HAC估计的性质与修正及其在伪回归中的应用研究

本文通过频谱分析揭示了预白化HAC和参数化VARHAC比非参数HAC具有明显优势,并指出传统预白化HAC法由于使用了存在有限样本偏差的OLS法来估计自回归参数,导致其存在有限样本偏差,由此构造的t统计量具有过度拒绝原假设倾向。为了减少预白化HAC的偏差,将OLS估计量的线性修正（LBC）和非线性修正（NBC）嵌入到预白化HAC中,研究表明该法能大大减少长期方差的估计偏差,并通过蒙特卡洛模拟证实对预白化HAC的修正估计能有效减少平稳过程之间的伪回归概率,从而提高了回归模型统计推断的可靠性。     

稳健的HAC法在多元平稳时间序列之间伪回归中的应用

本文在传统HAC法的基础上,将截断参数M设定为样本容量T,并推导新的模型显著性检验Wald*统计量的极限分布。通过比较分析,表明Wald*统计量能大大减少伪回归概率,且新统计量比传统检验统计量更加稳健,但是也发现新的统计量具有一定程度的检验水平扭曲,原因在于截断参数M的设定忽略了AR过程的持久性、MA过程的滞后阶等因素,从而导致Wald*存在检验水平扭曲,说明M的设定不当会产生伪回归和检验水平扭曲现象。     

沪深股市投机泡沫存在性检验的新视角——基于向最误差修正模型的MTAR协整分析

本文通过分析沪证和深证指数及与股票市场密切相关的国民经济运行变量的时间序列,建立向量自回归(VAR)模型,并在此基础上得出了我国股市与经济运行之间的长期均衡关系和短期变动的向量误差修正(VEC)模型.因此引入惯性门限自回归(MTAR)模型,通过检验协整残差的非对称调整假设,对我国股票市场发展是否存在泡沫现象进行进一步分析.针时崔畅等(2006)、王薛等(2008)运用MTAK协整检验时中国股市进行实证研究的MTAK模型平稳性的检验提出了质疑,并用同样的方法以新的视角时沪深股市泡沫重新进行了协整检验,得出了一些结论.     

沪深股市投机泡沫存在性检验的新视角——基于向量误差修正模型的MTAR协整分析

本文通过分析沪证和深证指数及与股票市场密切相关的国民经济运行变量的时间序列,建立向量自回归(VAR)模型,并在此基础上得出了我国股市与经济运行之间的长期均衡关系和短期变动的向量误差修正(VEC)模型。因此引入惯性门限自回归(MTAR)模型,通过检验协整残差的非对称调整假设,对我国股票市场发展是否存在泡沫现象进行进一步分析。针对崔畅等(2006)、王薛等(2008)运用MTAR协整检验对中国股市进行实证研究的MTAR模型平稳性的检验提出了质疑,并用同样的方法以新的视角对沪深股市泡沫重新进行了协整检验,得出了一些结论。     

广义Breitung非参数单位根检验研究——基于平稳假设下序列长期方差一致估计的分析

Breitung检验中生成序列的误差项的自相关会影响有限样本性质。本文用平稳假设下序列长期方差的一致估计量作为统计量的分母对其进行了修正。给出了修正后的统计量及其渐近理论,并对修正前后的有限样本性质进行了仿真。结果显示,修正后统计量概率密度的左偏有所减少;当误差项有自相关时,修正后检验的水平扭曲有所改进;当样本较小时,随误差项自回归(移动平均)系数或序列自回归系数的增加,修正后检验的势逐渐大于Breitung检验的势。     

基于VAR的金融业支持对新疆中小企业发展的影响分析

采用1980～2009年的时序数据,通过建立向量自回归模型分析新疆金融业水平与新疆中小企业发展之间的动态影响关系,并在对VAR模型进行残差检验和稳定性检验的基础上,运用脉冲响应函数和预测方差方法进行经济计量分析。研究结果表明:新疆中小企业发展对银行业规模冲击有正向响应,并趋向稳定,对银行业活跃程度有负向响应然后转向正向响应,对金融效率冲击有正向响应。     

储油罐的变位识别与罐容表标定问题

依据所给数据进行回归分析(regression analysis),得出无变位进油、无变位出油时罐内油位的预测方程,相比较于倾斜变位后的回归方程,通过残差分析,作残差图,认定方程成立,用Matlab软件将这些研究的结果加以归纳整理求得回归模型,通过预测及作图,检验模型成立.     

基于残差的非对称单位根自助法检验研究

本文在研究非对称单位根检验EG法并指出其优缺点的基础上,应用基于残差的块形非参数自助法(RBB法)对EG法进行了改进,并对改进后的新方法进行了仿真研究。仿真结果表明,新的EG法不仅可以降低原EG法的检验水平扭曲,而且也具有比较高的检验势(甚至在对称单位根检验中)。同时在仿真中也发现,通过RBB法改进后的EG法可以在一定程度上克服ADF法在近单位根过程中的低势缺陷。     

具有AR(p)误差的半参数回归模型的参数估计

近年来,半参数模型是处理回归问题的有力工具,进年来,已经成为当今回归分析的热点,引起了众多学者的关注。文章研究了具有AR(p)误差的半参数回归模型,首先对其误差的相关性进行了消除,然后将模型转变成为经典的半参数回归模型,运用惩罚最小二乘估计方法对模型参数进行了估计。     

面板单位根Hadri检验的有偏性及其修正

Hadri(2000)根据单一时间序列的KPSS检验,提出了以平稳性为原假设的面板数据单位根检验。但我们的仿真试验表明,对短时间序列数据,其基于残差的拉格朗日乘数(LM)统计量是有偏的,使得在此基础之上进行的Hadri检验不再服从标准正态渐进分布。本文通过蒙特卡罗仿真对LM统计量进行了修正,修正之后的Hadri检验统计量的渐进分布为标准正态分布。仿真的结果显示,修正了LM值的Hadri检验具有更好的小样本性质和更高的检验势。     

Prewhitening Bias in HAC Estimation*

Heteroskedasticity and autocorrelation consistent (HAC) estimation commonly involves the use of prewhitening filters based on simple autoregressive models. In such applications, small sample bias in the estimation of autoregressive coefficients is transmitted to the recolouring filter, leading to HAC variance estimates that can be badly biased. The present paper provides an analysis of these issues using asymptotic expansions and simulations. The approach we recommend involves the use of recursive demeaning procedures that mitigate the effects of small‐sample autoregressive bias. Moreover, a commonly used restriction rule on the prewhitening estimates (that first‐order autoregressive coefficient estimates, or largest eigenvalues, >0.97 be replaced by 0.97) adversely interferes with the power of unit‐root and [ Kwiatkowski, Phillips, Schmidt and Shin (1992) Journal of Econometrics, Vol. 54, pp. 159–178] (KPSS) tests. We provide a new boundary condition rule that improves the size and power properties of these tests. Some illustrations of the effects of these adjustments on the size and power of KPSS testing are given. Using prewhitened HAC estimates and the new boundary condition rule, the KPSS test is consistent, in contrast to KPSS testing that uses conventional prewhitened HAC estimates [ Lee, J. S. (1996) Economics Letters, Vol. 51, pp. 131–137].     

Spurious Regression and Trending Variables*

This paper analyses the asymptotic and finite‐sample implications of different types of non‐stationary behaviour among the dependent and explanatory variables in a linear spurious regression model. We study cases when the non‐stationarity in the dependent and explanatory variables is deterministic as well as stochastic. In particular, we derive the order in probability of the t‐statistic in a spurious regression equation under a variety of empirically relevant data generation processes, and show that the spurious regression phenomenon is present in all cases when both dependent and explanatory variables behave in a non‐stationary way. Simulation experiments confirm our asymptotic results.     

Indirect inference for dynamic panel models

Maximum likelihood (ML) estimation of the autoregressive parameter of a dynamic panel data model with fixed effects is inconsistent under fixed time series sample size and large cross section sample size asymptotics. This paper proposes a general, computationally inexpensive method of bias reduction that is based on indirect inference, shows unbiasedness and analyzes efficiency. Monte Carlo studies show that our procedure achieves substantial bias reductions with only mild increases in variance, thereby substantially reducing root mean square errors. The method is compared with certain consistent estimators and is shown to have superior finite sample properties to the generalized method of moment (GMM) and the bias-corrected ML estimator.     

Bias in dynamic panel estimation with fixed effects,incidental trends and cross section dependence

Explicit asymptotic bias formulae are given for dynamic panel regression estimators as the cross section sample size N→∞$N\to \infty$. The results extend earlier work by Nickell [1981. Biases in dynamic models with fixed effects. Econometrica 49, 1417–1426] and later authors in several directions that are relevant for practical work, including models with unit roots, deterministic trends, predetermined and exogenous regressors, and errors that may be cross sectionally dependent. The asymptotic bias is found to be so large when incidental linear trends are fitted and the time series sample size is small that it changes the sign of the autoregressive coefficient. Another finding of interest is that, when there is cross section error dependence, the probability limit of the dynamic panel regression estimator is a random variable rather than a constant, which helps to explain the substantial variability observed in dynamic panel estimates when there is cross section dependence even in situations where N is very large. Some proposals for bias correction are suggested and finite sample performance is analyzed in simulations.     

Reduced rank regression in cointegrated models

The coefficient matrix of a cointegrated first-order autoregression is estimated by reduced rank regression (RRR), depending on the larger canonical correlations and vectors of the first difference of the observed series and the lagged variables. In a suitable coordinate system the components of the least-squares (LS) estimator associated with the lagged nonstationary variables are of order 1/T, where T is the sample size, and are asymptotically functionals of a Brownian motion process; the components associated with the lagged stationary variables are of the order T^−1/2 and are asymptotically normal. The components of the RRR estimator associated with the stationary part are asymptotically the same as for the LS estimator. Some components of the RRR estimator associated with nonstationary regressors have zero error to order 1/T and the other components have a more concentrated distribution than the corresponding components of the LS estimator.     

Sampling Techniques for Big Data Analysis

In analysing big data for finite population inference, it is critical to adjust for the selection bias in the big data. In this paper, we propose two methods of reducing the selection bias associated with the big data sample. The first method uses a version of inverse sampling by incorporating auxiliary information from external sources, and the second one borrows the idea of data integration by combining the big data sample with an independent probability sample. Two simulation studies show that the proposed methods are unbiased and have better coverage rates than their alternatives. In addition, the proposed methods are easy to implement in practice.     

Bias corrections for exponentially transformed forecasts: Are they worth the effort?

In many economic applications, it is convenient to model and forecast a variable of interest in logs rather than in levels. However, the reverse transformation from log forecasts to levels introduces a bias. This paper compares different bias correction methods for such transformations of log series which follow a linear process with various types of error distributions. Based on Monte Carlo simulations and an empirical study of realized volatilities, we find no choice of correction method that is uniformly best. We recommend the use of the variance-based correction, either by itself or as part of a hybrid procedure where one first decides (using a pretest) whether the log series is highly persistent or not, and then proceeds either without bias correction (high persistence) or with bias correction (low persistence).     

Unit root quantile autoregression testing using covariates

This paper extends unit root tests based on quantile regression proposed by Koenker and Xiao [Koenker, R., Xiao, Z., 2004. Unit root quantile autoregression inference, Journal of the American Statistical Association 99, 775–787] to allow stationary covariates and a linear time trend. The limiting distribution of the test is a convex combination of Dickey–Fuller and standard normal distributions, with weight determined by the correlation between the equation error and the regression covariates. A simulation experiment is described, illustrating the finite sample performance of the unit root test for several types of distributions. The test based on quantile autoregression turns out to be especially advantageous when innovations are heavy-tailed. An application to the CPI-based real exchange rates using four different countries suggests that real exchange rates are not constant unit root processes.     

Asymptotics for Autocovariances and Integrated Periodograms for Linear Processes Observed at Lower Frequencies

One of the most frequently used class of processes in time series analysis is the one of linear processes. For many statistical quantities, among them sample autocovariances and sample autocorrelations, central limit theorems are available in the literature. We investigate classical linear processes under a nonstandard observation pattern; namely, we assume that we are only able to observe the linear process at a lower frequency. It is shown that such observation pattern destroys the linear structure of the observations and leads to substantially different asymptotic results for standard statistical quantities. Central limit theorems are given for sample autocovariances and sample autocorrelations as well as more general integrated periodograms and ratio statistics. Moreover, for specific autoregressive processes, the possibilities to estimate the parameters of the underlying autoregression from lower frequency observations are addressed. Finally, we suggest for autoregressions of order 2 a valid bootstrap procedure. A small simulation study demonstrates the performance of the bootstrap proposal for finite sample size.