered marginalized sequential Monte Carlo (SMC) sampler, a new class of samplers for full Bayesian inference of general state-space models. The dynamic states are approximately marginalized out using a particle filter, and the parameters are sampled via a sequential Monte Carlo sampler over a density-tempered bridge between the prior and the posterior. Our approach delivers exact draws from the joint posterior of the parameters and the latent states for any given number of state particles and is thus easily parallelizable in implementation. We also build into the proposed method a device that can automatically select a suitable number of state particles. Since the method incorporates sample information in a smooth fashion, it delivers good performance in the presence of outliers. We check the performance of the density-tempered SMC algorithm using simulated data based on a linear Gaussian state-space model with and without misspecification. We also apply it on real stock prices using a GARCH-type model with microstructure noise.     

A Method of Exploring the Mechanism of Inflationary Expectations Based on Qualitative Survey Data

The objective of this article is to propose a method of exploring the mechanism of expectation formation based on qualitative survey data. The survey data are regarded as a sample from a multinomial distribution whose parameters are time-variant functions of inflation expectations. The parameters are estimated using a Bayesian recursive approach, which is a generalization of the Kalman filtering technique. For illustrative purposes, the method is applied to Japanese data. One notable finding from the empirical analysis is that the expectation formation process of Japanese enterprises has varied greatly over time.     

Adaptive Estimation of Causal Periodic Autoregressive Model

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 Swensen , A. R. ( 1985 ). The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend . Journal of Multivariate Analysis 16 : 54 – 70 .[Crossref], [Web of Science ®] , [Google Scholar]) 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.     

Adaptive Estimation of Periodic First-Order Threshold Autoregressive Model

This paper focuses on the adaptive estimation problem of a Periodic Self-Exciting Threshold Autoregressive (PSETAR) model. The adapted sufficient conditions of Swensen (1985 Swensen, A. R. 1985. The asymptotic distribution of the likelihood ratio for autoregressive time series with a regression trend. Journal of Multivariate Analysis, 16: 54–70. [Crossref], [Web of Science ®] , [Google Scholar]) to our model, are verified and then explored to establish the Local Asymptotic Normality (LAN), the Local Asymptotic Quadratic (LAQ) and the Local Asymptotic properties satisfied by its central sequence. Using these results, we construct adaptive estimators for the parameter model where the innovation density is unspecified but symmetric, while satisfying only some general conditions. The performances of these adaptive estimations are shown via simulation studies and an application on the modeling of the Fraser River data.     

Model Selection for Vector Autoregressive Processes via Adaptive Lasso

Determination of the best subset is an important step in vector autoregressive (VAR) modeling. Traditional methods either conduct subset selection and parameter estimation separately or compute expensively. In this article, we propose a VAR model selection procedure using adaptive Lasso, for it is computational efficient and can select subset and estimate parameters simultaneously. By proper choice of tuning parameters, we can choose the correct subset and obtain the asymptotic normality of the non zero parameters. Simulation studies and real data analysis show that adaptive Lasso performs better than existing methods in VAR model fitting and prediction.     

Bayesian Analysis of a Growth Curve Model with a General Autoregressive Covariance Structure

In this paper we consider from maximum likelihood and Bayesian points of view the generalized growth curve model when the covariance matrix has a Toeplitz structure. This covariance is a generalization of the AR(1) dependence structure. Inferences on the parameters as well as the future values are included. The results are illustrated with several real data sets.     

An Adaptive Functional Autoregressive Forecast Model to Predict Electricity Price Curves

We propose an adaptive functional autoregressive (AFAR) forecast model to predict electricity price curves. With time-varying operators, the AFAR model can be safely used in both stationary and nonstationary situations. A closed-form maximum likelihood (ML) estimator is derived under stationarity. The result is further extended for nonstationarity, where the time-dependent operators are adaptively estimated under local homogeneity. We provide theoretical results of the ML estimator and the adaptive estimator. Simulation study illustrates nice finite sample performance of the AFAR modeling. The AFAR model also exhibits a superior accuracy in the forecast exercise of the California electricity daily price curves compared to several alternatives.     

非正态分布下具有自回归误差项的空间自回归模型变量选择研究

将变量选择引入空间计量模型,讨论具有自回归误差项的空间自回归模型的变量选择问题。在残差非正态独立同分布的条件下,通过最大化信息熵,提出空间信息准则,并证明其在该模型变量选择中具有一致性。模拟研究结果表明:无论对单个系数还是对全部系数,空间信息准则都能很好识别,且与经典的赤池准则相比具有较大的优势。因此,空间信息准则是一种更为有效的变量选择方法。     

Partial logistic relevance vector machines in survival analysis

The use of relevance vector machines to flexibly model hazard rate functions is explored. This technique is adapted to survival analysis problems through the partial logistic approach. The method exploits the Bayesian automatic relevance determination procedure to obtain sparse solutions and it incorporates the flexibility of kernel-based models. Example results are presented on literature data from a head-and-neck cancer survival study using Gaussian and spline kernels. Sensitivity analysis is conducted to assess the influence of hyperprior distribution parameters. The proposed method is then contrasted with other flexible hazard regression methods, in particular the HARE model proposed by Kooperberg et al. [16]. A simulation study is conducted to carry out the comparison. The model developed in this paper exhibited good performance in the prediction of hazard rate. The application of this sparse Bayesian technique to a real cancer data set demonstrated that the proposed method can potentially reveal characteristics of the hazards, associated with the dynamics of the studied diseases, which may be missed by existing modeling approaches based on different perspectives on the bias vs. variance balance.     

Sampling the Dirichlet Mixture Model with Slices

We provide a new approach to the sampling of the well known mixture of Dirichlet process model. Recent attention has focused on retention of the random distribution function in the model, but sampling algorithms have then suffered from the countably infinite representation these distributions have. The key to the algorithm detailed in this article, which also keeps the random distribution functions, is the introduction of a latent variable which allows a finite number, which is known, of objects to be sampled within each iteration of a Gibbs sampler.     

Best Spatial Two-Stage Least Squares Estimators for a Spatial Autoregressive Model with Autoregressive Disturbances

Estimation of a cross-sectional spatial model containing both a spatial lag of the dependent variable and spatially autoregressive disturbances are considered. [Kelejian and Prucha (1998)]described a generalized two-stage least squares procedure for estimating such a spatial model. Their estimator is, however, not asymptotically optimal. We propose best spatial 2SLS estimators that are asymptotically optimal instrumental variable (IV) estimators. An associated goodness-of-fit (or over identification) test is available. We suggest computationally simple and tractable numerical procedures for constructing the optimal instruments.     

A (Semi)Parametric Functional Coefficient Logarithmic Autoregressive Conditional Duration Model

In this article, we propose a class of logarithmic autoregressive conditional duration (ACD)-type models that accommodates overdispersion, intermittent dynamics, multiple regimes, and asymmetries in financial durations. In particular, our functional coefficient logarithmic autoregressive conditional duration (FC-LACD) model relies on a smooth-transition autoregressive specification. The motivation lies on the fact that the latter yields a universal approximation if one lets the number of regimes grows without bound. After establishing sufficient conditions for strict stationarity, we address model identifiability as well as the asymptotic properties of the quasi-maximum likelihood (QML) estimator for the FC-LACD model with a fixed number of regimes. In addition, we also discuss how to consistently estimate a semiparametric variant of the FC-LACD model that takes the number of regimes to infinity. An empirical illustration indicates that our functional coefficient model is flexible enough to model IBM price durations.     

Empirical Likelihood-based Inference for Stationary-ergodicity of the Generalized Random Coefficient Autoregressive Model

In this article, we consider the application of the empirical likelihood method to the generalized random coefficient autoregressive (GRCA) model. When the order of the model is 1, we derive an empirical likelihood ratio test statistic to test the stationary-ergodicity. Some simulation studies are also conducted to investigate the finite sample performances of the proposed test.