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工具变量回归中条件似然比检验的精确性质AI 解读

For a simplified structural equation/IV regression model with one right-side endogenous variable, we derive the exact conditional distribution function of Moreira's (2003) conditional likelihood ratio (CLR) test statistic. This is used to obtain the critical value function needed to implement the CLR test, and reasonably comprehensive graphical versions of this function are provided for practical use. The analogous functions are also obtained for the case of testing more…

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Rex Bergstrom 对连续时间宏观计量建模的贡献AI 解读

This paper reviews the contributions of Rex Bergstrom to the development of continuous time dynamic disequilibrium macroeconomic modeling since the early 1960s. The models provide an elegant integration of economic theory with analysis of steady state and stability properties. The subsequent contributions of his Ph.D. students, spawned by Bergstrom’s work over the years, is also reviewed. It was Bergstrom’s early pioneering vision 40 years ago of formulating and estimating…

含截距与趋势的稳定 AR(1) 模型中的 Bartlett 修正AI 解读

Bartlett corrections are derived for testing hypotheses about the autoregressive parameter ρ in the stable (a) AR(1) model, (b) AR(1) model with intercept, (c) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of ρ . In the models with deterministic terms, the correction factor is asymmetric in ρ . Furthermore, the Bartlett correction is monotonically increasing in ρ and tends to infinity when ρ approaches the stability boundary of…

持续期记忆参数向计数与已实现波动率传递的条件AI 解读

We establish sufficient conditions on durations that are stationary with finite variance and memory parameter $d \in [0,{\textstyle{1 \over 2}})$ to ensure that the corresponding counting process N ( t ) satisfies Var N ( t ) ~ Ct 2 d +1 ( C > 0) as t → ∞, with the same memory parameter $d \in [0,{\textstyle{1 \over 2}})$ that was assumed for the durations. Thus, these conditions ensure that the memory parameter in durations propagates to the same memory parameter in the…

线性过程加权和的中心极限定理：Lp 可逼近性与布朗运动方法AI 解读

Standardized slowly varying regressors are shown to be L p -approximable. This fact allows us to provide alternative proofs of asymptotic expansions of nonstochastic quantities and central limit results due to P.C.B. Phillips, under a less stringent assumption on linear processes. The recourse to stochastic calculus related to Brownian motion can be completely dispensed with.

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逆条件密度加权函数的半参数估计效率界AI 解读

Consider the unconditional moment restriction E[ m ( y , υ , w ; π 0 )/ f V | w ( υ | w ) − s ( w ; π 0 )] = 0, where m (·) and s (·) are known vector-valued functions of data ( y ┬ , υ , w ┬ ) ┬ . The smallest asymptotic variance that $\root \of n $ -consistent regular estimators of π 0 can have is calculated when f V | w (·) is only known to be a bounded, continuous, nonzero conditional density function. Our results show that “plug-in” kernel-based estimators of π 0…

高阶马尔可夫过程的 Copula 刻画AI 解读

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibit m -dependence, r -independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with…

工具变量回归中可容许的不变相似检验AI 解读

This paper studies a model widely used in the weak instruments literature and establishes admissibility of the weighted average power likelihood ratio tests recently derived by Andrews, Moreira, and Stock (2004, NBER Technical Working Paper 199). The class of tests covered by this admissibility result contains the Anderson and Rubin (1949, Annals of Mathematical Statistics 20, 46–63) test. Thus, there is no conventional statistical sense in which the Anderson and Rubin…

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横截面与时间维度均大时面板 AR(p) 模型的简便有效工具变量估计AI 解读

In this paper, we show that for panel AR( p ) models, an instrumental variable (IV) estimator with instruments deviated from past means has the same asymptotic distribution as the infeasible optimal IV estimator when both N and T , the dimensions of the cross section and time series, are large. If we assume that the errors are normally distributed, the asymptotic variance of the proposed IV estimator is shown to attain the lower bound when both N and T are large. A…

相依异质过程向随机幂积分的收敛AI 解读

Building on work of Hansen (1992, Econometric Theory 8, 489–501), we show weak convergence for power transformations of integrated processes, with possibly serially correlated and heterogeneously distributed increments, to stochastic power integrals. The theory is applicable when testing the unit root or cointegration hypothesis in nonlinear systems by regression-based test statistics.

工具变量数量较大时的最优不变推断AI 解读

This paper studies the asymptotic behavior of a Gaussian linear instrumental variables model in which the number of instruments diverges with the sample size. Asymptotic efficiency bounds are obtained for rotation invariant inference procedures and are shown to be attainable by procedures based on the limited information maximum likelihood estimator. The bounds are obtained by characterizing the limiting experiment associated with the model induced by the rotation invariance…

局部时密度估计与非参数协整回归的渐近理论AI 解读

Asymptotic theory is developed for local time density estimation for a general class of functionals of integrated and fractionally integrated time series. The main result provides a convenient basis for developing a limit theory for nonparametric cointegrating regression and nonstationary autoregression. The treatment directly involves local time estimation and the density function of the processes under consideration, providing an alternative approach to the Markov chain…

矩不等式参数的子抽样与代入式渐近推断有效性AI 解读

This paper considers inference for parameters defined by moment inequalities and equalities. The parameters need not be identified. For a specified class of test statistics, this paper establishes the uniform asymptotic validity of subsampling, m out of n bootstrap, and “plug-in asymptotic” tests and confidence intervals for such parameters. Establishing uniform asymptotic validity is crucial in moment inequality problems because the pointwise asymptotic distributions of the…

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实际单位根检验：应对趋势与初始条件的不确定性AI 解读

In this paper we focus on two major issues that surround testing for a unit root in practice, namely, (i) uncertainty as to whether or not a linear deterministic trend is present in the data and (ii) uncertainty as to whether the initial condition of the process is (asymptotically) negligible or not. In each case simple testing procedures are proposed with the aim of maintaining good power properties across such uncertainties. For the first issue, if the initial condition is…

半强 GARCH 模型的拟最大似然估计AI 解读

This note proves the consistency and asymptotic normality of the quasi–maximum likelihood estimator (QMLE) of the parameters of a generalized autoregressive conditional heteroskedastic (GARCH) model with martingale difference centered squared innovations. The results are obtained under mild conditions and generalize and improve those in Lee and Hansen (1994, Econometric Theory 10, 29–52) for the local QMLE in semistrong GARCH(1,1) models. In particular, no restrictions on…

GARCH 模型参数设定误检验的一阶渐近理论AI 解读

This paper develops a framework for the construction and analysis of parametric misspecification tests for generalized autoregressive conditional heteroskedastic (GARCH) models, based on first-order asymptotic theory. The principal finding is that estimation effects from the correct specification of the conditional mean (regression) function can be asymptotically nonnegligible. This implies that certain procedures, such as the asymmetry tests of Engle and Ng (1993, Journal…

含某些多频 I(1) 回归变量时 OLS 估计误差的几乎必然界AI 解读

Lai and Wei (1983, Annals of Statistics 10, 154–166) state in their Theorem 1 that the estimators of the regression coefficients in the regression $y_t = x_t^' \beta + \varepsilon _{\rm{t}} $ , t ∈ ℕ are almost surely (a.s.) consistent under the assumption that the minimum eigenvalue λ min ( T ) of $\sum\nolimits_{t = 1}^T {x_t } x'_t $ tends to infinity (a.s.) and log( λ max ( T ))/ λ min ( T ) → 0 (a.s.) where λ max ( T ) denotes the maximal eigenvalue.…