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非标准条件下的最优估计AI 解读

We analyze optimality properties of maximum likelihood (ML) and other estimators when the problem does not necessarily fall within the locally asymptotically normal (LAN) class, therefore covering cases that are excluded from conventional LAN theory such as unit root nonstationary time series. The classical Hájek–Le Cam optimality theory is adapted to cover this situation. We show that the expectation of certain monotone “bowl-shaped” functions of the squared estimation…

类单位根情形中的可容许与不可容许检验AI 解读

This paper investigates the asymptotic behavior of tests in situations where the likelihood is locally asymptotically quadratic. Necessary and sufficient conditions are given for a test to be admissible. Even without these restrictive parametric assumptions, it is shown that certain common procedures—such as the augmented Dickey–Fuller test in cases where no deterministic trend is present or standard tests for restrictions on cointegrating relationships—are asymptotically…

时间序列计量模型的实证极限AI 解读

This paper characterizes empirically achievable limits for time series econometric modeling and forecasting. The approach involves the concept of minimal information loss in time series regression and the paper shows how to derive bounds that delimit the proximity of empirical measures to the true probability measure (the DGP) in models that are of econometric interest. The approach utilizes joint probability measures over the combined space of parameters and observables and…

针对 ARMA(1,1) 备择的序列相关检验AI 解读

This article is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against autoregressive moving average model ARMA(1, 1) alternatives is considered. The likelihood ratio (LR), sup Lagrange multiplier (LM), and exponential average LM and LR tests are shown to be asymptotically admissible for ARMA(1, 1) alternatives. In addition, they are shown to be consistent…

以ARMA(1,1)为备择的序列相关检验AI 解读

This paper is concerned with tests for serial correlation in time series and in the errors of regression models. In particular, the nonstandard problem of testing for white noise against ARMA(1,1) alternatives is considered. Sup Lagrange multiplier (LM) and exponential average LM tests are introduced and are shown to be asymptotically admissible for ARMA(1,1) alternatives. In addition, they are shown to be consistent against all (weakly stationary strong mixing) non-white…

时间序列贝叶斯推断的渐近理论AI 解读

This paper develops an asymptotic theory of Bayesian inference for time series. A limiting representation of the Bayesian data density is obtained and shown to be of the same general exponential form for a wide class of likelihoods and prior distributions. Continuous time and discrete time cases are studied. In discrete time, an embedding theorem is given which shows how to embed the exponential density in a continuous time process. From the embedding we obtain a large…

基于 OLS 残差的抗趋势结构变化检验AI 解读

We discuss the null distribution and local power of an OLS-based version of the CUSUM test and show that this, contrary to other tests for structural change like, e.g., the Ploberger-Kontrus-Krämer fluctuation test, can also be applied to trending data.

正态线性回归中的最优变点检验AI 解读

This paper determines a class of finite-sample optimal tests for the existence of a changepoint at an unknown time in a normal linear multiple regression model with known variance. Optimal tests for multiple changepoints are also derived. It is shown that the results cover some models of cointegration. Power comparisons of several tests are provided based on simulations.

干扰参数仅在备择假设下存在时的最优检验AI 解读

This paper derives asymptotically optimal tests for testing problems in which a nuisance parameter exists under the alternative hypothesis but not under the null. For example, the results apply to tests of structural change with unknown changepoint. The testing problem considered is nonstandard and the classical asymptotic optimality results for the Lagrange multiplier, Wald, and likelihood ratio do not apply. A weighted average power criterion is used here to generate…

结合数据驱动模型选择的单位根后验赔率检验AI 解读

The Kalman filter is used to derive updating equations for the Bayesian data density in discrete time linear regression models with stochastic regressors. The implied “Bayes model” has time varying parameters and conditionally heterogeneous error variances. A σ-finite Bayes model measure is given and used to produce a new-model-selection criterion (PIC) and objective posterior odds tests for sharp null hypotheses like the presence of a unit root. This extends earlier work by…

使用普通最小二乘残差的 CUSUM 检验AI 解读

The authors show that the CUSUM test of the stability over time of the coefficients of a linear regression model, which is usually based on recursive residuals, can also be applied to ordinary least squares residuals. The authors derive the limiting null distribution of the resulting test and compare its local power to that of the standard procedure. It turns out that neither version is uniformly superior to the other. Copyright 1992 by The Econometric Society.

CUSUM 与平方 CUSUM 检验的局部功效AI 解读

We consider the local power of the cusum and cusum of squares tests for structural change in the linear regression model. We show that the local power of the cusum of squares test equals its size for a wide class of structural changes, as compared to a nontrivial local power for the cusum test. The conventional ranking of these procedures is thus reversed.

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.