结构突变对KPSS检验水平与检验功效的影响 ——基于有限样本情形的模拟及实证研究

 本文从理论模拟和实证分析两个角度研究了以平稳过程为原假设的KPSS检验在存在结构突变的情形下该检验的有限样本性质,包括实际检验水平和检验功效的分析。结论表明当忽略数据生成过程中的结构突变时,KPSS检验的实际检验水平会发生严重扭曲,从而出现“Perron现象”。本研究针对的是有限样本情形,这不但补充和完善了相关理论,同时对实证分析工作具有很强的借鉴和指导意义。     

中国季度GDP核算数据质量研究

如何核算和发布季度GDP数据是一个主要难题。中国2017年改革了GDP核算方法,将季度GDP核算分为初步核算和最终核实两个步骤,取消了原先的初步核实,进一步研究取消初步核实的合理性。从理论角度,构造了一个新的等预测精度检验,新建立的检验具有更好的有限样本性质;从实证角度,首先基于季度GDP数据和第一、二、三产业的数据,排除了三大产业数据存在偏差相互抵消的可能,证实了初步核算数据以及初步核实数据均为真实数据的无偏有效估计,并基于新建立的检验比较了初步核算数据和初步核实数据的预测精度,发现初步核实数据预测精度更高,但两者预测精度差异并不显著,因此改革方案具有合理性。     

结合景气指数的GDP组合预测模型研究

文章首先对中国季度GDP序列建立了AR-GMDH预测模型;然后加入对GDP相关性较大的景气指数,建立了ARCH模型;最后利用GMDH自组织建模方法提出新的组合预测模型.对比分析各模型预测结果表明:两种单一模型预测误差均在可接受范围之内,基于GMDH组合的GDP预测模型的拟合和预测效果比单一模型更优.     

季度实际GDP增长率混频预报单调性的统计检验

本文从统计意义上检验了因子混频数据模型对我国季度实际GDP增长率的实时预报误差是否会随着新数据信息的采用而逐渐降低,并呈现出单调递减的统计特征。实证结果表明：无论伪样本内外长度比和数据更新时间间隔如何,基于因子混频数据模型生成的预报单调性检验结果都从总体上证实,实时更新的月度数据信息可逐步改善季度实际GDP增长率的预报精度,且在样本的时变特征和阶段属性发生变化时,预报单调性检验方法仍具有稳健性。预报单调性检验是对现有预测和预报评估方法的有效补充和扩展,可为政府部门、相关机构和投资者实时评估宏观经济状况提供有价值的信息和参考。     

整数值时间序列模型单位根检验问题研究

非整数值时间序列单位根检验研究已趋成熟,而整数值时间序列单位根检验则刚起步.本文主要采用蒙特卡洛模拟方法对INAR(1)模型单位根检验中的DF统计量和∑Tt=1=1I{△Xt＜0}统计量进行了研究.研究发现:DF统计量渐近服从标准正态分布,有限样本情形下,该统计量的实际分布会受到样本容量与扰动项均值的影响;DF统计量不存在水平扭曲现象,能很好控制犯第一类错误的概率,由于数据生成特点,∑Tt=1I{△Xt＜0}统计量犯第一类错误的概率始终为0;DF统计量和∑Tt=1I{△Xt＜0}统计量的检验功效受到样本容量、自回归系数和扰动项均值的影响,多数情形下,∑Tt=1=1I{ △Xt＜0}统计量的检验功效高于DF统计量.     

中国GDP的季度调整模型及预测分析

基于全国2000年1季度至2014年4季度的GDP季度数据,文章采用乘法模型的时间序列分解法对其进行季度调整,得到不合有季节性特征的时间序列,然后进行趋势性分析以及趋势模型的建立、估计与检验,并结合季节指数预测出2015年1季度至2016年4季度的季度GDP.     

时间序列的单位根检验与伪检验

文章证明了平稳性的三个结论,即平稳序列的子序列仍是平稳的;非平稳序列子序列单整阶数不会超过原序列;一个序列乘以一个大于0的常数,平稳性不会改变。并利用得到的结论分析GDP序列,指出一些文献中的检验属于伪检验。对GDP数据序列（1952～2008）的平稳性检验得出结论：实际GDP取自然对数后是I（1）序列;实际人均GDPI（2）序列;实际人均GDP对数序列是I（1）序列;实际GDP增长率是I（0）序列。     

中、日、韩长期购买力平价的非线性检验——基于1994-2009年的经验分析

购买力平价理论是一种基本的汇率决定理论,主要是检验实际汇率是否稳定。以往的研究主要是在线性模型的框架下,应用ADF和PP检验考察购买力平价是否成立。尝试在非线性的研究框架下,基于ESTAR模型应用KPSS检验方法对中、日、韩三国的长期购买力平价进行检验。实证分析结果表明,基于非线性的KPSS检验方法发现日本的实际汇率为非平稳时间序列,而中国和韩国的实际汇率为平稳序列。这说明长期中日本的购买力平价不成立,而中国和韩国的购买力平价成立。     

基于非线性ECM模型的贝叶斯门限协整研究

 现有门限协整检验方法由于模型似然函数具有多峰、不连续特征,导致冗余参数识别存在困难,最优化计算相对复杂。本文提出基于非线性误差修正模型的贝叶斯门限协整分析,结合参数的后验条件分布设计MCMC抽样方案,进行贝叶斯门限协整检验;并利用Monte Carlo仿真研究了贝叶斯门限协整检验的有限样本性质,发现贝叶斯门限协整检验方法具有良好的有限样本性质。同时,利用不同期限的美国利率序列进行了实证研究,结果发现1个月与3个月利率之间、3个月与6个月利率之间以及3个月与1年利率之间均存在门限协整关系。研究结果表明：贝叶斯门限协整检验方法解决了冗余参数识别的难题,使计算变得相对简单,并提高了估计的精确度和检验的准确性。     

两类错误条件下的样本容量选择

应该抽取多少样本,这是在社会调查各个阶段中均会遇到的基本问题.众所周知,在统计假设检验中,会发生"弃真"和"取伪"两类错误,一般的统计检验中,往往随意确定样本容量,且只重视第一类错误,那么对于一些重要的检验,第二类错误就无法控制.文章从两类错误的定义,探讨了两类错误与样本容量的关系;并在控制两类错误的条件下,分别就均值检验、成数检验和方差检验给出了样本容量的确定公式.     

Operational ridge regression estimators under the prediction goal

In this paper we study the Mean Square Error and Conditional Mean Forecasting of Operational Ordinary Ridge Estimator. We use the G( ) functions to provide both the exact and the approximate bias and Mean Square Error of ordinary ridge estimator (ORE), We show, among other things, that ORE dominates OLS up to a certain order of approximation under the conditional mean forecasting sense.     

Kalman filtering with censored measurements

This paper concerns Kalman filtering when the measurements of the process are censored. The censored measurements are addressed by the Tobit model of Type I and are one-dimensional with two censoring limits, while the (hidden) state vectors are multidimensional. For this model, Bayesian estimates for the state vectors are provided through a recursive algorithm of Kalman filtering type. Experiments are presented to illustrate the effectiveness and applicability of the algorithm. The experiments show that the proposed method outperforms other filtering methodologies in minimizing the computational cost as well as the overall Root Mean Square Error (RMSE) for synthetic and real data sets.     

Minimum variance unbiased estimation of stress–strength reliability under bivariate normal and its comparisons

In many industrial and natural phenomena, we need the probability that a component is smaller than the other component. Under a stress–strength model, this is reliability of an item. Under independent setup, there are different approaches for the estimation of such reliability. Here, estimation is considered under the dependent case. Under bi-variate setup uniformly minimum variance unbiased estimator is obtained. Also comparison with available estimator based on Maximum Likelihood Estimate (MLE) is done through Mean Square Error (MSE) and bias. Also these are compared by computing L₁ distance between their distribution functions. From this idea and numerical computations, UMVUE appears to be good.     

Bias reduction in kernel density estimation

In this paper, we propose two kernel density estimators based on a bias reduction technique. We study the properties of these estimators and compare them with Parzen–Rosenblatt's density estimator and Mokkadem, A., Pelletier, M., and Slaoui, Y. (2009, ‘The stochastic approximation method for the estimation of a multivariate probability density’, J. Statist. Plann. Inference, 139, 2459–2478) is density estimators. It turns out that, with an adequate choice of the parameters of the two proposed estimators, the rate of convergence of two estimators will be faster than the two classical estimators and the asymptotic MISE (Mean Integrated Squared Error) will be smaller than the two classical estimators. We corroborate these theoretical results through simulations.     

Maximum likelihood estimation of variance components-a Monte Carlo study

The estimation of the parameter of a mixed model analysis of variance by maximum likelihood methods is discussed. The functional iteration method is studied and found to have good comptuational properties. The estimates are studied via Monte Carlo techniques and their small sample properties are observed; it is found that the MLE's may be biased but that they have good Mean Square Error properties.     

Sequential procedures in identification

In this paper we study the problem of identifying a popula-tion with one of the two populations, with an aim to control both types of errors. We assume that the populations are normal with unknown means, but with unit variance. We have cited examples from anthropological studies where our formulation of the problem fits in quite nicely. We observe that SPRT’s based on the maximal invariant may not terminate with probability one. Simulation studies reported here show a substantial saving in the average number of samples compared to the best invariant fixed sample test.     

Study of partial least squares and ridge regression methods

This article considers both Partial Least Squares (PLS) and Ridge Regression (RR) methods to combat multicollinearity problem. A simulation study has been conducted to compare their performances with respect to Ordinary Least Squares (OLS). With varying degrees of multicollinearity, it is found that both, PLS and RR, estimators produce significant reductions in the Mean Square Error (MSE) and Prediction Mean Square Error (PMSE) over OLS. However, from the simulation study it is evident that the RR performs better when the error variance is large and the PLS estimator achieves its best results when the model includes more variables. However, the advantage of the ridge regression method over PLS is that it can provide the 95% confidence interval for the regression coefficients while PLS cannot.     

An optimal property of the “(r,k ) class estimators”

The purpose of this work is to display optimal conditions, in terms of the Mean Square Error criterion of the (r,k) class estimators. This will be done with respect to the ordinary ridge repression, principal components and ordinary least squares estimate.     

Probability Generating Function Based Jeffrey's Divergence for Statistical Inference

Statistical inference procedures based on transforms such as characteristic function and probability generating function have been examined by many researchers because they are much simpler than probability density functions. Here, a probability generating function based Jeffrey's divergence measure is proposed for parameter estimation and goodness-of-fit test. Being a member of the M-estimators, the proposed estimator is consistent. Also, the proposed goodness-of-fit test has good statistical power. The proposed divergence measure shows improved performance over existing probability generating function based measures. Real data examples are given to illustrate the proposed parameter estimation method and goodness-of-fit test.     

幂平均数若干性质之证明

幂平均数作为算术平均数、几何平均数、调和平均数等的一般形式,它与各具体形式之间必存在一定的关系。在目前的一些教材中,这种逻辑关系的描述是不正确的。又由于这些教材对所作的描述并未给予证明,因此,错误被隐藏起来。本文重新描述这种逻辑关系,并给予数学证明。