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具有 GARCH(1,1) 误差的单位根过程渐近推断AI 解读

This paper investigates the so-called one-step local quasi–maximum likelihood estimator for the unit root process with GARCH(1,1) errors. When the scaled conditional errors (the ratio of the disturbance to the conditional standard deviation) follow a symmetric distribution, the asymptotic distribution of the estimated unit root is derived only under the second-order moment condition. It is shown that this distribution is a functional of a bivariate Brownian motion as in Ling…

对 Neuberg《因果性》书评的评论AI 解读

I am grateful to Professor Neuberg for taking the time to study my book Causality and for summarizing its main ideas in a language familiar to readers of Econometric Theory . I will comment on several issues that I believe warrant further discussion. First, I will summarize in my own style what economists can learn from Causality , and, second, I will correct several inaccuracies in the summary of Professor Neuberg.

书评：詹姆斯·戴维森《计量经济学理论》AI 解读

Professor Davidson's Econometric Theory offers a clear, well written, graduate level econometrics textbook, which would be highly appropriate as the principal text for the second and/or third semester of a general Ph.D. econometrics sequence or for a specialized course on time series. It provides good reading material for anyone interested in deepening his or her understanding of econometrics and also a valuable reference source for econometricians. Although the book reviews…

分段协整的推断AI 解读

A cointegration relation is often interpreted as a long-run equilibrium relation whereas short-run deviations are allowed to a certain extent. In practice, however, real data often fail to confirm cointegration for a well understood economic relation. This paper proposes that in many cases failure of confirming cointegration is due to nonstationary deviations in a relatively small portion of the data period (“short-run”) whereas a cointegration relation prevails in the other…

界限置信区域的构造AI 解读

We modify the procedure for constructing exact bounds confidence regions introduced by Dufour (1990, Econometrica 58, 475–494) so as to drop the requirement that the confidence regions for the nuisance parameters are marginal with respect to the parameters of interest, i.e., that they are the same for all values of the parameters of interest. We illustrate this modified procedure with an application to a dependent variable heteroskedasticity model and, using a Monte Carlo…

GARCH(1,1) 序列最大矩指数的估计AI 解读

We propose an estimator for the maximal moment exponent of a GARCH(1,1) sequence. We establish its consistency asymptotic normality with rate n−1/2. Finite sample properties are investigated by means of a small simulation study.The research for this paper was partially supported by NSF grant INT-0223262. István Berkes and Lajos Horváth were supported by the Hungarian National Foundation for Scientific Research, grant T 29621. Piotr Kokoszka and Lajos Horváth were supported…

GARCH 平方残差相关性的渐近理论AI 解读

We develop an asymptotic theory for quadratic forms of the autocorrelations of squared residuals from a GARCH(p,q) model. Denoting by , k ≥ 1, these autocorrelations computed from a realization of length n, we show that the statistic is a matrix computed from the data, converges to the chi-square distribution with K degrees of freedom for any 1 ≤ i1 < ··· < iK. Our results are valid under weak assumptions on the innovations and model coefficients that admit that arbitrary…

计量经济学的远见与影响：约翰·丹尼斯·萨根AI 解读

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…

丹尼斯·萨根：若干历史视角AI 解读

I attempt to present Denis Sargan's work in some kind of historical perspective, in two ways. First, I discuss some previous members of the Tooke Chair of Economic Science and Statistics, which was founded in 1859 and which Sargan held. Second, I discuss one of his articles, “Asymptotic Theory and Large Models,” in relation to modern preoccupations with semiparametric econometrics.This research was supported by a Leverhulme Trust Personal Research Professorship and ESRC…

丹尼斯·萨根与 LSE 计量经济学方法论的起源AI 解读

I review the part played by John Denis Sargan in the formation of the “LSE approach” to dynamic econometric modeling. Despite his unassuming demeanor and his location at LSE—which had earlier dismissed a substantive role for econometric evidence—Sargan nevertheless radically altered the econometric approach of a generation, establishing a powerful approach to empirical modeling of economic time series. His main contributions to econometric methodology, and the subsequent…

LSE 近三十年计量经济学的发展AI 解读

I was very pleased to be invited to the Universidad Carlos III as visiting professor, to meet all my old Spanish friends again, and to have the opportunity to give this public lecture. My address will have two themes: a brief review of the history and current status of the London School of Economics, and then a discussion of the strong tradition which has developed there of the study of mathematical methods in the social sciences, particularly in economics, by building…

计量经济学的当前问题：一场个人观点演讲AI 解读

Forty-five years ago when I started to study econometrics seriously I was full of confidence that the application of mathematics and statistical methodology would soon lead to a better understanding of the economic system, and, ultimately, to better public and private policies. Now, with the world economy poised on the edge of a world slump and Eastern Europe and the undeveloped world in turmoil my general hope seems optimistic. Even within econometrics, experience proves…

ARMA representation of squared Markov switching heteroskedastic models—solution.

Fixed effects estimation of the population-averaged slopes in a panel data random coefficient model.

单位根检验的功效函数与功效包络AI 解读

This paper studies power functions and envelopes for covariate augmented unit root tests. The power functions are calculated by integrating the characteristic function, allowing accurate evaluation of the power envelope and the power functions. Using the power functions, we study the selection among point optimal invariant unit root tests. An “optimal” point optimal test is proposed based on minimizing the integrated power difference. We find that when there are covariate…

《金融计量经济学》书评：Gourieroux与Jasiak著AI 解读

Over the past decade financial econometrics has evolved from a small subfield of econometrics to a rapidly growing area of research that maintains its own journals and dominates the applied time series sessions in many major conferences. Financial econometrics is a conglomerate of statistical models and techniques to summarize regular features of financial data sets and to evaluate theoretical models and hypotheses that have been set forth by financial economists. Besides…

若干季节单位根检验的渐近性质AI 解读

This paper analyzes the large sample behavior of the seasonal unit root tests of Dickey, Hasza, and Fuller (1984, Journal of the American Statistical Association 79, 355–367) when applied to a series that admits a unit root at the zero but not seasonal spectral frequencies. We show that in such cases the Dickey et al. statistics have nondegenerate limiting distributions. Consequently, there is a nonzero probability that, taken in isolation, they will lead the applied…

方差比检验的渐近功效AI 解读

The variance-ratio (VR) test statistic, which is based on k -period differences of the data, is commonly used in empirical finance and economics to test the random walk hypothesis. We obtain the asymptotic power function of the VR test statistic when the differencing period k is increasing with the sample size n such that k / n → δ > 0. We show that the test is inconsistent against a variety of mean-reverting alternatives, confirm the result in simulations, and then…

向量 ARMA-GARCH 模型的渐近理论AI 解读

This paper investigates the asymptotic theory for a vector autoregressive moving average–generalized autoregressive conditional heteroskedasticity (ARMA-GARCH) model. The conditions for the strict stationarity, the ergodicity, and the higher order moments of the model are established. Consistency of the quasi-maximum-likelihood estimator (QMLE) is proved under only the second-order moment condition. This consistency result is new, even for the univariate autoregressive…

检测 GMM 中的识别不足AI 解读

This paper proposes a test of the null of underidentification in the nonlinear-in-parameters generalized method of moments model. It can be thought of as a nonlinear analog of the usual linear instrumental variables first-stage F-test. It can be used as a diagnostic to warn a researcher when conventional asymptotic theory is unlikely to work well.I am grateful to Don Andrews, Jon Faust, John Fernald, Jim Stock, and two anonymous referees for their helpful comments on earlier…

自回归过程中的多步预测AI 解读

In this paper, two competing types of multistep predictors, i.e., plug-in and direct predictors, are considered in autoregressive (AR) processes. When a working model AR(k) is used for the h-step prediction with h > 1, the plug-in predictor is obtained from repeatedly using the fitted (by least squares) AR(k) model with an unknown future value replaced by their own forecasts, and the direct predictor is obtained by estimating the h-step prediction model's coefficients…

02.1.2 特定对称幂等矩阵问题：解答AI 解读

It is easy to see that Problem 02.1.2 holds more generally in that the result is valid for B Hermitian complex (rather than “symmetric real”), for m = 0,1,…, q (rather than just for “ m < q ”), for r ≠ 0 (rather than just for “integer r > 1”), and for tr( B k ) = tr( C k ), k = 1,2,3,4 (rather than for “ k = 1,2,…”), as shown by Shanbhag (1970).

Consider the following stationary time series regression.

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

Louis (1982) presents a method for computing the observed information matrix and standard errors of maximum likelihood estimates obtained via the EM algorithm based on the complete-data log likelihood function. The problem illustrates the well-known method of Louis (1982) for a widely used qualitative response model in econometrics. The observed-data log likelihood function for the following model can, of course, be easily differentiated to obtain the observed information…