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A class of simple distribution-free rank-based unit root tests

一类简单的分布无关秩单位根检验

We propose a class of distribution-free rank-based tests for the null hypothesis of a unit root. This class is indexed by the choice of a reference density g, which need not coincide with the unknown actual innovation density f. The validity of these tests, in terms of exact finite-sample size, is guaranteed, irrespective of the actual underlying density, by distribution-freeness. Those tests are locally and asymptotically optimal under a particular asymptotic scheme, for…

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Asymptotic distributions of impulse response functions in short panel vector autoregressions

短面板向量自回归中脉冲响应函数的渐近分布

This paper establishes the asymptotic distributions of the impulse response functions in panel vector autoregressions with a fixed time dimension. It also proves the asymptotic validity of a bootstrap approximation to their sampling distributions. The autoregressive parameters are estimated using the GMM estimators based on the first differenced equations and the error variance is estimated using an extended analysis-of-variance type estimator. Contrary to the time series…

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Causal Effects of Monetary Shocks: Semiparametric Conditional Independence Tests with a Multinomial Propensity Score

货币冲击的因果效应:基于多项倾向得分的半参数条件独立检验

We develop semiparametric tests for conditional independence in time series models of causal effects. Our approach is motivated by empirical studies of monetary policy effects and is semiparametric in the sense that we model the process determining the distribution of treatment—the policy propensity score—but leave the model for outcomes unspecified. A conceptual innovation is that we adapt the cross-sectional potential outcomes framework to a time series setting. We also…

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ASYMPTOTIC BEHAVIOR OF THE CUSUM OF SQUARES TEST UNDER STOCHASTIC AND DETERMINISTIC TIME TRENDS

随机与确定性时间趋势下平方累积和检验的渐近行为

We generalize the cumulative sum of squares (CUSQ) test to the case of nonstationary autoregressive distributed lag models with deterministic time trends. The test may be implemented with either ordinary least squares residuals or standardized forecast errors. In explosive cases the asymptotic theory applies more generally for the least squares residuals-based test. Preliminary simulations of the tests suggest a very modest difference between the tests and a very modest…

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TAIL AND NONTAIL MEMORY WITH APPLICATIONS TO EXTREME VALUE AND ROBUST STATISTICS

尾部与非尾部记忆:极值及稳健统计的应用

New notions of tail and nontail dependence are used to characterize separately extremal and nonextremal information, including tail log-exceedances and events, and tail-trimmed levels. We prove that near epoch dependence (McLeish, 1975; Gallant and White, 1988) and L 0 -approximability (Pötscher and Prucha, 1991) are equivalent for tail events and tail-trimmed levels, ensuring a Gaussian central limit theory for important extreme value and robust statistics under general…

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BLOCK BOOTSTRAP HAC ROBUST TESTS: THE SOPHISTICATION OF THE NAIVE BOOTSTRAP

区块自助法 HAC 稳健检验:朴素自助法的精细性质

This paper studies the properties of naive block bootstrap tests that are scaled by zero frequency spectral density estimators (long-run variance estimators). The naive bootstrap is a bootstrap where the formula used in the bootstrap world to compute standard errors is the same as the formula used on the original data. Simulation evidence shows that the naive bootstrap can be much more accurate than the standard normal approximation. The larger the HAC bandwidth, the greater…

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DYNAMIC TIME SERIES BINARY CHOICE

动态时间序列二元选择模型

This paper considers dynamic time series binary choice models. It proves near epoch dependence and strong mixing for the dynamic binary choice model with correlated errors. Using this result, it shows in a time series setting the validity of the dynamic probit likelihood procedure when lags of the dependent binary variable are used as regressors, and it establishes the asymptotic validity of Horowitz’s smoothed maximum score estimation of dynamic binary choice models with…

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SIMULTANEOUS SPECIFICATION TESTING OF MEAN AND VARIANCE STRUCTURES IN NONLINEAR TIME SERIES REGRESSION

非线性时间序列回归中均值与方差结构的联合设定检验

This paper proposes a nonparametric simultaneous test for parametric specification of the conditional mean and variance functions in a time series regression model. The test is based on an empirical likelihood (EL) statistic that measures the goodness of fit between the parametric estimates and the nonparametric kernel estimates of the mean and variance functions. A unique feature of the test is its ability to distribute natural weights automatically between the mean and the…

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COMMENT ON “WEAK CONVERGENCE TO A MATRIX STOCHASTIC INTEGRAL WITH STABLE PROCESSES”

评《含稳定过程的矩阵随机积分弱收敛》

In this comment we identify a lacuna in a proof in the paper by M. Caner published in 1997 in Econometric Theory concerning the weak limit behavior of various expressions involving heavy-tailed multivariate vectors and the convergence of stochastic integrals. In a later paper (Caner, 1998) the results for these limit relations are used to formulate tests for cointegration with infinite variance errors.

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Conditional Markov chain and its application in economic time series analysis

条件马尔可夫链及其在经济时间序列分析中的应用

Motivated by the great moderation in major US macroeconomic time series, we formulate the regime switching problem through a conditional Markov chain. We model the long-run volatility change as a recurrent structure change, while short-run changes in the mean growth rate as regime switches. Both structure and regime are unobserved. The structure is assumed to be Markovian. Conditioning on the structure, the regime is also Markovian, whose transition matrix is…

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Simulation-based tests of forward-looking models under VAR learning dynamics

VAR 学习动态下前瞻模型的模拟检验

In this paper we propose a simulation-based technique to investigate the finite sample performance of likelihood ratio (LR) tests for the nonlinear restrictions that arise when a class of forward-looking (FL) models typically used in monetary policy analysis is evaluated with vector autoregressive (VAR) models. We consider ‘one-shot’ tests to evaluate the FL model under the rational expectations hypothesis and sequences of tests obtained under the adaptive learning…

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Forecasting large datasets with Bayesian reduced rank multivariate models

利用贝叶斯降秩多元模型预测大型数据集

The paper addresses the issue of forecasting a large set of variables using multivariate models. In particular, we propose three alternative reduced rank forecasting models and compare their predictive performance for US time series with the most promising existing alternatives, namely, factor models, large-scale Bayesian VARs, and multivariate boosting. Specifically, we focus on classical reduced rank regression, a two-step procedure that applies, in turn, shrinkage and…

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An I(2) cointegration model with piecewise linear trends

含分段线性趋势的I(2)协整模型

This paper presents likelihood analysis of the I(2) cointegrated vector autoregression which allows for piecewise linear deterministic terms. Limiting behaviour of the maximum likelihood estimators are derived, which is used to further derive the limiting distribution of the likelihood ratio statistic for the cointegration ranks, extending Nielsen and Rahbek. The provided asymptotic theory extends also the results in Johansen et al. where asymptotic inference is discussed in…

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Fitting dynamic factor models to non-stationary time series

非平稳时间序列的动态因子模型拟合

Factor modelling of a large time series panel has widely proven useful to reduce its cross-sectional dimensionality. This is done by explaining common co-movements in the panel through the existence of a small number of common components, up to some idiosyncratic behaviour of each individual series. To capture serial correlation in the common components, a dynamic structure is used as in traditional (uni- or multivariate) time series analysis of second order structure, i.e.…

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Cross-sectional dependence robust block bootstrap panel unit root tests

对横截面依赖稳健的面板单位根区块自助检验

In this paper we consider the issue of unit root testing in cross-sectionally dependent panels. We consider panels that may be characterized by various forms of cross-sectional dependence including (but not exclusive to) the popular common factor framework. We consider block bootstrap versions of the group-mean (Im et al., 2003) and the pooled (Levin et al., 2002) unit root coefficient DF tests for panel data, originally proposed for a setting of no cross-sectional…

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Testing for structural breaks in dynamic factor models

动态因子模型中的结构突变检验

In this paper we investigate the consequences of structural breaks in the factor loadings for the specification and estimation of factor models based on principal components and suggest procedures for testing for structural breaks. It is shown that structural breaks severely inflate the number of factors identified by the usual information criteria. The hypothesis of a structural break is tested by using LR, LM and Wald statistics. The LM test (which performs best in our…

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A characterization of vector autoregressive processes with common cyclical features

具有共同周期特征的向量自回归过程刻画

This paper presents necessary and sufficient conditions for the existence of common cyclical features in Vector Auto Regressive (VAR) processes integrated of order 0, 1, 2, where the common cyclical features correspond to common serial correlation (CS), commonality in the final equations (CE) and co-dependence (CD). The results are based on local rank factorizations of the reversed AR polynomial around the poles of its inverse. All processes with CS structures are found to…

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The general dynamic factor model: One-sided representation results

一般动态因子模型的单边表示结果

Recent dynamic factor models have been almost exclusively developed under the assumption that the common components span a finite-dimensional vector space. However, this finite-dimension assumption rules out very simple factor-loading patterns and is therefore severely restrictive. The general case has been studied, using a frequency domain approach, in Forni et al. (2000). That paper produces an estimator of the common components that is consistent but is based on filters…

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Dynamic factors in the presence of blocks

具有分块结构的动态因子分析

Macroeconometric data often come under the form of large panels of time series, themselves decomposing into smaller but still quite large subpanels or blocks. We show how the dynamic factor analysis method proposed in Forni et al. (2000), combined with the identification method of Hallin and Liska (2007), allows for identifying and estimating joint and block-specific common factors. This leads to a more sophisticated analysis of the structures of dynamic interrelations…

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Infinite-dimensional VARs and factor models

无限维 VAR 与因子模型

This paper proposes a novel approach for dealing with the 'curse of dimensionality' in the case of infinite-dimensional vector autoregressive (IVAR) models. It is assumed that each unit or variable in the IVAR is related to a small number of neighbors and a large number of non-neighbors. The neighborhood effects are fixed and do not change with the number of units (N), but the coefficients of non-neighboring units are restricted to vanish in the limit as N tends to infinity.…

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Real-Time Density Forecasts From Bayesian Vector Autoregressions With Stochastic Volatility

含随机波动率的贝叶斯向量自回归实时密度预测

Central banks and other forecasters are increasingly interested in various aspects of density forecasts. However, recent sharp changes in macroeconomic volatility, including the Great Moderation and the more recent sharp rise in volatility associated with increased variation in energy prices and the deep global recession—pose significant challenges to density forecasting. Accordingly, this paper examines, with real-time data, density forecasts of U.S. GDP growth,…

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A Test Against Spurious Long Memory

识别伪长记忆的检验

This paper proposes a test statistic for the null hypothesis that a given time series is a stationary long-memory process against the alternative hypothesis that it is affected by regime change or a smoothly varying trend. The proposed test is in the frequency domain and is based on the derivatives of the profiled local Whittle likelihood function in a degenerating neighborhood of the origin. The assumptions used are mild, allowing for non-Gaussianity or conditional…

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Predictability of Output Growth and Inflation: A Multi-Horizon Survey Approach

产出增长与通胀的可预测性:多期限调查方法

We develop an unobserved-components approach to study surveys of forecasts containing multiple forecast horizons. Under the assumption that forecasters optimally update their beliefs about past, current, and future state variables as new information arrives, we use our model to extract information on the degree of predictability of the state variable and the importance of measurement errors in the observables. Empirical estimates of the model are obtained using survey…

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Comparing Density Forecasts Using Threshold- and Quantile-Weighted Scoring Rules

利用阈值加权与分位数加权评分规则比较密度预测

We propose a method for comparing density forecasts that is based on weighted versions of the continuous ranked probability score. The weighting emphasizes regions of interest, such as the tails or the center of a variable’s range, while retaining propriety, as opposed to a recently developed weighted likelihood ratio test, which can be hedged. Threshold- and quantile-based decompositions of the continuous ranked probability score can be illustrated graphically and provide…

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