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THE ASYMPTOTIC EFFICIENCY OF COINTEGRATION ESTIMATORS UNDER TEMPORAL AGGREGATION

时间聚合下协整估计量的渐近效率

This paper examines the effects of temporal aggregation on the asymptotic variances of estimators in cointegrated systems. Two important findings are obtained. First, estimators based on flow data alone are more efficient than when the data are all stocks or a mixture of stocks and flows. Second, estimators based on flow data are as efficient as when the data are recorded continuously. A method of improving efficiency with stock variables is also proposed, and an empirical…

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A NOTE ON THE POWER OF BOOTSTRAP UNIT ROOT TESTS

关于自助法单位根检验功效的说明

In this note we consider the asymptotic power functions of some bootstrap unit root tests under local alternatives and show that they are in fact the same as for ordinary unit root tests. This is regardless of whether the differences of the observations, i.e., the so-called restricted residuals, or the ordinary least squares residuals are used to construct the resampled observations. We also consider models containing a constant and a linear trend and the DF-GLS tests…

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Fully Nonparametric Estimation of Scalar Diffusion Models

标量扩散模型的完全非参数估计

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other function is considered a nuisance parameter. The asymptotic behavior of the estimators is examined as the observation frequency increases and as the time span lengthens. We prove almost…

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Inferential Theory for Factor Models of Large Dimensions

高维因子模型的推断理论

This paper develops an inferential theory for factor models of large dimensions. The principal components estimator is considered because it is easy to compute and is asymptotically equivalent to the maximum likelihood estimator (if normality is assumed). We derive the rate of convergence and the limiting distributions of the estimated factors, factor loadings, and common components. The theory is developed within the framework of large cross sections ("N") and a large time…

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Business Cycle Asymmetries

商业周期的不对称性

Tests for business cycle asymmetries are developed for Markov-switching autoregressive models. The tests of deepness, steepness, and sharpness are Wald statistics, which have standard asymptotics. For the standard two-regime model of expansions and contractions, deepness is shown to imply sharpness (and vice versa), whereas the process is always nonsteep. Two and three-state models of U.S. GNP growth are used to illustrate the approach, along with models of U.S. investment…

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Testing for Nonlinear Autoregression

非线性自回归检验

conditional mean of an economic time series is linear in past values. Two specific tests are discussed, the Cramer-von Mises and the Kolmogorov-Smirnov tests. The particular feature of the proposed tests is that the bootstrap is used to estimate the nonstandard asymptotic distributions of the test statistics considered. The tests are justified theoretically by asymptotics, and their finite-sample behaviors are studied by means of Monte Carlo experiments. The tests are…

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Tests of Rank in Reduced Rank Regression Models

降秩回归模型中的秩检验

There has recently been renewed research interest in the development of tests of the rank of a matrix. This article evaluates the performance of some asymptotic tests of rank determination in reduced rank regression models together with bootstrapped versions through simulation experiments. The bootstrapped procedures significantly improve on the performance of the corresponding asymptotic tests. The article also presents a Monte Carlo exercise comparing the forecasting…

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Indirect Inference, Nuisance Parameter, and Threshold Moving Average Models

间接推断、干扰参数与门限移动平均模型

nuisance parameter is not identified under the null hypothesis. We develop a testing procedure adapted to this simulation-based estimation method, and detail its use for detecting the threshold effect in threshold moving average models with contemporaneous and lagged asymmetries. In contrast to existing threshold models, these models allow taking into account the presence of asymmetric effects of current and lagged random shocks. We use them to measure the persistence of…

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Time-Varying Smooth Transition Autoregressive Models

时变平滑转换自回归模型

perceived as competing alternatives to linearity. In this article we study the so-called time-varying smooth transition autoregressive (TV-STAR) model, which can be used both for describing simultaneous nonlinearity and structural change and for distinguishing between these features. Two modeling strategies for empirical specification of TV-STAR models are developed. Monte Carlo simulations show that neither of the two strategies dominates the other. A…

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Bayesian Analysis of Endogenous Delay Threshold Models

内生延迟门限模型的贝叶斯分析

autoregressive models: endogenous delay threshold. We apply our methods to the commonly used sunspot data set and find strong evidence in favor of the Endogenous Delay Threshold Autoregressive (EDTAR) model over linear and traditional threshold autoregressions.

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Valid Bayesian Estimation of the Cointegrating Error Correction Model

协整误差修正模型的有效贝叶斯估计

linear restrictions and the nonlinear method of Johansen's maximum likelihood procedure. That the linear method can produce invalid estimates while the Johansen approach always produces valid estimates has been recognized in several recent articles. Because all Bayesian studies to date have used linear restrictions, this article presents a Bayesian method for obtaining estimates of cointegrating vectors that will always be valid. In addition, it also presents an approach for…

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On Unit-Root Tests When the Alternative Is a Trend-Break Stationary Process

备择为趋势突变平稳过程时的单位根检验

of break under the alternative evolves according to the crash, changing growth, and mixed models. It is shown that serious power distortions occur if the form of break is misspecified, and thus the practitioner should use the mixed model as the appropriate alternative in empirical applications. The mixed model may reveal useful information regarding the location and form of break. The maximum F statistic for the joint null of a unit-root and no breaks is shown to have…

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A simple framework for analysing bull and bear markets

分析牛市与熊市的简明框架

Abstract Bull and bear markets are a common way of describing cycles in equity prices. To fully describe such cycles one would need to know the data generating process (DGP) for equity prices. We begin with a definition of bull and bear markets and use an algorithm based on it to sort a given time series of equity prices into periods that can be designated as bull and bear markets. The rule to do this is then studied analytically and it is shown that bull and bear market…

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Computation and analysis of multiple structural change models

多重结构变化模型的计算与分析

Abstract In a recent paper, Bai and Perron ( 1998 ) considered theoretical issues related to the limiting distribution of estimators and test statistics in the linear model with multiple structural changes. In this companion paper, we consider practical issues for the empirical applications of the procedures. We first address the problem of estimation of the break dates and present an efficient algorithm to obtain global minimizers of the sum of squared residuals. This…

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John W. Tukey's work on time series and spectrum analysis

约翰·W.图基在时间序列与谱分析方面的工作

The contributions of John W. Tukey to time series analysis, particularly spectrum analysis, are reviewed and discussed. The contributions include: methods, their properties, terminology, popularization, philosophy, applications and education. Much of Tukey's early work on spectrum analysis remained unpublished for many years, but the 1959 book by Blackman and Tukey made his approach accessible to a wide audience. In 1965 the Cooley-Tukey paper on the Fast Fourier Transform…

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An optimal test against a random walk component in a non‐orthogonal unobserved components model

非正交不可观测成分模型中针对随机游走成分的最优检验

In this paper we consider the problem of testing the null hypothesis that a series has a constant level (possibly as part of a more general deterministic mean) against the alternative that the level follows a random walk. This problem has previously been studied by, inter alia, Nyblom and Makelainen (1983) in the context of the orthogonal Gaussian random walk plus noise model. This model postulates that the noise component and the innovations to the random walk are…

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Residual‐based diagnostics for conditional heteroscedasticity models

条件异方差模型的残差诊断

We examine the residual-based diagnostics for univariate and multivariate conditional heteroscedasticity models. The tests are based on the parameter estimates of an autoregression with the squared standardized residuals or the cross products of the standardized residuals as dependent variables. As the regression involves estimated regressors the standard distribution theories of the ordinary least squares estimates do not apply. We provide the asymptotic variance of the…

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Moments and dynamic structure of a time‐varying parameter stochastic volatility in mean model

时变参数随机波动率均值模型的矩与动态结构

This paper introduces and discusses some of the statistical properties of a time-varying parameter stochastic volatility (SV) in mean model. We derive the autocovariance function of an observed series, under the assumption that the conditional variance follows a flexible parameterization, which nests the autoregressive SV and the exponential GARCH specifications. Furthermore, the mean parameter can be time varying. We also present the autocovariance functions of higher…

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Bounds for inference with nuisance parameters present only under the alternative

仅在备择假设下存在干扰参数时的推断界

In hypothesis testing with nuisance parameters present only under the alternative two issues typically arise: (i) critical values are data dependent and so cannot be tabulated; (ii) we need to choose a functional over the nuisance parameter space. We address the first issue by providing easily computable bounds for the case of dependent and heterogeneous observations. We tackle the second issue by suggesting a weighted average statistic with weights given by the (quasi)…

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