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VAR for VaR: Measuring tail dependence using multivariate regression quantiles

用于 VaR 的 VAR:以多元回归分位数衡量尾部依赖

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyze spillovers in the…

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Testing conditional independence via empirical likelihood

基于经验似然的条件独立检验

We construct two classes of smoothed empirical likelihood ratio tests for the conditional independence hypothesis by writing the null hypothesis as an infinite collection of conditional moment restrictions indexed by a nuisance parameter. One class is based on the CDF; another is based on smoother functions. We show that the test statistics are asymptotically normal under the null hypothesis and a sequence of Pitman local alternatives. We also show that the tests possess an…

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Granger causality, exogeneity, cointegration, and economic policy analysis

格兰杰因果、外生性、协整与经济政策分析

Policy analysis had long been a main interest of Clive Granger’s. Here, we present a framework for economic policy analysis that provides a novel integration of several fundamental concepts at the heart of Granger’s contributions to time-series analysis. We work with a dynamic structural system analyzed by White and Lu (2010) with well defined causal meaning; under suitable conditional exogeneity restrictions, Granger causality coincides with this structural notion. The…

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TESTING STRUCTURAL CHANGE IN PARTIALLY LINEAR MODELS

部分线性模型的结构变化检验

We consider two tests of structural change for partially linear time-series models. The first tests for structural change in the parametric component, based on the cumulative sums of gradients from a single semiparametric regression. The second tests for structural change in the parametric and nonparametric components simultaneously, based on the cumulative sums of weighted residuals from the same semiparametric regression. We derive the limiting distributions of both tests…

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A NONPARAMETRIC HELLINGER METRIC TEST FOR CONDITIONAL INDEPENDENCE

基于 Hellinger 距离的非参数条件独立检验

We propose a nonparametric test of conditional independence based on the weighted Hellinger distance between the two conditional densities, f ( y | x , z ) and f ( y | x ), which is identically zero under the null. We use the functional delta method to expand the test statistic around the population value and establish asymptotic normality under β-mixing conditions. We show that the test is consistent and has power against alternatives at distance n −1/2 h − d /4 . The cases…

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Mixtures of t-distributions for finance and forecasting

用于金融与预测的 t 分布混合

We explore convenient analytic properties of distributions constructed as mixtures of scaled and shifted t-distributions. Particularly desirable for econometric applications are closed-form expressions for antiderivatives (e.g., the cumulative density function). We illustrate the usefulness of these distributions in two applications. In the first application, we produce density forecasts of U.S. inflation and show that these forecasts are more accurate, out-of-sample, than…

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Testing for Regime Switching

状态切换检验

We analyze use of a quasi-likelihood ratio statistic for a mixture model to test the null hypothesis of one regime versus the alternative of two regimes in a Markov regime-switching context. This test exploits mixture properties implied by the regime-switching process, but ignores certain implied serial correlation properties. When formulated in the natural way, the setting is nonstandard, involving nuisance parameters on the boundary of the parameter space, nuisance…

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Tests of Conditional Predictive Ability

条件预测能力检验

We propose a framework for out-of-sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite…

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Bootstrap Standard Error Estimates for Linear Regression

线性回归的自助法标准误估计

Standard errors of parameter estimates are widely used in empirical work. The bootstrap often can provide a convenient means of estimating standard errors. The conditions under which bootstrap standard error estimates are theoretically justified have not received much attention, however. This article establishes conditions for the consistency of the moving blocks bootstrap estimators of the variance of the least squares estimator in linear dynamic models with dependent data.…

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Asymptotic Distribution Theory for Nonparametric Entropy Measures of Serial Dependence

序列依赖非参数熵度量的渐近分布理论

Entropy is a classical statistical concept with appealing properties. Establishing asymptotic distribution theory for smoothed nonparametric entropy measures of dependence has so far proved challenging. In this paper, we develop an asymptotic theory for a class of kernel-based smoothed nonparametric entropy measures of serial dependence in a time-series context. We use this theory to derive the limiting distribution of Granger and Lin's (1994) normalized entropy measure of…

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A COMPARISON OF COMPLEMENTARY AUTOMATIC MODELING METHODS: RETINA AND PcGets

互补自动建模方法的比较:RETINA 与 PcGets

In Perez-Amaral, Gallo, and White (2003, Oxford Bulletin of Economics and Statstics 65, 821–838), the authors proposed an automatic predictive modeling tool called relevant transformation of the inputs network approach (RETINA). It is designed to embody flexibility (using nonlinear transformations of the predictors of interest), selective search within the range of possible models, control of collinearity, out-of-sample forecasting ability, and computational simplicity. In…

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A Reality Check for Data Snooping

数据窥探的现实检验

Data snooping occurs when a given set of data is used more than once for purposes of inference or model selection. When such data reuse occurs, there is always the possibility that any satisfactory results obtained may simply be due to chance rather than to any merit inherent in the method yielding the results. This problem is practically unavoidable in the analysis of time-series data, as typically only a single history measuring a given phenomenon of interest is available…

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CENTRAL LIMIT AND FUNCTIONAL CENTRAL LIMIT THEOREMS FOR HILBERT-VALUED DEPENDENT HETEROGENEOUS ARRAYS WITH APPLICATIONS

Hilbert 空间值依赖异质数组的中心极限定理与函数中心极限定理及应用

We obtain new central limit theorems (CLT's) and functional central limit theorems (FCLT's) for Hilbert-valued arrays near epoch dependent on mixing processes, and also new FCLT's for general Hilbert-valued adapted dependent heterogeneous arrays. These theorems are useful in delivering asymptotic distributions for parametric and nonparametric estimators and their functionals in time series econometrics. We give three significant applications for near epoch dependent…

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Monitoring Structural Change

结构变化的实时监测

Contemporary tests for structural change are designed to detect a structural break within a given historical data set of fixed size. Due to the law of the iterated logarithm, these one-shot tests cannot be applied to monitor out-of-sample stability each time new data arrive. The authors propose and analyze two real-time monitoring procedures with controlled size asymptotically: the fluctuation and CUSUM monitoring procedures. Simulation results show that the proposed…

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A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks

利用线性模型与人工神经网络评估期限结构信息的模型选择方法

We take a model selection approach to the question of whether forward interest rates are useful in predicting future spot rates, using a variety of out-of-sample forecast-based model selection criteria: forecast mean squared error, forecast direction accuracy, and forecast-based trading system profitability. We also examine the usefulness of a class of novel prediction models called 'artificial neural networks,' and investigate the issue of appropriate window sizes for…

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Testing for neglected nonlinearity in time series models

时间序列模型中遗漏非线性的检验

In this paper a new test, the neural network test for neglected nonlinearity, is compared with the Keenan test, the Tsay test, the White dynamic information matrix test, the McLeod-Li test, the Ramsey RESET test, the Brock-Dechert-Scheinkman test, and the Bispectrum test. The neural network test is based on the approximating ability of neural network modeling techniques recently developed by cognitive scientists. This test is a Lagrange multiplier test that statistically…

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A Direct Test for Changing Trend

趋势变化的直接检验

The authors consider tests for changing trend that do not require prior knowledge about the location of the changepoint. The limiting distribution is derived from the functional central limit theorem and the critical value from the hitting probability of a Brownian bridge. Applying a test sensitive to the alternative of trend stationarity with structural breaks, they find that for real gross national product, real per capita gross national product, and real wages before…

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Some Invariance Principles and Central Limit Theorems for Dependent Heterogeneous Processes

相依异质过程的不变性原理与中心极限定理

Building on work of McLeish, we present a number of invariance principles for doubly indexed arrays of stochastic processes which may exhibit considerable dependence, heterogeneity, and/or trending moments. In particular, we consider possibly time-varying functions of infinite histories of heterogeneous mixing processes and obtain general invariance results, with central limit theorems following as corollaries. These results are formulated so as to apply to economic time…

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Nonlinear Regression with Dependent Observations

相依观测下的非线性回归

This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of…

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