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Identifying factor‐augmented vector autoregression models via changes in shock variances

利用冲击方差变化识别因子增强向量自回归模型

Summary This study proposes a method to identify factor‐augmented vector autoregression models without imposing uncorrelatedness or any timing restrictions among observed and unobserved factors in the vector autoregression system. To this end, we utilize changes in unconditional shock variances following Rigobon (2003). The proposed method can incorporate both observed and unobserved factors in the structural vector autoregression system and allows the contemporaneous matrix…

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The global component of inflation volatility

通胀波动的全球成分

Summary Global developments play an important role for domestic inflation rates. Earlier literature has found that a substantial amount of the variation in a large set of national inflation rates can be explained by a single global factor. However, inflation volatility has been typically neglected, although it is clearly relevant both from a policy point of view and for structural analysis and forecasting. We study the evolution of inflation rates in several countries, using…

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How to estimate a vector autoregression after March 2020

2020年3月之后如何估计向量自回归模型

Summary This paper illustrates how to handle a sequence of extreme observations—such as those recorded during the COVID‐19 pandemic—when estimating a vector autoregression, which is the most popular time‐series model in macroeconomics. Our results show that the ad hoc strategy of dropping these observations may be acceptable for the purpose of parameter estimation. However, disregarding these recent data is inappropriate for forecasting the future evolution of the economy,…

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Asymptotics of sample tail autocorrelations for tail-dependent time series: phase transition and visualization

尾部依赖时间序列的样本尾部自相关:相变与可视化

Summary In this article we develop an asymptotic theory for sample tail autocorrelations of time series data that can exhibit serial dependence in both tail and non-tail regions. Unlike with the traditional autocorrelation function, the study of tail autocorrelations requires a double asymptotic scheme to capture the tail phenomena, and our results do not impose any restrictions on the dependence structure in non-tail regions and allow processes that are not necessarily…

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Inverse moment methods for sufficient forecasting using high-dimensional predictors

利用高维预测变量进行充分预测的逆矩方法

Summary We consider forecasting a single time series using a large number of predictors in the presence of a possible nonlinear forecast function. Assuming that the predictors affect the response through the latent factors, we propose to first conduct factor analysis and then apply sufficient dimension reduction on the estimated factors to derive the reduced data for subsequent forecasting. Using directional regression and the inverse third-moment method in the stage of…

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Testing for unit roots based on sample autocovariances

基于样本自协方差的单位根检验

Summary We propose a new unit-root test for a stationary null hypothesis $H_0$ against a unit-root alternative $H_1$. Our approach is nonparametric as $H_0$ assumes only that the process concerned is $I(0)$, without specifying any parametric forms. The new test is based on the fact that the sample autocovariance function converges to the finite population autocovariance function for an $I(0)$ process, but diverges to infinity for a process with unit roots. Therefore, the new…

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Single step estimation of ARMA roots for nonfundamental nonstationary fractional models

非基本非平稳分数阶模型中 ARMA 根的单步估计

Summary We propose a single step estimator for the autoregressive and moving average roots (without imposing causality or invertibility restrictions) of a nonstationary Fractional ARMA process. These estimators employ an efficient tapering procedure, which allows for a long memory component in the process, but avoids estimating the nonstationarity component, which can be stochastic and/or deterministic. After selecting automatically the order of the model, we robustly…

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Permanent-Transitory decomposition of cointegrated time series via dynamic factor models, with an application to commodity prices

基于动态因子模型的协整时间序列永久—暂时分解:商品价格应用

Summary We propose a cointegration-based Permanent-Transitory decomposition for nonstationary dynamic factor models (DFMs). Our methodology exploits the cointegration relations among the observable variables and assumes they are driven by a common and an idiosyncratic component. The common component is further split into a long-term nonstationary and a short-term stationary part. A Monte Carlo experiment shows that incorporating the cointegration structure into the DFM leads…

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Detecting common breaks in the means of high dimensional cross-dependent panels

高维截面相关面板均值共同断点的检测

Summary The problem of detecting change points in the mean of high dimensional panel data with potentially strong cross-sectional dependence is considered. Under the assumption that the cross-sectional dependence is captured by an unknown number of common factors, a new CUSUM-type statistic is proposed. We derive its asymptotic properties under three scenarios depending on to what extent the common factors are asymptotically dominant. With panel data consisting of N cross…

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Robust Inference in Models Identified via Heteroskedasticity

通过异方差识别的模型中的稳健推断

Abstract Identification via heteroskedasticity exploits variance changes between regimes to identify parameters in simultaneous equations. Weak identification occurs when shock variances change very little or multiple variances change close to proportionally, making standard inference unreliable. I propose an F-test for weak identification in a common simple version of the model. More generally, I establish conditions for validity of nonconservative robust inference on…

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Robust Bayesian inference in proxy SVARs

代理 SVAR 的稳健贝叶斯推断

We develop methods for robust Bayesian inference in structural vector autoregressions (SVARs) where the parameters of interest are set-identified using external instruments, or ‘proxy SVARs’. Set-identification in these models typically occurs when there are multiple instruments for multiple structural shocks. Existing Bayesian approaches to inference in proxy SVARs require researchers to specify a single prior over the model’s parameters, but, under set-identification, a…

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Bayesian estimation of long-run risk models using sequential Monte Carlo

利用序贯蒙特卡洛进行长期风险模型的贝叶斯估计

We propose a likelihood-based Bayesian method that exploits up-to-date sequential Monte Carlo methods to efficiently estimate long-run risk models in which the conditional variance of consumption growth follows either an autoregressive (AR) process or an autoregressive gamma (ARG) process. We use the U.S. quarterly consumption and asset returns data from the postwar period to implement estimation. Our findings are: (1) informative priors on the preference parameters can help…

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Copula-based time series with filtered nonstationarity

滤除非平稳性的 Copula 时间序列模型

Economic and financial time series data can exhibit nonstationary and nonlinear patterns simultaneously. This paper studies copula-based time series models that capture both patterns. We introduce a procedure where nonstationarity is removed via a filtration, and then the nonlinear temporal dependence in the filtered data is captured via a flexible Markov copula. We propose two estimators of the copula dependence parameters: the parametric (two-step) copula estimator where…

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Nonlinear Spectral Analysis: A Local Gaussian Approach

非线性谱分析:局部高斯方法

The spectral distribution f(ω) of a stationary time series {Yt}t∈Z can be used to investigate whether or not periodic structures are present in {Yt}t∈Z, but f(ω) has some limitations due to its dependence on the autocovariances γ(h). For example, f(ω) can not distinguish white iid noise from GARCH-type models (whose terms are dependent, but uncorrelated), which implies that f(ω) can be an inadequate tool when {Yt}t∈Z contains asymmetries and nonlinear dependencies.…

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Center-Outward R-Estimation for Semiparametric VARMA Models

半参数 VARMA 模型的中心向外秩估计

We propose a new class of R-estimators for semiparametric VARMA models in which the innovation density plays the role of the nuisance parameter. Our estimators are based on the novel concepts of multivariate center-outward ranks and signs. We show that these concepts, combined with Le Cam’s asymptotic theory of statistical experiments, yield a class of semiparametric estimation procedures, which are efficient (at a given reference density), root-n consistent, and…

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Learning Latent Factors From Diversified Projections and Its Applications to Over-Estimated and Weak Factors

从分散化投影学习潜在因子:因子数高估与弱因子的应用

Estimations and applications of factor models often rely on the crucial condition that the number of latent factors is consistently estimated, which in turn also requires that factors be relatively strong, data are stationary and weakly serially dependent, and the sample size be fairly large, although in practical applications, one or several of these conditions may fail. In these cases, it is difficult to analyze the eigenvectors of the data matrix. To address this issue,…

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The Locally Gaussian Partial Correlation

局部高斯偏相关

It is well known in econometrics and other fields that the dependence structure for jointly Gaussian variables can be fully captured using correlations, and that the conditional dependence structure in the same way can be described using partial correlations. The partial correlation does not, however, characterize conditional dependence in many non-Gaussian populations. This article introduces the local Gaussian partial correlation (LGPC), a new measure of conditional…

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Semiparametric Tests for the Order of Integration in the Possible Presence of Level Breaks

可能存在水平突变时的积分阶数半参数检验

Lobato and Robinson developed semiparametric tests for the null hypothesis that a series is weakly autocorrelated, or I(0), about a constant level, against fractionally integrated alternatives. These tests have the advantage that the user is not required to specify a parametric model for any weak autocorrelation present in the series. We extend this approach in two distinct ways. First, we show that it can be generalized to allow for testing of the null hypothesis that a…

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The Effect of Dependence on European Market Risk. A Nonparametric Time Varying Approach

依赖关系对欧洲市场风险的影响:非参数时变方法

Multivariate dependence measures are crucial for risk management, where variables usually have heavy tails and non-Gaussian distributions. We propose a multivariate time varying Kendall’s tau estimator in a nonparametric context, allowing for local stationary variables. Consistency and asymptotic normality of the estimator are provided. A simulation study is conducted which supports the idea of better performance than other related methods in many complex scenarios. The…

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Bayesian Approach to Lorenz Curve Using Time Series Grouped Data

基于时间序列分组数据的洛伦兹曲线贝叶斯估计

This study is concerned with estimating the inequality measures associated with the underlying hypothetical income distribution from the times series grouped data on the income proportions. We adopt the Dirichlet likelihood approach where the parameters of the Dirichlet likelihood are set to the differences between the Lorenz curve of the hypothetical income distribution for the consecutive income classes and propose a state-space model which combines the transformed…

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Risk Analysis via Generalized Pareto Distributions

基于广义帕累托分布的风险分析

We compute the value-at-risk of financial losses by fitting a generalized Pareto distribution to exceedances over a threshold. Following the common practice of setting the threshold as high sample quantiles, we show that, for both independent observations and time-series data, the asymptotic variance for the maximum likelihood estimation depends on the choice of threshold, unlike the existing study of using a divergent threshold. We also propose a random weighted bootstrap…

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Locally Stationary Quantile Regression for Inflation and Interest Rates

通胀与利率的局部平稳分位数回归

Motivated by the potential time-varying and quantile-specific relation between inflation and interest rates, we propose a locally stationary quantile regression approach to model the inflation and interest rates relation. Large sample theory for estimation and inference of quantile-varying and time-varying coefficients are established. In empirical analysis of inflation and interest rates relation, it is found that the estimated functional coefficients vary with time in a…

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Multifrequency-Band Tests for White Noise Under Heteroscedasticity

异方差下的多频带白噪声检验

This article proposes a new family of multifrequency-band tests for the white noise hypothesis by using the maximum overlap discrete wavelet packet transform. At each scale, the proposed multifrequency-band test has the chi-square asymptotic null distribution under mild conditions, which allow the data to be heteroscedastic. Moreover, an automatic multifrequency-band test is further proposed by using a data-driven method to select the scale, and its asymptotic null…

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Long Memory Factor Model: On Estimation of Factor Memories

长记忆因子模型:因子记忆参数的估计

This article considers the estimation of the integration orders of the latent factors in an approximate factor model. Both the common factors and idiosyncratic error terms are potentially nonstationary fractionally integrated processes. We propose a two-stage approach to estimate the factor memories. We show the consistency and asymptotic normality of the proposed estimator. Applying the estimator to the log-squared returns of the U.S. financial institutions, we find…

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