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畑中道雄教授访谈AI 解读

This interview with Michio Hatanaka is the first in this series given in the East, of which we are very proud. Hatanaka is a pioneer of econometrics in Japan. In the early 1950s he traveled to the United States to study as a graduate student at Vanderbilt University. That step was really unusual in the Japanese profession at that time. His stay in the States was extended to 1966, during which time he taught at Princeton and Rochester. His pathfinding behavior influenced and…

多元时间序列谱密度矩阵相关统计量的分布渐近展开及应用AI 解读

Let { X ( t )} be a multivariate Gaussian stationary process with the spectral density matrix f 0 (ω), where θ is an unknown parameter vector. Using a quasi-maximum likelihood estimator θ̂ of θ, we estimate the spectral density matrix f 0 (ω) by f θ̂ (ω). Then we derive asymptotic expansions of the distributions of functions of f θ̂ (ω). Also asymptotic expansions for the distributions of functions of the eigenvalues of f θ̂ (ω) are given. These results can be applied to…

自回归模型中若干预测量的有限样本性质AI 解读

We compare the distributional properties of the four predictors commonly used in practice. They are based on the maximum likelihood, two types of the least squared, and the Yule-Walker estimators. The asymptotic expansions of the distribution, bias, and mean-squared error for the four predictors are derived up to O ( T −1 ), where T is the sample size. Examining the formulas of the asymptotic expansions, we find that except for the Yule-Walker type predictor, the other three…

时间序列回归中 OLS 估计量的 Edgeworth 展开AI 解读

In this paper we consider the situation in which ordinary least squares (OLS) is used to estimate an ARMA (1,1) model with one exogenous variable. Applying Edgeworth expansion techniques, we examine the misspecification errors and the approximate distributions of the OLS estimator. Extensive numerical studies were performed and selected results are shown graphically. In addition, a technical device is developed to calculate the Edgeworth coefficients.