异方差性F的参数估计

在经典经济计量理论中,异方差现象的存在破坏了普通最小二乘法(OLS)参数估计中关于随机序列独立同分布的基本假定,从而使得用OLS法估计得到的模型Y=Xβ失去优良性,如(?)不再是参数β的最小方差线性无偏估计(BLUE),继而参数的显著性检验失去意义,预测误差加大等等,致使模型失效。在实际建模中,一般是这样处理这一问题的:(1)用图示法或等级相关系数、Goldfeld-Quandt、Bartlett等方法检查异方差现象是否存在于待建模型中。(2)对探明有异方差现象的模型,通过加权最小二乘法(WLS)、Glejser法和正确引入解释变量等方法将异方差模型转化为同方差模型后再进行参数估计。经典计量经济理论认为扰动项方差σ_t~2是解释变量X_t的函数,即σ_t~2=f(X_t)σ~2,之所以出现异方差现象,是因为对于不同的X_t∈R~p,f(X_t)发生了变化。如果已知函数f的具体形式,     

空间回归模型估计中的最小二乘法

空间回归模型由于引入了空间地理信息而使得其参数估计变得复杂,因为主要采用最大似然法,致使一般人认为在空间回归模型参数估计中不存在最小二乘法。通过分析空间回归模型的参数估计技术,研究发现,最小二乘法和最大似然法分别用于估计空间回归模型的不同的参数,只有将两者结合起来才能快速有效地完成全部的参数估计。数理论证结果表明,空间回归模型参数最小二乘估计量是最佳线性无偏估计量。空间回归模型的回归参数可以在估计量为正态性的条件下而实施显著性检验,而空间效应参数则不可以用此方法进行检验。     

空间滞后面板平滑转换模型的估计及数值模拟

将空间滞后项引入面板平滑转换模型,构建了空间滞后面板平滑转换模型,通过综合应用拟极大似然法和非线性最小二乘法,构造了该模型的参数估计方法,并通过蒙特卡洛数值模拟探讨了参数估计方法的小样本性质;数值模拟结果显示,提出的估计方法在小样本条件下表现良好,参数估计值随着样本容量的增大而收敛到参数的真值。     

基于全最小一乘准则的灰色GM(1,1)模型参数估计

针对传统灰色GM(1,1)模型参数估计的最小二乘算法稳健性较差,在分析全最小一乘算法比最小二乘算法具有较好稳健性的基础上,文章提出了基于全最小一乘准则估计灰色GM(1,1)模型的参数,并给出了求解该算法的LINGO程序和规划模型方法,并通过计算实例说明,基于全最小一乘准则参数估计的GM(1,1)模型比传统灰色GM(1,1)模型具有更好的抗干扰性能和受异常点影响小的优点,从而拓展了灰色GM(1,1)模型的适用范围。     

一类扩散过程的参数估计及其Matlab实现

文章考虑平方根扩散过程(CIR)模型的参数估计,分别采用了普通最小二乘法、精确极大似然函数法、Euler法等三种方法,并提供了Matlab的操作实现程序,最后考虑了在上证指数中的应用。     

具有线性趋势的残差自回归模型的估计方法

为了探寻具有线性趋势的残差自回归模型的较为合适的估计方法,文章以残差AR(2)模型为例,对直接最小二乘法、两步法、非线性最小二乘法和化归法进行了Monte Carlo模拟,拟合和预测结果显示非线性最小二乘法和化归法的均方误差和平均绝对误差相同且最小.此外,还利用1980-2013年河南省人均GDP经济数据进行了拟合与预测实证分析,得到了与模拟比较相类似的结果,这说明非线性最小二乘法和化归法是较优的估计方法.进一步地,基于非线性最小二乘法,给出了河南省人均GDP的短期预测.     

OLS与ML：回归模型两种参数估计方法的比较研究

最小二乘法(OLS)和最大似然法(ML)是回归模型参数估计的两种最重要的方法。 但二者有着明显的差别,本文就二者之间的有关差别进行比较。     

基于数据拟合的非线性方法及Matlab解决方案

基于数据拟合思想及其方法的比较与选择在数量经济模型参数估计问题的研究过程中具有十分重要的意义.文章给出了Bass模型和品牌生命周期模型的参数估计具体的估计过程,并依据可绝系数和残差平方和分析及实例,证实了非线性最小二乘优于普通最小二乘;在分析Matlab中lsqcurvefit函数数据拟合Gauss-Newton和Levenberg-Marquart算法原理的基础上,给出了品牌生命周期模型的Matlab非线性参数估计解决方案及最优化方法.     

新产品市场渗透预测模型:泛函回归

1 Bass模型 作为传播理论的一个分支,扩散理论很早就引起了市场营销等领域中学者们的重视.1969年,Bass通过对11种耐用品的市场扩散研究,提出了耐用品的一次购买模型(简称Bass模型)[1].该模型把新产品的扩散速度归结为两大因素的影响:一是创新的或外部的影响,这种影响主要通过大众媒介(如广告)传播;二是模仿的或内部的影响,它是指人与人之间(即使用者对未使用者)的影响.     

改进的Gompertz模型参数估计方法比较研究

讨论改进的Gompertz模型两种参数估计方法:三和法和非线性最小二乘估计法,并通过蒙特卡洛实验比较两种估计方法的精度和收敛率,得出非线性最小二乘估计法在估计精度和估计的成功率两方面都优于三和法的结论;利用Gompertz曲线拟合中国电影票房数据并对其未来发展作出预测:中国电影票房最终可以在2025年左右到达饱和状态,饱和状态总规模大约为1 676.5亿元。     

Non-parametric Kernel Estimation of the Coefficient of a Diffusion

In this work we exhibit a non-parametric estimator of kernel type, for the diffusion coefficient when one observes a one-dimensional diffusion process at times i / n for i = , ..., n and study its asymptotics as n ←∞. When the diffusion coefficient has regularity r ≥ 1, we obtain a rate 1/ n ^{r /(1+2 r )}, both for pointwise estimation and for estimation on a compact subset of R: this is the same rate as for non-parametric estimation of a density with i.i.d. observations.     

Empirically feasible solutions and explicit dynamics for rational expectation models

Fairly general rational expectation (RE) models are proved to have linear vector autoregressive moving average (VARMA) models as their reduced forms, using Muth's method of undetermined coefficients (MUC). An advantage of using VARMAs is that RE estimation can benefit from well-developed theory of solutions of stochastic difference equations and computer packages for VARMA and state space (SS) models. For example, we report theoretical derivations of explicit dynamics associated with the RE structure for Muth's and Lucas-Sargent-Wallace's models, suggesting generalizations and new solutions. We illustrate an RE structure estimation by using energy prices and Fackler and Krieger's (J. Bus. Econom. Statist. 4 (1986), 71–80) study of five major macroeconomic variables.     

Optimal design of repetitive group sampling plans for Weibull and gamma distributions with applications and comparison to the Birnbaum–Saunders distribution

In this paper, we propose a multiple deferred state repetitive group sampling plan which is a new sampling plan developed by incorporating the features of both multiple deferred state sampling plan and repetitive group sampling plan, for assuring Weibull or gamma distributed mean life of the products. The quality of the product is represented by the ratio of true mean life and specified mean life of the products. Two points on the operating characteristic curve approach is used to determine the optimal parameters of the proposed plan. The plan parameters are determined by formulating an optimization problem for various combinations of producer's risk and consumer's risk for both distributions. The sensitivity analysis of the proposed plan is discussed. The implementation of the proposed plan is explained using real-life data and simulated data. The proposed plan under Weibull distribution is compared with the existing sampling plans. The average sample number (ASN) of the proposed plan and failure probability of the product are obtained under Weibull, gamma and Birnbaum–Saunders distributions for a specified value of shape parameter and compared with each other. In addition, a comparative study is made between the ASN of the proposed plan under Weibull and gamma distributions.     

Estimation of General Stationary Processes by Variable Length Markov Chains

We develop new results about a sieve methodology for the estimation of minimal state spaces and probability laws in the class of stationary processes defined on finite categorical spaces. Using a sieve approximation with variable length Markov chains of increasing order, we show that an adapted version of the Context algorithm yields asymptotically correct estimates for the minimal state space and for the underlying probability distribution. As a side product, the method of sieves yields a nice graphical tree representation for the potentially infinite dimensional minimal state space of the data generating process, which is very useful for exploration of the memory.     

Deviation of order p for estimators of the variance in first-order stochastic differential equation (SDE)

In this work, we consider a non-parametric estimator of the variance in one-dimensional diffusion models or, more generally, in Itô processes with a deterministic diffusion term and a general non-anticipative drift. The estimation is based on the quadratic variation of discrete time observations over a finite interval. In particular, a central limit theorem (CLT) is proved for the deviation in L ^p norm (p≥; 1) between the variance and this estimator. The method of the proof consists in writing the L ^p norm of the deviation, when the drift term is equal to zero, as a sum of 4-dependent random variables. The moments are then computed by means of a Gaussian approximation and a CLT for m-dependent random variables is applied. The convergence is stable in law, this allows the result for processes with general drifts to be obtained, by using Girsanov's formula.     

Estimation of Integrated Volatility in Continuous-Time Financial Models with Applications to Goodness-of-Fit Testing

Abstract.  Properties of a specification test for the parametric form of the variance function in diffusion processes are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable x it is known that the corresponding statistics have an asymptotic normal distribution. However, most models of mathematical finance use a volatility function which depends on the state x . In this paper we prove that in the general case, where σ depends also on x the estimates of integrals of the volatility converge stably in law to random variables with a non-standard limit distribution. The limit distribution depends on the diffusion process X _t itself and we use this result to develop a bootstrap test for the parametric form of the volatility function, which is consistent in the general diffusion model.     

The Time-Varying-Parameter Model for Modeling Changing Conditional Variance: The Case of the Lucas Hypothesis

The main econometric issue in testing the Lucas (1973) hypothesis in a time series context is estimation of the forecast-error variance conditional on past information. The conditional variance may vary through time as monetary policy evolves and agents are obliged to infer its present state. Under the assumption that a monetary policy regime is continuously changing, a time-varying-parameter model is proposed for the monetary-growth function. Based on Kalman-filtering estimation of recursive forecast errors and their conditional variances, the Lucas hypothesis is tested for the U.S. economy (1964:1–1985:4) using monetary growth as aggregate demand variable. The Lucas hypothesis is rejected in favor of Friedman's (1977) hypothesis—the conditional variance of monetary growth affects real output directly, not through the coefficients on the forecast-error term in the Lucas-type output equation.     

Inference for ergodic diffusions plus noise

We research an adaptive maximum‐likelihood–type estimation for an ergodic diffusion process where the observation is contaminated by noise. This methodology leads to the asymptotic independence of the estimators for the variance of observation noise, the diffusion parameter, and the drift one of the latent diffusion process. Moreover, it can lessen the computational burden compared to simultaneous maximum likelihood–type estimation. In addition to adaptive estimation, we propose a test to see if noise exists or not and analyze real data as the example such that the data contain observation noise with statistical significance.     

Analytical uses of Kalman filtering in econometrics — A survey

This paper surveys the different uses of Kalman filtering in the estimation of statistical (econometric) models. The Kalman filter will be portrayed as (i) a natural generalization of exponential smoothing with a time-dependent smoothing factor, (ii) a recursive estimation technique for a variety of econometric models amenable to a state space formulation in particular for econometric models with time varying coefficients (iii) an instrument for the recursive calculation of the likelihood of the (constant) state space coefficients (iv) a means of helping to implement the scoring⁻ and EM-method for iteratively maximizing this likelihood (v) an analytical tool in asymptotic estimation theory. The concluding section points to the importance of Kalman filtering for alternatives to maximum⁻ likelihood estimation of state space parameters.     

Parameter estimation for multivariate diffusion processes with the time inhomogeneously positive semidefinite diffusion matrix

Statistical inference for the diffusion coefficients of multivariate diffusion processes has been well established in recent years; however, it is not the case for the drift coefficients. Furthermore, most existing estimation methods for the drift coefficients are proposed under the assumption that the diffusion matrix is positive definite and time homogeneous. In this article, we put forward two estimation approaches for estimating the drift coefficients of the multivariate diffusion models with the time inhomogeneously positive semidefinite diffusion matrix. They are maximum likelihood estimation methods based on both the martingale representation theorem and conditional characteristic functions and the generalized method of moments based on conditional characteristic functions, respectively. Consistency and asymptotic normality of the generalized method of moments estimation are also proved in this article. Simulation results demonstrate that these methods work well.