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GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

有无单位根的 AR(1) 时间序列中的高斯推断

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform $\sqrt{n}$ rate of convergence. En route, a useful central limit theorem (CLT) for sample…

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LONG-RUN COVARIANCE MATRICES FOR FRACTIONALLY INTEGRATED PROCESSES

分数单整过程的长期协方差矩阵

An asymptotic expansion is given for the autocovariance matrix of a vector of stationary long-memory processes with memory parameters d ∈ [0,½). The theory is then applied to deliver formulas for the long-run covariance matrices of multivariate time series with long memory.Phillips acknowledges partial support from a Kelly Fellowship and from the NSF under grant SES 04-142254. This may be proved directly using a Fourier integral asymptotic expansion when the spectrum of the…

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REGRESSION WITH SLOWLY VARYING REGRESSORS AND NONLINEAR TRENDS

缓慢变化回归变量与非线性趋势回归

Slowly varying (SV) regressors arise commonly in empirical econometric work, particularly in the form of semilogarithmic regression and log periodogram regression. These regressors are asymptotically collinear. Usual regression formulas for asymptotic standard errors are shown to remain valid, but rates of convergence are affected and the limit distribution of the regression coefficients is shown to be one dimensional. Some asymptotic representations of partial sums of SV…

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A REMARK ON BIMODALITY AND WEAK INSTRUMENTATION IN STRUCTURAL EQUATION ESTIMATION

结构方程估计中双峰性与弱工具变量的一点说明

In a simple model composed of a structural equation and identity, the finite-sample distribution of the instrumental variable/limited information maximum likelihood (IV/LIML) estimator is always bimodal, and this is most apparent when the concentration parameter is small. Weak instrumentation is the energy that feeds the secondary mode, and the coefficient in the structural identity provides a point of compression in the density that gives rise to it. The IV limit…

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HAC ESTIMATION BY AUTOMATED REGRESSION

通过自动化回归进行 HAC 估计

A simple regression approach to HAC and LRV estimation is suggested. The method exploits the fact that the quantities of interest relate to only one point of the spectrum (the origin). The new estimator is simply the explained sum of squares in a linear regression whose regressors are a set of trend basis functions. Positive definiteness in the estimate is therefore automatically enforced, and the technique can be implemented with standard regression packages. No kernel…

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AUTOMATED DISCOVERY IN ECONOMETRICS

计量经济学中的自动发现

Our subject is the notion of automated discovery in econometrics. Advances in computer power, electronic communication, and data collection processes have all changed the way econometrics is conducted. These advances have helped to elevate the status of empirical research within the economics profession in recent years, and they now open up new possibilities for empirical econometric practice. Of particular significance is the ability to build econometric models in an…

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NOTES AND PROBLEMS: A new format for the PROBLEMS AND SOLUTIONS SERIES

“札记与问题”:问题与解答系列的新形式

In establishing the Problems and Solutions (P&S) series of Econometric Theory , the primary objective was pedagogical—to provide an intellectual resource for students, instructors, and researchers through the publication of student exercises and research-level problems in econometrics. Over the past 20 years, the P&S series has successfully served this goal. Large numbers of worked exercises and problems have now been published, and the series has promoted interaction…

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EXPANSIONS FOR THE DISTRIBUTION OF THE MAXIMUM LIKELIHOOD ESTIMATOR OF THE FRACTIONAL DIFFERENCE PARAMETER

分数差分参数极大似然估计量的分布展开

The maximum likelihood estimator (MLE) of the fractional difference parameter in the Gaussian ARFIMA(0,d,0) model is well known to be asymptotically N(0,6/π2). This paper develops asymptotic expansions to the distribution of this statistic under the assumption of a known unit variance. The correction term for the density is shown to be independent of d, so that the MLE is second-order pivotal for d. This feature of the MLE is unusual, at least in time series contexts.…

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VISION AND INFLUENCE IN ECONOMETRICS: JOHN DENIS SARGAN

计量经济学的远见与影响:约翰·丹尼斯·萨根

Denis Sargan's intellectual influence in econometrics is discussed and some of his visions for the future of econometrics are considered in this memorial article. One of Sargan's favorite topics in econometric theory was finite sample theory, including both exact theory and various types of asymptotic expansions. We provide some summary discussion of asymptotic expansions of the type that Sargan developed in this field and give explicit representations of Sargan's formula…

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