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Redundancy of lagged regressors in a conditionally heteroskedastic time series regression—solution.

03.1.2 条件异方差时间序列回归中滞后解释变量的冗余性：解答AI 解读

Redundancy of lagged regressors in a conditionally heteroskedastic time series regressionAn excellent solution has been independently proposed by the S. Anatolyev, the poser of the problem.—solution.

03.1.1 利用完全数据似然推导有序 Probit 与 Logit 观测信息矩阵：解答AI 解读

Deriving the observed information matrix in ordered probit and logit models using the complete-data likelihood function—solution.

Correcting for heteroskedasticity of unspecified form.

04.1.1 基于固定效应与误差成分两阶段最小二乘差异的 Hausman 检验AI 解读

A Hausman test based on the difference between fixed effects two-stage least squares and error components two-stage least squares.

预测方法组合的若干理论结果AI 解读

We study some methods of combining procedures for forecasting a continuous random variable. Statistical risk bounds under the square error loss are obtained under distributional assumptions on the future given the current outside information and the past observations. The risk bounds show that the combined forecast automatically achieves the best performance among the candidate procedures up to a constant factor and an additive penalty term. In terms of the rate of…

TVP-GQARCH-M(1,1) 模型的扩散极限AI 解读

This paper presents results on the issue of weak convergence of a TVP-GQARCH-M(1,1) process. These suggest that the weak limit of this endogenous volatility model is an exogenous (stochastic) volatility continuous time process. Under the appropriate assumptions, we derive the invariant distributions at which the process converges in various cases. They reveal an approximate distributional relation between the GARCH or the asymmetric GQARCH variance processes and the…

ARCH(∞) 模型的平稳性与记忆AI 解读

We establish the necessary and sufficient conditions for covariance stationarity of ARCH(∞), for both the levels and the squares. The result applies to any form of the conditional variance coefficients. This includes GARCH(p,q) and also specifications with hyperbolically decaying coefficients, such as the autoregressive coefficients of the autoregressive fractionally integrated moving average model. The covariance stationarity condition for the levels rules out long memory…

二次差分检验：去均值、去趋势方法与初始值的作用AI 解读

In this paper we investigate the impact that starting values have upon the double differencing tests of Hasza and Fuller (1979, Annals of Statistics 7, 1106–1120) and Sen and Dickey (1987, Journal of Business and Economic Statistics 5, 463–473), based on ordinary least squares (OLS) and simple symmetric least squares (SSLS) estimation, respectively. We demonstrate that, contrary to what is observed for conventional unit root tests, when based on data that have been demeaned,…

利用协变量的平稳性检验AI 解读

Two new stationarity tests are proposed. Both tests can be viewed as generalizations of existing stationarity tests and dominate these in terms of local asymptotic power. Improvements are achieved by accommodating stationary covariates. A Monte Carlo investigation of the small sample properties of the tests is conducted, and an empirical illustration from international finance is provided.This paper has benefited from the comments of Pentti Saikkonen (the co-editor), two…

近积分非高斯模型中的最优推断与稳健推断AI 解读

Elliott, Rothenberg, and Stock (1996, Econometrica 64, 813–836) derive a class of point-optimal unit root tests in a time series model with Gaussian errors. Other authors have proposed “robust” tests that are not optimal for any model but perform well when the error distribution has thick tails. I derive a class of point-optimal tests for models with non-Gaussian errors. When the true error distribution is known and has thick tails, the point-optimal tests are generally more…

非线性函数与布朗运动收敛：超越连续映射定理AI 解读

Weak convergence results for sample averages of nonlinear functions of (discrete-time) stochastic processes satisfying a functional central limit theorem (e.g., integrated processes) are given. These results substantially extend recent work by Park and Phillips (1999, Econometric Theory 15, 269–298) and de Jong (2002, working paper), in that a much wider class of functions is covered. For example, some of the results hold for the class of all locally integrable functions,…

非平稳单变量模型中的有效似然推断AI 解读

Recent literature shows that embedding fractionally integrated time series models with spectral poles at the long-run and/or seasonal frequencies in autoregressive frameworks leads to estimators and test statistics with nonstandard limiting distributions. However, we demonstrate that when embedding such models in a general I(d) framework the resulting estimators and tests regain desirable properties from standard statistical analysis. We show the existence of a local time…

Autoregression and redundant instruments—solution.

02.6.1. Oblique projectors—solution.

Unbiasedness of the OLS estimator with random regressors.

The central limit theorem for student's distribution.

问题 02.6.1：斜投影算子——解答AI 解读

02.6.1. Oblique projectorsTwo solutions are published, proposed independently by Götz Trinkler (the poser of the problem) and by Hans Joachim Werner. Excellent solutions have been independently proposed by G. Dhaene, L. Lauwers, S. Lawford, and H. Neudecker.—solution.

贝塞尔过程分布的临界值与 p 值：计算及结构突变检验应用AI 解读

The p values of structural break tests, when the break date or dates are unknown, must be calculated in terms of the probability distributions of functions of Bessel processes. The literature so far has maintained that direct computation of these p values and of the corresponding critical values is too difficult and has relied on approximations based on simulations, asymptotic expansions, or curve fitting. This paper presents a fast simple method of calculating exact p…

集合 VC 类的一个等价性结果AI 解读

Let and Θ be infinite sets and let × Θ. We show that the class of projections of A onto is a Vapnik–Chervonenkis ( VC ) class of sets if and only if the class of projections of A onto Θ is a VC class. We illustrate the result in the context of semiparametric estimation of a transformation model. In this application, the VC property is hard to establish for the projection class of interest but easy to establish for the other projection class.

非线性时间序列模型充分性的诊断检验AI 解读

We propose a new diagnostic test for linear and nonlinear time series models, using a generalized spectral approach. Under a wide class of time series models that includes autoregressive conditional heteroskedasticity (ARCH) and autoregressive conditional duration (ACD) models, the proposed test enjoys the appealing “nuisance-parameter-free” property in the sense that model parameter estimation uncertainty has no impact on the limit distribution of the test statistic. It is…

异方差样本选择模型的半参数估计AI 解读

This paper considers estimation of a sample selection model subject to conditional heteroskedasticity in both the selection and outcome equations. The form of heteroskedasticity allowed for in each equation is multiplicative, and each of the two scale functions is left unspecified. A three-step estimator for the parameters of interest in the outcome equation is proposed. The first two stages involve nonparametric estimation of the “propensity score” and the conditional…

因变量可能受限的可分模型半参数估计AI 解读

In this paper we introduce a general method for estimating semiparametrically the different components in separable models. The family of separable models is quite popular in economic research because this structure offers clear interpretation, has straightforward economic consequences, and is often justified by theory. This family is also of statistical interest because it allows us to estimate high-dimensional complexity semiparametrically without running into the curse of…

平稳过程谱参数最小对比估计量的高阶渐近理论AI 解读

Let g(λ) be the spectral density of a stationary process and let fθ(λ), θ ∈ Θ, be a fitted spectral model for g(λ). A minimum contrast estimator of θ is defined that minimizes a distance between , where is a nonparametric spectral density estimator based on n observations. It is known that is asymptotically Gaussian efficient if g(λ) = fθ(λ). Because there are infinitely many candidates for the distance function , this paper discusses higher order asymptotic theory for in…