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若干系数恒定性检验统计量的分布AI 解读

This paper investigates the distribution of the locally best invariant test for coefficient constancy, against the random walk alternative, in a regression model which may contain nonvarying coefficients. Unfortunately, the distribution of the locally best invariant test depends critically on the exogenous variables of the model, even asymptotically. A modification is suggested which has a known asymptotic distribution regardless of the regression effect.

非参数回归在模型检验中的应用AI 解读

The use of nonparametric regression is explored to check the fit of a parametric regression model. The principal aim is to check the validity of the regression curve rather than necessarily to detect outliers. A pseudo likelihood ratio test is developed to provide a global assessment of fit and simulation bands are used to indicate the nature of departures from the model. The types of data considered include discrete response variables, where standard diagnostic techniques…

自回归中利用 Bootstrap 进行 Edgeworth 修正AI 解读

We prove that the distribution of least-squares estimates in autoregressions can be bootstrapped with accuracy $o(n^{-1/2})$ a.s., thereby improving the normal approximation error of $O(n^{-1/2})$.

判定时间序列非平稳性的图形方法AI 解读

Integrated processes as models for time series data have proved to be an important component of the highly flexible class of ARIMA(p, d, q) models. Determining the amount of differencing, d, has been a difficult task: too little and the process is not yet second-order stationary; too much and the process is more variable than it need be. It is shown that by introducing the notion of generalized covariances, developed by Matheron (1973) for spatial processes, the amount of…

针对一阶序列依赖的随机性秩检验AI 解读

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

共同趋势检验AI 解读

Cointegrated multiple time series share at least one common trend. Two tests are developed for the number of common stochastic trends (i.e., for the order of cointegration) in a multiple time series with and without drift. Both tests involve the roots of the ordinary least squares coefficient matrix obtained by regressing the series onto its first lag. Critical values for the tests are tabulated, and their power is examined in a Monte Carlo study. Economic time series are…

针对一阶序列依赖的基于秩的随机性检验AI 解读

Optimal rank-based procedures were derived in Hallin, Ingenbleek, and Puri (1985, 1987) and Hallin and Puri (1988) for some fundamental testing problems arising in time series analysis. The optimality properties of these procedures are of an asymptotic nature, however, whereas much of the attractiveness of rank-based methods lies in their small-sample applicability and robustness features. Accordingly, the objective of this article is twofold: (a) a study of the…

非高斯时间序列的相位滞后估计AI 解读

An important problem in the physical sciences is estimation of the innovations of a noninvertible linear process. Here the problem of deconvolving such a time series containing a phase-lead is investigated. A compensating phase-lag filter is sought, and is estimated by maximization of a chosen statistic or projection index. It is demonstrated by simulation that a statistic which is superior to another in the ideal case of a full-band time series can be substantially inferior…

《联合数据生成过程的非参数时间序列估计与向量自回归》证明问题说明AI 解读

Several problems with the proofs of Theorems 2, 3, and 4 given in the above article were drawn to our attention by Professor P. M. Robinson. A complete and rigorous set of conditions under which the main results of these theorems hold has not been found yet.

Durbin–Watson 检验的局部最优性质AI 解读

Although originally designed to detect AR(1) disturbances in the linear-regression model, the Durbin-Watson test is known to have good power against other forms of disturbance behavior. In this paper, we identify disturbance processes involving any number of parameters against which the Durbin–Watson test is approximately locally best invariant uniformly in a range of directions from the null hypothesis. Examples include the sum of q independent ARMA(1,1) processes, certain…

回归结构稳定性的多重决策理论分析AI 解读

Using the theory of multiple decisions, this paper conducts an analysis of structural stability in location and variance for the linear-regression model. It shows that both cusum and cusum-of-squares techniques are in certain senses optimal. However, the same tests are optimal for changes in location and variance. It is also shown that there is an inherent contradiction between the use of recursive residuals and cusum techniques. The concept of a localized Bayes rule is…

含单整过程回归的统计推断：第一部分AI 解读

This paper develops a multivariate regression theory for integrated processes which simplifies and extends much earlier work. Our framework allows for both stochastic and certain deterministic regressors, vector autoregressions, and regressors with drift. The main focus of the paper is statistical inference. The presence of nuisance parameters in the asymptotic distributions of regression F tests is explored and new transformations are introduced to deal with these…

自回归移动平均过程的若干精确公式AI 解读

This paper demonstrates that for a finite stationary autoregressive moving average process the inverse of the covariance matrix differs from the matrix of the covariances of the inverse process by a matrix of low rank. The formula for the exact inverse of the covariance matrix of the scalar or multivariate process is provided. We obtain approximations based on this formula and evaluate some of the approximate results in the existing literature. Applications to computational…

通过鞅逼近证明样本协方差矩阵向随机积分的弱收敛AI 解读

Under general conditions the sample covariance matrix of a vector martingale and its differences converges weakly to the matrix stochastic integral ∫ 0 1 BdB′ , where B is vector Brownian motion. For strictly stationary and ergodic sequences, rather than martingale differences, a similar result obtains. In this case, the limit is ∫ 0 1 BdB′ + Λ and involves a constant matrix Λ of bias terms whose magnitude depends on the serial correlation properties of the sequence. This…

相依非同分布随机变量的大数定律AI 解读

This paper provides L 1 and weak laws of large numbers for uniformly integrable L 1 -mixingales. The L 1 -mixingale condition is a condition of asymptotic weak temporal dependence that is weaker than most conditions considered in the literature. Processes covered by the laws of large numbers include martingale difference, ø(·), ρ(·), and α(·) mixing, autoregressive moving average, infinite-order moving average, near epoch dependent, L 1 -near epoch dependent, and mixingale…

连续时间计量经济模型的历史AI 解读

Although it is only during the last decade that continuous-time models have been extensively used in applied econometric work, the development of statistical methods applicable to such models commenced over 40 years ago. The first significant contribution to the problem of estimating the parameters of continuous-time stochastic models from discrete data was made by the British statistician Bartlett [1946] only three years after the pioneering contribution of Haavelmo [1943]…

回归变量具有单位根时的渐近正态性AI 解读

Under fairly general conditions, ordinary least squares and linear instrumental variables estimators are asymptotically normal when a regression equation has nonstationary right hand side variables. Standard formulas may be used to calculate a consistent estimate of the asymptotic variance-covariance matrix of the estimated parameter vector, even if the disturbances are conditionally heteroskedastic and autocorrelated. So inference may proceed in the usual way. The key…

利用面板数据估计向量自回归模型AI 解读

This paper considers estimation and testing of vector autoregressio n coefficients in panel data, and applies the techniques to analyze the dynamic relationships between wages an d hours worked in two samples of American males. The model allows for nonstationary individual effects and is estimated by applying instrumental variables to the quasi-differenced autoregressive equations. The empirical results suggest the absence of lagged hours in the wage forecasting equation.…

动态模型中的结构变化检验AI 解读

The well-known CUSUM test for structural change is investigated whe n there are lagged dependent variables among the regressors in a linear model. The authors show that both a modified CUSUM test, suggested b y J. M. Dufour (1982), and the straightforward CUSUM test retain their asymptotic significance levels in dynamic models, and find that the power depends crucially on the angle between the mean regressor and the structural shift. Copyright 1988 by The Econometric Society.

时间序列分析中的趋势与随机游走AI 解读

This paper studies the effects of spurious detrending in regression. The asymptotic behavior of traditional least squares estimators and tests are examined in the context of models where the generating mechanism is systematically misspecified by the presence of deterministic time trends. Most previous work on the subject has relied upon Monte Carlo studies to understand the issues involved in detrending data that is generated by integrated processes and our analytical…

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存在结构变化的非线性计量模型推断AI 解读

This paper extends the classical test for structural change in linear regression models (see Chow (1960)) to a wide variety of nonlinear models, estimated by a variety of different procedures. Wald, Lagrange multiplier-like, and likelihood ratio-like test statistics are introduced. The results allow for heterogeneity and temporal dependence of the observations. In the process of developing the above tests, the paper also provides a compact presentation of general unifying…

十九个 OECD 国家实际 GDP 的长期与周期行为：1957—1983年AI 解读

Log per capita real gross domestic product is modeled as a third-order autoregression with a pair of complex roots whose amplitude is smaller than the amplitude of the real root. The behavior of this terms series is interpreted in terms of these two amplitudes, the periodicity of the complex roots, and the standard deviation of the disturbance. Restrictions are evaluated and inference is conducted using the likelihood principle, applying Monte Carlo integration with…

差分模型估计中的陷阱AI 解读

This article assesses the potential magnitude of the loss of estimation efficiency caused by the adoption of a differenced model when the disturbances of the original (levels) linear regression model follow either a stable (autoregressive) AR(1) process or a fixed start-up random-walk process (hence no filtering is necessary from the standpoint of estimation). The magnitude of the loss, which can be quite large, is found to be affected by both the form of the original model…