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Reverse Stress Testing for Multivariate Scenarios: A Conditional Framework for Stressed Time Series

多变量情景的反向压力测试:受压时间序列的条件框架

This paper develops a methodological framework for reverse stress testing (RST) in which a multivariate stress scenario, coherent with the empirical dependence structure of a market, is reconstructed from a single exogenous shock prescribed on one asset class. The problem is formulated as the maximisation of the conditional density given the imposed shock, and is solved under three progressively weaker distributional assumptions. In the parametric setting, joint Gaussianity…

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Backward Coherence and Hidden-State Stability in Recurrent Neural Networks: A Quasi-Reverse-Martingale Theory

循环神经网络的向后相干性与隐状态稳定性:准逆鞅理论

Recurrent neural networks maintain a hidden state $h_t$, but its probabilistic meaning is often unclear. We study hidden-state stability through \emph{backward coherence}: the extent to which $h_t$ can be reconstructed from $h_{t+1}$ by a learned backward projector $g_φ$. Under contraction and summable backward drift, the hidden-state sequence forms a quasi-reverse-martingale. This yields almost-sure convergence, rates under mixing, an interpretable limiting representation,…

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Estimator Averaging of Local Projection and VAR Impulse Responses

局部投影与VAR脉冲响应的估计量平均

Local projections (LP) and vector autoregressions (VAR) are the two standard tools for impulse response analysis, but they often display a finite-sample trade-off: LP is typically less biased but more volatile, while VAR is more precise but can be biased under misspecification. We propose an easy-to-implement estimator-averaging approach that combines LP and VAR at each horizon by minimizing the mean squared error of the impulse response itself, rather than in-sample fit. We…

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Sparse High-Dimensional Vector Autoregressive Bootstrap

稀疏高维向量自回归自助法

We introduce a high-dimensional multiplier bootstrap for time series data based on capturing dependence through a sparsely estimated vector autoregressive model. We prove its consistency for inference on high-dimensional means under two different moment assumptions on the errors, namely sub-gaussian moments and a finite number of absolute moments. In establishing these results, we derive a Gaussian approximation for the maximum mean of a linear process, which may be of…

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Heavy Tails and Predictive Ability Testing

厚尾与预测能力检验

We study the asymptotic behaviour of widely used tests for evaluating and comparing predictive accuracy when forecast errors exhibit heavy tails. In particular, when loss differentials have infinite variance, the Diebold-Mariano test statistic converges to a nonstandard limit involving non-Gaussian stable random variables. As a consequence, conventional critical values can yield severely distorted inference: a nominal 5$\%$ test may reject a true null as often as 70$\%$ of…

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Large datasets for the Euro Area and its member countries and the dynamic effects of the common monetary policy

欧元区及成员国大型数据集与共同货币政策的动态效应

We introduce EA-MD-QD, a new publicly available dataset comprising 1136 macroeconomic time series for the euro area (EA) and its ten largest member countries observed at monthly or quarterly frequency. Since January 2024, EA-MD-QD has been updated monthly and continuously revised, providing a valuable resource for policy analysis in the EA. Using EA-MD-QD, we study country-specific impulse responses to an EA-wide monetary policy shock. Results reveal moderate yet significant…

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Tests for Independence of High-Dimensional Nonstationary Time Series

高维非平稳时间序列的独立性检验

This manuscript studies the problem of independence testing between two high-dimensional time series without assuming weak stationarity, that is, allowing their autocovariances to vary over time. To this end, we propose a bimodal weighted-average test statistic that removes the bias induced by temporal dependence under the null hypothesis, thereby avoiding the need to whiten the time series prior to hypothesis testing -- a procedure that is challenging in high-dimensional…

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Regime-Switching Models for Disaggregated Data

面向细分数据的状态转换模型

We show analytically and via simulation that cross-sectional aggregation can substantially attenuate regime-switching signals in time-series data, making regime switches harder to detect. Building on this, we develop regime-switching models and an estimation algorithm which allow for autoregressive dynamics and grouped heterogeneity. We apply the approach to a U.S. macroeconomic dataset of 94 series, covering components of real gross domestic product, industrial production,…

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An information criterion for detecting periodicities in functional time series

检测函数型时间序列周期成分的信息准则

We propose an information criterion for determining an unknown number of periodic components in functional time series. Identifying the number of frequencies in large-scale time series has been a central focus. To achieve this goal, we suggest an iterative procedure, utilizing the residual process obtained through least squares fitting. This iterative approach demonstrates broad applicability. We establish the consistency of the estimated number of periodic components by…

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A Distributed Lag Approach to the Generalised Dynamic Factor Model

广义动态因子模型的分布滞后估计方法

We propose a simple estimator for the dynamic decomposition of the Generalized Dynamic Factor Model that avoids frequency-domain methods. First, we show that it is a reasonable approximation to assume that the dynamic common component of the Generalized Dynamic Factor Model admits a representation in terms of current and lagged statically pervasive factors. Then, assuming finite lag order, this simplification reduces estimation to a regression of the observed variables on…

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A Structural Matrix Autoregressive Model for the Joint Dynamics of Volume, Volatility, and Returns

交易量、波动率与收益联合动态的结构矩阵自回归模型

This paper proposes a Structural Matrix Autoregressive (SMAR) model for the joint analysis of asset returns, realized volatility, and trading volume in a large-dimensional setting. This framework simultaneously captures dynamic spillovers across financial variables and cross-sectional dependence across assets while preserving a parsimonious parameterization relative to conventional vector autoregressive models. The model is estimated on daily data for the constituents of the…

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Multi-relational Network Autoregression Model with Latent Group Structures

具有潜在群组结构的多关系网络自回归模型

Multi-relational networks among entities are frequently observed in the era of big data. Quantifying the effects of multiple networks have attracted significant research interest recently. In this work, we model multiple network effects through an autoregressive framework for tensor-valued time series. To characterize the potential heterogeneity of the networks and handle the high dimensionality of the time series data simultaneously, we assume a separate group structure for…

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Causality versus Serial Correlation: an Asymmetric Portmanteau Test

因果性与序列相关:非对称 Portmanteau 检验

This paper studies specification testing in dynamic linear models in the presence of omitted variables. The null hypothesis of interest is weak exogeneity: shocks have zero conditional expectation given their own past and the past of omitted variables. Existing tests based on quadratic forms of serial cross-correlations suffer from size distortions because their variance incorporates symmetric dependence in both directions, including causality from past shocks to present…

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CausalAlpha: A Real-Time Geopolitical Risk Index from OSINT Channels for Causal Discovery in Financial Markets

CausalAlpha:基于开源情报的实时地缘政治风险指数与金融因果发现

We introduce CausalAlpha, an open-source framework that constructs a high-frequency Geopolitical Risk (GPR) index from Telegram OSINT channels using natural language processing, and applies causal discovery methods to identify the directed causal structure between geopolitical uncertainty and financial market variables. Unlike standard sentiment indices or Granger-causality approaches, CausalAlpha employs the Peter-Clark (PC) algorithm to recover the directed acyclic graph…

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Directional-Shift Dirichlet ARMA Models for Compositional Time Series with Structural Break Intervention

具有结构突变干预的方向位移 Dirichlet ARMA 组成时间序列模型

Compositional time series frequently exhibit structural breaks due to external shocks, policy changes, or market disruptions. Standard methods either ignore such breaks or handle them through fixed effects that cannot extrapolate beyond the sample, or step-function dummies that impose instantaneous adjustment. We develop a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism that captures structural breaks through three interpretable…

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The $α$--regression for compositional data: a unified framework for standard, temporal and spatial regression models including compositional predictors

组成数据的 α 回归:涵盖时间、空间及组成型解释变量的统一框架

We revisit the $α$--regression framework for compositional data. We formulate $α$--regression as a non--linear least squares problem, study its asymptotic properties, and provide efficient estimation via the Levenberg--Marquardt algorithm. We then propose a permutation--based hypothesis testing procedure, derive marginal effects for interpretation, and provide a visual inspection of the effect of each predictor. We further discuss robustified versions, the inclusion of…

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Forecasting of volatility and risk premia in electricity markets

电力市场波动率与风险溢价预测

We study forecasting of the realized covariation in electricity markets. The realized covariation in this context is a matrix-valued representation of the latent infinite-dimensional covariance operator and a parsimonious matrix-HAR type model is constructed to facilitate estimation. We test the model on one-week ahead forecasts of the weekly realized covariation and find that the inclusion of longer time horizons and renewable generation information adds important…

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Quasi-maximum likelihood estimation for scalable ARMA models

可扩展 ARMA 模型的拟极大似然估计

The recently proposed scalable ARMA model preserves the parsimony of traditional VARMA models while achieving greater computational tractability. However, existing studies are limited to regularized least squares estimation (LSE) for high-dimensional settings, which is not only statistically less efficient but also requires the sub-Gaussian assumption for its theoretical guarantees. Moreover, it still lacks inference tool for real applications. To fill this gap, we develop a…

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Inference in stochastic differential equations using the Laplace approximation: Demonstration and examples

利用 Laplace 近似进行随机微分方程推断:演示与实例

Stochastic differential equations are a natural framework for dynamic systems and time series in ecology, because they allow for non-linear first-principle knowledge and uncertainty in the dynamics, and can be combined with measurement errors. However, estimation methods are often technically and computationally challenging. Here, we demonstrate that the Laplace approximation is useful for estimating states and parameters in these models, when done correctly. We give special…

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Identification of Information Structures in Bayesian Games

贝叶斯博弈中信息结构的识别

To what extent can an external observer infer the underlying information structure from an equilibrium action distribution in an incomplete-information game? We investigate this question in a general linear-quadratic-Gaussian framework. A simple class of canonical information structures is offered and proves rich enough to rationalize any equilibrium action distribution that can arise under an arbitrary information structure. Moreover, this class is parsimonious in the sense…

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ReSGA: A Large Tail Risk Model for Learning Value-at-Risk and Expected Shortfall

ReSGA:学习风险价值与预期损失的大型尾部风险模型

Learning Value-at-Risk (VaR) and Expected Shortfall (ES) is important for managing financial risks effectively. Existing approaches with limited parameters are vulnerable to model misspecification in the era of big data. To address this limitation, we propose a large tail risk model, the retrieval-enhanced self-grouping autoencoder (ReSGA), which is designed with millions of parameters to exploit the rich cross-sectional dependence and long-term temporal dynamics of assets…

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Beyond Point Estimates: Reliable Evaluation of Prediction Performance Metrics under Clustered Data

超越点估计:聚类数据下预测性能指标的可靠评估

Prediction performance metrics such as accuracy and the F1 score are typically reported as single numbers, with no measure of uncertainty. The omission has been tolerable in exploratory settings, where model evaluation is used for informal comparison rather than formal decision-making. But as machine learning is deployed in real-world applications, evaluation results are increasingly used to support binary decisions -- whether a model meets a required standard or not --…

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Network Time Series Models for Multivariate Volatility Forecasting

用于多变量波动率预测的网络时间序列模型

Realized volatility has become a standard tool for measuring latent variation in financial assets, and its forecasting is crucial for a wide range of financial applications. We propose a network-based model for forecasting a vector of realized variance processes through the heterogeneous autoregressive (HAR) approach. The generalised network HAR (GNHAR) model incorporates cross-sectional spillovers through a directed graph inferred from Granger-causality tests or…

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Estimation of Treatment Effects Under Nonstationarity via the Truncated Policy Gradient Estimator

利用截断策略梯度估计量估计非平稳环境中的治疗效应

Randomized experiments (or A/B tests) are widely used to evaluate interventions in dynamic systems such as recommendation platforms, marketplaces, and digital health. In these settings, interventions affect both current and future system states, so estimating the global average treatment effect (GATE) requires accounting for temporal dynamics, which is especially challenging in the presence of nonstationarity; existing approaches suffer from high bias, high variance, or…

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