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面板 MA 单位根与平稳性检验的极限局部功效及功效包络计算AI 解读

The present article discusses panel unit root tests for two classes of models. One is the moving average (MA) model and the other is the error components model. We conduct score type tests for these models, allowing for various types of regressors, and examine the cross-sectional effect explicitly by presenting an efficient way of computing limiting local powers. It is found that the existence of common regressors does not affect the asymptotic behavior of tests, although…

基于鞅近似的分数布朗运动二次泛函分布AI 解读

The present paper deals with the distributions related to the fractional Brownian motion (fBm). In particular, we try to compute the distributions of (ratios of) its quadratic functionals, not by simulations, but by numerically inverting the associated characteristic functions (c.f.s). Among them is the fractional unit root distribution. It turns out that the derivation of the c.f.s based on the standard approaches used for the ordinary Bm is inapplicable. Here the…

线性非平稳模型：P. C. B. Phillips 工作述评AI 解读

The work of Professor P.C.B. Phillips, even if it is focused on the area of linear nonstationary models, is enormous. So it is hard for me to explore the whole of his work in this paper. Therefore, I have decided to take up only a few results of his work. The topics chosen here are applications of the martingale approximation and the problem of choosing between stochastic and deterministic trends, which I discuss and, hopefully, extend.

时间序列模型测量误差问题的统一方法AI 解读

The measurement error problem that we consider in this paper is concerned with the situation where time series data of various kinds—short memory, long memory, and random walk processes—are contaminated by white noise. We suggest a unified approach to testing for the existence of such noise. It is found that the power of our test crucially depends on the underlying process.

非平稳分数单位根AI 解读

This paper deals with a scalar I ( d ) process { y j }, where the integration order d is any real number. Under this setting, we first explore asymptotic properties of various statistics associated with { y j }, assuming that d is known and is greater than or equal to ½. Note that { y j } becomes stationary when d < ½, whose case is not our concern here. It turns out that the case of d = ½ needs a separate treatment from d > ½. We then consider, under the normality…

伪回归、协整与近协整渐近理论的另一种研究方法AI 解读

An alternative approach is taken to the asymptotic theory of cointegration. The present approach gives a different expression for the limiting distributions of statistics associated with cointegration, which enables us to compute accurately the distribution functions. Alternative interpretations of cointegration are given and a notion of near cointegration is introduced. We then devise tests which take cointegration as the null and discuss the limiting local power under the…

移动平均单位根检验AI 解读

Testing for a unit root in the moving average model is discussed. First, for the stationary MA(1) model, we suggest a score type test which is locally best invariant and unbiased. Performance of the test for finite samples is compared with the most powerful test. The asymptotic behavior of the test is also considered by computing the limiting power under a sequence of local alternatives. We then extend the model to an infinite order MA and suggest a test for this extended…

非平稳与不可逆时间序列模型渐近推断的 Fredholm 方法AI 解读

A unified approach which I call the Fredholm approach is suggested for the study of asymptotic behavior of estimators and" test statistics arising from nonstationary and/or noninvertible time series models. Some limit theorems are given concerning the distribution of (the ratio of) quadratic (plus linear) forms in random variables generated by a linear process that is not necessarily stationary. Especially, the limiting characteristic function is derived explicitly via the…

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…

非稳定自回归误差下时间序列回归估计量极限分布的一般方法AI 解读

The authors consider the time series regression model where the error term follows a nonstable autoregressive process and present a general approach for delivering the limiting distribution of a normalized estimator for the autoregressive parameter. The present approach is quite straightforward and leads them to an accurate evaluation of the distribution function, unlike the other approaches suggested in the literature. The authors' methodology is illustrated and percent…

不可逆移动平均模型中极大似然与非线性最小二乘估计的渐近性质AI 解读

Dealing with noninvertible, infinite-order moving average (MA) models, we study the asymptotic properties of an estimator of the noninvertible coefficient. The estimator is constructed acting as if the data were generated from a Gaussian MA process. Allowing for two cases on the initial values of the error process, we first discuss the condition for the existence of a consistent estimator. We then compute the probability of the estimator occurring at the boundary of the…

回归系数恒定性对随机游走备择检验的渐近理论AI 解读

The LBI (locally best invariant) test is suggested under normality for the constancy of regression coefficients against the alternative hypothesis that one component of the coefficients follows a random walk process. We discuss the limiting null behavior of the test statistic without assuming normality under two situations, where the initial value of the random walk process is known or unknown. The limiting distribution is that of a quadratic functional of Brownian motion…

正态性下周期图及相关统计量的近似分布AI 解读

Under normality, we obtain higher-order approximations to the distributions of the periodogram and related statistics. Our approach is based on the theorem which decomposes the periodogram into the sum of two independent random variables. It is seen that this decomposition enables us to study fairly closely the higher-order properties of not only the periodogram, but also periodogram-based statistics such as the estimators of the spectrum and prediction error variance. Some…

ARMA 模型极大似然估计量的渐近展开AI 解读

SUMMARY A technique is given for the Edgeworth type asymptotic expansion for the joint as well as marginal and conditional distributions of the maximum likelihood estimators in autoregressive moving-average (ARMA) models. Our methodology is illustrated and results on the expansions for some simple ARMA models are presented.

AR(p)模型对含测量误差AR(p)模型的单侧拉格朗日乘子检验AI 解读

SUMMARY The one-sided Lagrange multiplier test is suggested for testing the null autoregressive (AR) model against the AR model with measurement error. The test statistic is shown to be asymptotically N(0, 1) under the null. Finite sample properties of the test both under the null and under the alternative are examined briefly by simulations.