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Asymptotic Normality of the QMLE Estimator of ARCH in the Nonstationary Case

We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the linear ARCH model. Contrary to the existing literature, we allow the parameters to be in the region where no stationary version of the process exists. This implies that the estimator is always asymptotically normal.

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GMM Estimation of Autoregressive Roots Near Unity with Panel Data

This paper investigates a generalized method of moments (GMM) approach to the estimation of autoregressive roots near unity with panel data and incidental deterministic trends. Such models arise in empirical econometric studies of firm size and in dynamic panel data modeling with weak instruments. The two moment conditions in the GMM approach are obtained by constructing bias corrections to the score functions under OLS and GLS detrending, respectively. It is shown that the…

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More powerful panel data unit root tests with an application to mean reversion in real exchange rates

更高功效的面板单位根检验及其实际汇率均值回复应用

Abstract Unit root tests, seeking mean or trend reversion, are frequently applied to panel data. We show that more powerful variants of commonly applied tests are readily available. Moreover, power gains persist when the modifications are applied to bootstrap procedures that may be employed when cross‐correlation of a rather general sort among individual panel members is suspected. Copyright © 2004 John Wiley & Sons, Ltd.

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Power Transformations to Induce Normality and their Applications

改善正态近似的幂变换及其应用

Summary Random variables which are positive linear combinations of positive independent random variables can have heavily right-skewed finite sample distributions even though they might be asymptotically normally distributed. We provide a simple method of determining an appropriate power transformation to improve the normal approximation in small samples. Our method contains the Wilson–Hilferty cube root transformation for χ2 random variables as a special case. We also…

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Estimation and Testing Stationarity for Double-Autoregressive Models

双重自回归模型的估计与平稳性检验

Summary The paper considers the double-autoregressive model yt = φyt−1+ɛt with ɛt =ηt√(ω+αyt−12). Consistency and asymptotic normality of the estimated parameters are proved under the condition E ln |φ +√αηt|<0, which includes the cases with |φ|=1 or |φ|>1 as well as E(εt2)=∞. It is well known that all kinds of estimators of φ in these cases are not normal when ɛt are independent and identically distributed. Our result is novel and surprising. Two tests are proposed for…

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A generalized EWMA control chart and its comparison with the optimal EWMA, CUSUM and GLR schemes

广义 EWMA 控制图及其与 EWMA、CUSUM、GLR 的比较

It is known that both the optimal exponentially weighted moving average (EWMA) and cumulative sum (CUSUM) control charts are based on a given reference value $\delta$, which, for the CUSUM chart, is the magnitude of a shift in the mean to be detected quickly. In this paper a generalized EWMA control chart (GEWMA) which does not depend on $\delta$ is proposed for detecting the mean shift. We compare theoretically the GEWMA control chart with the optimal EWMA, CUSUM and the…

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Estimation of Educational Borrowing Constraints Using Returns to Schooling

利用教育回报估计教育借贷约束

This paper measures the importance of borrowing constraints on education decisions. Empirical identification of borrowing constraints is secured by the economic prediction that opportunity costs and direct costs of schooling affect borrowing-constrained and unconstrained persons differently. Direct costs need to be financed during school and impose a larger burden on credit-constrained students. By contrast, gross forgone earnings do not have to be financed. We explore the…

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03.1.2. 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

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.

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COMBINING FORECASTING PROCEDURES: SOME THEORETICAL RESULTS

预测方法组合的若干理论结果

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…

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THE DIFFUSION LIMIT OF A TVP-GQARCH-M(1,1) MODEL

TVP-GQARCH-M(1,1) 模型的扩散极限

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…

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STATIONARITY AND MEMORY OF ARCH([infty infinity]) MODELS

ARCH(∞) 模型的平稳性与记忆

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…

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ON TESTS FOR DOUBLE DIFFERENCING: METHODS OF DEMEANING AND DETRENDING AND THE ROLE OF INITIAL VALUES

二次差分检验:去均值、去趋势方法与初始值的作用

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,…

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STATIONARITY TESTING WITH COVARIATES

利用协变量的平稳性检验

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…

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OPTIMAL VERSUS ROBUST INFERENCE IN NEARLY INTEGRATED NON-GAUSSIAN MODELS

近积分非高斯模型中的最优推断与稳健推断

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…

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NONLINEAR FUNCTIONS AND CONVERGENCE TO BROWNIAN MOTION: BEYOND THE CONTINUOUS MAPPING THEOREM

非线性函数与布朗运动收敛:超越连续映射定理

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,…

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EFFICIENT LIKELIHOOD INFERENCE IN NONSTATIONARY UNIVARIATE MODELS

非平稳单变量模型中的有效似然推断

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…

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Income Variance Dynamics and Heterogeneity

收入方差动态与异质性

Recent theoretical work has shown the importance of measuring microeconomic uncertainty for models of both general and partial equilibrium under imperfect insurance. In this paper the assumption of i.i.d. income innovations used in previous empirical studies is removed and the focus of the analysis is placed on models for the conditional variance of income shocks, which is related to the measure of risk emphasized by the theory. We first discriminate amongst various models…

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