非参数随机条件持续期模型及其迭代算法

 随机条件持续期（SCD）模型能有效刻画超高频时间序列中持续期的变化,但该模型假定期望持续期生成机制固定,且模型参数估计存在一定的困难。文章在不假定条件均值形式和冲击项分布的基础上结合核估计方法提出了非参数SCD模型及其迭代求解方法。然后,基于TEACD(1,1)模型生成的模拟数据,将非参数SCD模型与用卡尔漫滤波进行伪似然估计的参数SCD模型和用Gibbs抽样进行马尔科夫蒙特卡罗估计的参数SCD模型的拟合效果进行比较,实证表明在大样本条件下非参数SCD模型的拟合效果与用MCMC估计的参数SCD模型的拟合结果相差不大,但明显优于用QML估计的参数SCD模型的拟合结果,且非参数SCD模型能为参数SCD模型的参数设定提供参考。     

二次趋势模型的误设检验与仿真分析

在介绍两种生成二次趋势模型的基础上,指明两者具有某种内在的关系,并以隐性趋势模型为数据生成过程,使用显性趋势模型作为估计对象,进行参数估计和相应的假设检验。理论分析结果表明:显性趋势模型的参数、t检验统计量和联合F检验统计量的极限具有非标准的分布,且高度显著;以显性趋势模型为数据生成过程,使用隐性趋势模型作为估计对象,结果表明隐性趋势模型是带趋势项的单位根过程;采用LLR检验统计量对两类模型进行区分检验,使用仿真技术进行模拟,仿真结果支持上述理论分析结论和LLR统计量能够区分两种模型。     

多类型复发事件数据下一类半参数转移模型

复发事件数据频繁的出现在纵向研究中,基于生物医学中的多类型复发事件数据,提出了一类半参数转移模型,该模型包含了一些重要的半参数模型。同时,模型允许协变量具有加性和乘性的影响,且加性影响随时间而变化。利用广义估计方程的思想,对模型中未知参数和非参数函数进行了估计,并且证明了估计的相合性和渐近正态性。     

基于卡尔曼滤波估计的连续性抽样调查研究

 针对连续性抽样调查中如何提高连续调查数据准确性的问题，本文引入时间序列分析方法，分别考虑连续性抽样调查中的重复样本和轮换样本等不同情况，建立了连续性抽样调查下的状态空间模型，利用成熟的卡尔曼滤波估计方法给出了总体均值的估计量。由于状态空间模型及卡尔曼滤波估计方法能够充分利用各期连续样本的调查信息，给出了精度更高的估计量，从而能够产生更加准确的连续性时间序列数据。     

双因素效应的动态二值logit模型的参数估计及应用

文章考虑了带有个体效应和时间效应的双因素面板数据动态二值logit模型，在周期T固定的条件下，提出了一种新的方法估计模型参数。从理论层面指出了该估计量满足一致性和渐近正态性；数值模拟研究了估计量的小样本性质，模拟结果表明，该估计方法在有限样本下具有良好的统计性质。最后，将该方法应用于洗涤剂的购买数据进行实证分析。     

真实固定效应空间随机前沿模型的贝叶斯估计

忽略个体效应和空间效应会严重干扰效率测算,其中忽略个体效应使得技术无效率项发生偏移,忽略空间相关性导致估计量有偏且不一致。本文基于真实固定效应随机前沿模型（引入了个体效应）,引入因变量和双边误差项的空间滞后项,构建了适用性更佳的真实固定效应空间随机前沿模型。对模型进行组内变化以消除额外参数,使用贝叶斯方法（需推导未知参数的后验分布并执行MCMC抽样）估计参数和技术效率。该方法真正克服了额外参数问题,比同类方法直观、简便。数值模拟结果表明,本文方法对参数、个体截距项及技术无效率项的估计精度均较高,且增加样本容量,估计精度变优。     

基于随机抽取的AR模型定阶和参数评估

文章基于对平稳时间序列数据的随机抽取,选用AR模型研究其模型定阶方法和参数评估准则.根据数据有序性的特点,提出利用交叉验证的方法确定自回归模型阶数,并通过对原数据的无放回抽取实现对系数参数估计的评估.实例分析结果表明,交叉验证的定阶与AIC准则定阶结果保持较高一致性,新的参数评估在一定的模型误差范围内可以得到更为简单有效的系数估计区间.     

单指标纵向数据模型的估计

纵向数据是一类重要的相关性数据,广泛出现在诸多科研领域。单指标模型是多元非参数回归中重要的降维方法,在纵向数据下研究单指标模型是统计研究的热点问题。针对纵向数据单指标模型,提出惩罚改进二次推断函数方法来讨论模型的参数和非参数估计问题。该方法利用多项式样条回归方法逼近模型中的未知联系函数,将联系函数的估计转化为回归样条系数的估计,然后构造关于样条回归系数和单指标系数的惩罚改进二次推断函数,最小化惩罚改进二次推断函数便可得到模型的估计。理论结果显示,估计结果具有相合性和渐近正态性,最后得到了较好的数值模拟结果和实例数据分析结果,结果显示该方法适用于半参数纵向模型的参数和非参数估计问题。     

纵向数据下半参数Logistic模型的变量选择

文章研究了纵向数据半参数Logistic回归模型的估计问题,给出了模型中未知参数和未知函数的估计方法,探讨了参数部分的变量选择问题,并对不同的变量选择方法进行比较分析.从模拟结果可以看到,文中给出的方法具有很好的估计效果.     

适用于大数据集的广义可加模型

通常情况下,对用电量进行预测的问题可以采用广义可加模型(GAM),但当数据集很大时,在计算机上实现起来就非常困难,甚至是不可行的.因此,本文给出了大数据集下实用的广义可加模型拟合方法,模型中的平滑项用惩罚回归样条函数来表示.只需保证在任何时候模型矩阵的子矩阵可以在计算机上实现,该方法就可以通过迭代更新的方式得到模型矩阵的因子.本文研究证明,该方法可以有效地对平滑参数进行估计.当有新数据加入时,用电量预测模型需要不断地拟合更新,并且需要对新的用电量数据序列的自相关性进行处理.本文给出了处理这些问题的方法,以及在计算机上的实现过程.该方法可以实现使用一般的中型计算机来处理大数据集的广义可加模型的估计问题.最后,对法国用电量预测的实证研究表明,降秩样条平滑方法也能够很好地处理复杂的模型问题.     

An insight into technology diffusion of tractor through Weibull growth model

Most of the technological innovation diffusion follows an S-shaped curve. But, in many practical situations this may not hold true. To this end, Weibull model was proposed to capture the diffusion of new technological innovation, which does not follow any specific pattern. Nonlinear growth models play a very important role in getting an insight into the underlying mechanism. These models are generally ‘mechanistic’ as the parameters have meaningful interpretation. The nonlinear method of estimation of parameters of Weibull model fails to converge. Taking this problem into consideration, we propose the use of a powerful technique of genetic algorithm for parameter estimation. The methodology is also validated by simulation study to check whether parameter estimates are closer to the real value. For illustration purpose, we model the tractor density time-series data of India as a whole and some major states of India. It is seen that fitted Weibull model is able to capture the technology diffusion process in a reasonable manner. Further, comparison is also made with Logistic and Gompertz model; and is found to perform better for the data sets under consideration.     

Efficient and flexible model-based clustering of jumps in diffusion processes

Jump–diffusion processes involving diffusion processes with discontinuous movements, called jumps, are widely used to model time-series data that commonly exhibit discontinuity in their sample paths. The existing jump–diffusion models have been recently extended to multivariate time-series data. The models are, however, still limited by a single parametric jump-size distribution that is common across different subjects. Such strong parametric assumptions for the shape and structure of a jump-size distribution may be too restrictive and unrealistic for multiple subjects with different characteristics. This paper thus proposes an efficient Bayesian nonparametric method to flexibly model a jump-size distribution while borrowing information across subjects in a clustering procedure using a nested Dirichlet process. For efficient posterior computation, a partially collapsed Gibbs sampler is devised to fit the proposed model. The proposed methodology is illustrated through a simulation study and an application to daily stock price data for companies in the S&P 100 index from June 2007 to June 2017.     

Hierarchical Bayes estimation in small area estimation using cross-sectional and time-series data

Bayesian methods have been extensively used in small area estimation. A linear model incorporating autocorrelated random effects and sampling errors was previously proposed in small area estimation using both cross-sectional and time-series data in the Bayesian paradigm. There are, however, many situations that we have time-related counts or proportions in small area estimation; for example, monthly dataset on the number of incidence in small areas. This article considers hierarchical Bayes generalized linear models for a unified analysis of both discrete and continuous data with incorporating cross-sectional and time-series data. The performance of the proposed approach is evaluated through several simulation studies and also by a real dataset.     

Large sample estimation and prediction for explosive growth curve models

Asymptotic distributions of maximum likelihood estimators for the parameters in explosive growth curve models are derived. Limit distributions of prediction errors when the parameters are estimated are also obtained. The growth curve models are viewed as multivariate time-series models, and the usual time-series methods are used for prediction. Estimation constrained by a hypothesis of homogeneity of growth rates is also considered.     

A Bayesian analysis on time series structural equation models

Structural equation models (SEM) have been extensively used in behavioral, social, and psychological research to model relations between the latent variables and the observations. Most software packages for the fitting of SEM rely on frequentist methods. Traditional models and software are not appropriate for analysis of the dependent observations such as time-series data. In this study, a structural equation model with a time series feature is introduced. A Bayesian approach is used to solve the model with the aid of the Markov chain Monte Carlo method. Bayesian inferences as well as prediction with the proposed time series structural equation model can also reveal certain unobserved relationships among the observations. The approach is successfully employed using real Asian, American and European stock return data.     

Kalman filter-based modelling and forecasting of stochastic volatility with threshold

We propose a parametric nonlinear time-series model, namely the Autoregressive-Stochastic volatility with threshold (AR-SVT) model with mean equation for forecasting level and volatility. Methodology for estimation of parameters of this model is developed by first obtaining recursive Kalman filter time-update equation and then employing the unrestricted quasi-maximum likelihood method. Furthermore, optimal one-step and two-step-ahead out-of-sample forecasts formulae along with forecast error variances are derived analytically by recursive use of conditional expectation and variance. As an illustration, volatile all-India monthly spices export during the period January 2006 to January 2012 is considered. Entire data analysis is carried out using EViews and matrix laboratory (MATLAB) software packages. The AR-SVT model is fitted and interval forecasts for 10 hold-out data points are obtained. Superiority of this model for describing and forecasting over other competing models for volatility, namely AR-Generalized autoregressive conditional heteroscedastic, AR-Exponential GARCH, AR-Threshold GARCH, and AR-Stochastic volatility models is shown for the data under consideration. Finally, for the AR-SVT model, optimal out-of-sample forecasts along with forecasts of one-step-ahead variances are obtained.     

Restrictions on Risk Prices in Dynamic Term Structure Models

Restrictions on the risk-pricing in dynamic term structure models (DTSMs) tighten the link between cross-sectional and time-series variation of interest rates, and make absence of arbitrage useful for inference about expectations. This article presents a new econometric framework for estimation of affine Gaussian DTSMs under restrictions on risk prices, which addresses the issues of a large model space and of model uncertainty using a Bayesian approach. A simulation study demonstrates the good performance of the proposed method. Data for U.S. Treasury yields calls for tight restrictions on risk pricing: only level risk is priced, and only changes in the slope affect term premia. Incorporating the restrictions changes the model-implied short-rate expectations and term premia. Interest rate persistence is higher than in a maximally flexible model, hence expectations of future short rates are more variable—restrictions on risk prices help resolve the puzzle of implausibly stable short-rate expectations in this literature. Consistent with survey evidence and conventional macro wisdom, restricted models attribute a large share of the secular decline in long-term interest rates to expectations of future nominal short rates. Supplementary materials for this article are available online.     

Bayesian model averaging in longitudinal regression models with AR(1) errors with application to a myopia data set

We propose a new iterative algorithm, called model walking algorithm, to the Bayesian model averaging method on the longitudinal regression models with AR(1) random errors within subjects. The Markov chain Monte Carlo method together with the model walking algorithm are employed. The proposed method is successfully applied to predict the progression rates on a myopia intervention trial in children.     

双回归（AR—R）预测模型之新探——及其在中国人口中短期预测上的应用

构造一种称为双回归的时间序列预测新方法。本文作者利用与因变量自身相关性紧密的因变量前几期取值,综合前一次的自变量构建了双回归(时间序列自回归-多元线性回归)预测组合模型。这种方法克服了以往时间序列预测只是自身拓展而不考虑多项因素(变量)的不足,也弥补了回归分析预测法必须已知同时期各个自变量值才能预测的缺陷。并用这种新方法对中国的人口总量进行预测,预测效果比较理想。