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Testing Quantile Forecast Optimality

分位数预测最优性检验

Quantile forecasts made across multiple horizons have become an important output of many financial institutions, central banks and international organisations. This paper proposes misspecification tests for such quantile forecasts that assess optimality over a set of multiple forecast horizons and/or quantiles. The tests build on multiple Mincer-Zarnowitz quantile regressions cast in a moment equality framework. Our main test is for the null hypothesis of autocalibration, a…

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Investigating Growth-at-Risk Using a Multicountry Nonparametric Quantile Factor Model

利用多国非参数分位数因子模型研究增长风险

We develop a nonparametric quantile panel regression model.Within each quantile, the quantile function is a combination of linear and nonlinear parts, which we approximate using Bayesian Additive Regression Trees (BART).Cross-sectional information is captured through a conditionally heteroscedastic latent factor.The nonparametric feature enhances flexibility, while the panel feature increases the number of observations in the tails.We develop Bayesian methods for inference…

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Maximum-Subsampling Test of Equal Predictive Ability

预测能力相等的最大子抽样检验

In comparing the accuracy of any two competing forecasts, under the assumption that the loss differentials are covariance stationary, Diebold and Mariano (DM) proposed a test statistic that is asymptotically normal. This test is further studied by Giacomini and White (GW). However, under the DM-GW framework, the estimator of the variance of the DM test can be inaccurate in small samples, which yields size distortions; see, for example, Coroneo and Iacone (CI). To alleviate…

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Noncommon Breaks

非共同结构断点

We develop a new Bayesian approach to estimate noncommon structural breaks in panel regression models. Any subset of the cross-section may be hit at different times within a break window. Break-specific parameters are learned from the cross-section. They reflect whether (i) breaks hit many or few series and (ii) there is a long or short lag between the first and final series hit by a break. In an empirical application to international stock return predictability, the method…

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Linking Frequentist and Bayesian Change-Point Methods

连接频率学派与贝叶斯变点方法

We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods,…

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Scenario-based quantile connectedness of the U.S. interbank liquidity risk network

美国银行间流动性风险网络的情景分位数连通性

We characterize the U.S. interbank liquidity risk network based on a supervisory dataset, using a scenario-based quantile network connectedness approach. In terms of methodology, we consider a quantile vector autoregressive model with unobserved heterogeneity and propose a Bayesian nuclear norm estimation method. A common factor structure is employed to deal with unobserved heterogeneity that may exhibit endogeneity within the network. Then we develop a scenario-based…

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Reprint of: Out-of-sample tests for conditional quantile coverage: An application to Growth-at-Risk

重刊:条件分位数覆盖率的样本外检验及增长风险应用

This paper proposes tests for out-of-sample comparisons of interval forecasts based on parametric conditional quantile models. The tests rank the distance between actual and nominal conditional coverage with respect to the set of conditioning variables from all models, for a given loss function. We propose a pairwise test to compare two models for a single predictive interval. The set-up is then extended to a comparison across multiple models and/or intervals. The limiting…

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Target PCA: Transfer learning large dimensional panel data

目标主成分分析:高维面板数据的迁移学习

This paper develops a novel method to estimate a latent factor model for a large target panel with missing observations by optimally using the information from auxiliary panel data sets. We refer to our estimator as target-PCA. Transfer learning from auxiliary panel data allows us to deal with a large fraction of missing observations and weak signals in the target panel. We show that our estimator is more efficient and can consistently estimate weak factors, which are not…

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Testing for differences in survey‐based density expectations: A compositional data approach

调查密度预期差异检验:组成数据方法

Summary We propose to treat survey‐based density expectations as compositional data when testing either for heterogeneity in density forecasts across different groups of agents or for changes over time. Monte Carlo simulations show that the proposed test has more power relative to both a bootstrap approach based on the KLIC and an approach that involves multiple testing for differences of individual parts of the density. In addition, the test is computationally much faster…

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Large Bayesian SVARs with linear restrictions

带线性约束的大型贝叶斯结构向量自回归模型

This paper develops a Markov Chain Monte Carlo (MCMC) algorithm for Bayesian inference in large structural vector autoregressions (SVARs) with linear restrictions. Our proposed method is based on a novel parameter transformation scheme, which aims to facilitate sampling from the posterior distribution of model parameters when linear equality and inequality restrictions are imposed on contemporaneous impulse responses. A prominent feature of the proposed methodology is its…

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Empirical risk minimization for time series: Nonparametric performance bounds for prediction

时间序列的经验风险最小化:预测表现的非参数界

Empirical risk minimization is a standard principle for choosing algorithms in learning theory. In this paper we study the properties of empirical risk minimization for time series. The analysis is carried out in a general framework that covers different types of forecasting applications encountered in the literature. We are concerned with 1-step-ahead prediction of a univariate time series belonging to a class of location-scale parameter-driven processes. A class of…

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Expecting the unexpected: Stressed scenarios for economic growth

应对意外:经济增长的压力情景

Summary We propose the construction of conditional growth densities under stressed factor scenarios to assess the level of exposure of an economy to small probability but potentially catastrophic economic and/or financial scenarios, which can be either domestic or international. The choice of severe yet plausible stress scenarios is based on the joint probability distribution of the underlying factors driving growth, which are extracted with a multilevel dynamic factor model…

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Tests for equal forecast accuracy under heteroskedasticity

异方差下的预测准确性相等检验

Summary Heteroskedasticity is a common feature in empirical time series analysis, and in this paper, we consider the effects of heteroskedasticity on statistical tests for equal forecast accuracy. In such a context, we propose two new Diebold–Mariano‐type tests for equal accuracy that employ nonparametric estimation of the loss differential variance function. We demonstrate that these tests have the potential to achieve power improvements relative to the original…

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Scaling and measurement error sensitivity of scoring rules for distribution forecasts

分布预测评分规则对缩放和测量误差的敏感性

Summary This paper examines the impact of data rescaling and measurement error on scoring rules for distribution forecast. First, I show that all commonly used scoring rules for distribution forecasts are robust to rescaling the data. Second, the forecast ranking based on the continuous ranked probability score is less sensitive to gross measurement error than the ranking based on the log score. The theoretical results are complemented by a simulation study aligned with…

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Real‐time weakness of the global economy

全球经济疲弱程度的实时测度

Summary We propose an empirical framework to measure the real‐time weakness of the global economy. This framework relies on nonlinear factor models to identify recessionary and expansionary episodes, fitted to several macroeconomic variables, for the largest advanced and emerging economies. The country‐specific inferences are then combined to construct both a Global Weakness Index and a Global Intensity Index. As new economic data become available from different regions,…

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Constructing density forecasts from quantile regressions: Multimodality in macrofinancial dynamics

由分位数回归构造密度预测:宏观金融动态中的多峰性

Summary Quantile regression methods are increasingly used to forecast tail risks and uncertainties in macroeconomic outcomes. This paper reconsiders how to construct predictive densities from quantile regressions. We compare a popular two‐step approach that fits a specific parametric density to the quantile forecasts with a nonparametric alternative that lets the “data speak.” Simulation evidence and an application revisiting GDP growth uncertainties in the United States…

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Identification and forecasting of bull and bear markets using multivariate returns

利用多元收益识别和预测牛熊市场

Summary Bull and bear market identification generally focuses on a broad index of returns through a univariate analysis. This paper proposes a new approach to identify and forecast bull and bear markets through multivariate returns. The model assumes that all assets are directed by a common discrete state variable from a hierarchical Markov switching model. The hierarchical specification allows the cross‐section of state‐specific means and variances to differ over bull and…

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Robust Leave-One-Out Cross-Validation for High-Dimensional Bayesian Models

高维贝叶斯模型的稳健留一交叉验证

Leave-one-out cross-validation (LOO-CV) is a popular method for estimating out-of-sample predictive accuracy. However, computing LOO-CV criteria can be computationally expensive due to the need to fit the model multiple times. In the Bayesian context, importance sampling provides a possible solution but classical approaches can easily produce estimators whose asymptotic variance is infinite, making them potentially unreliable. Here we propose and analyze a novel mixture…

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Variational Inference for Large Bayesian Vector Autoregressions

大型贝叶斯向量自回归的变分推断

We propose a novel variational Bayes approach to estimate high-dimensional Vector Autoregressive (VAR) models with hierarchical shrinkage priors.Our approach does not rely on a conventional structural representation of the parameter space for posterior inference.Instead, we elicit hierarchical shrinkage priors directly on the matrix of regression coefficients so that (a) the prior structure maps into posterior inference on the reduced-form transition matrix and (b) posterior…

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Modeling and Forecasting Macroeconomic Downside Risk

宏观经济下行风险的建模与预测

We model permanent and transitory changes of the predictive density of US GDP growth. A substantial increase in downside risk to US economic growth emerges over the last 30 years, associated with the long-run growth slowdown started in the early 2000s. Conditional skewness moves procyclically, implying negatively skewed predictive densities ahead and during recessions, often anticipated by deteriorating financial conditions. Conversely, positively skewed distributions…

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FNETS: Factor-Adjusted Network Estimation and Forecasting for High-Dimensional Time Series

FNETS:高维时间序列的因子调整网络估计与预测

–We propose FNETS, a methodology for network estimation and forecasting of high-dimensional time series exhibiting strong serial- and cross-sectional correlations. We operate under a factor-adjusted vector autoregressive (VAR) model which, after accounting for pervasive co-movements of the variables by common factors, models the remaining idiosyncratic dynamic dependence between the variables as a sparse VAR process. Network estimation of FNETS consists of three steps: (i)…

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Powerful Backtests for Historical Simulation Expected Shortfall Models

历史模拟预期损失模型的高功效回测

Since 2016, the Basel Committee on Banking Supervision has regulated banks to switch from a Value-at-Risk (VaR) to an Expected Shortfall (ES) approach to measuring the market risk and calculating the capital requirement. In the transition from VaR to ES, the major challenge faced by financial institutions is the lack of simple but powerful tools for evaluating ES forecasts (i.e., backtesting ES). This article first shows that the unconditional backtest is inconsistent in…

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Gender pension gaps in a private retirement accounts system: A dynamic model of household labor supply and savings

私人退休账户制度中的性别养老金差距:家庭劳动供给与储蓄动态模型

This paper develops and estimates a dynamic model of individuals’ and couples’ labor supply, savings, and retirement decisions to analyze how the design of Chile’s privatized pension system and a reform undertaken in 2008 affect gender pension gaps and old-age poverty. Chile has one of the longest-running private retirements accounts systems in the world, which has served as a model for many countries. The paper estimates the dynamic model using pre-reform data and compares…

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On LASSO for high dimensional predictive regression

高维预测回归中的 LASSO

This paper examines LASSO, a widely-used L1-penalized regression method, in high dimensional linear predictive regressions, particularly when the number of potential predictors exceeds the sample size and numerous unit root regressors are present. The consistency of LASSO is contingent upon two key components: the deviation bound of the cross product of the regressors and the error term, and the restricted eigenvalue of the Gram matrix. We present new probabilistic bounds…

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