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Forecasting Multivariate Time Series under Predictive Heterogeneity: A Validation-Driven Clustering Framework

预测异质性下的多元时间序列预测:验证驱动的聚类框架

We study adaptive pooling under predictive heterogeneity in high-dimensional multivariate time series forecasting, where global models improve statistical efficiency but may fail to capture heterogeneous predictive structure, while naive specialization can induce negative transfer. We formulate adaptive pooling as a statistical decision problem and propose a validation-driven framework that determines when and how specialization should be applied. Rather than grouping series…

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Bias-Corrected Adaptive Conformal Inference for Multi-Horizon Time Series Forecasting

多预测期时间序列预测的偏差校正自适应共形推断

Adaptive Conformal Inference (ACI) provides distribution-free prediction intervals with asymptotic coverage guarantees for time series under distribution shift. However, ACI only adapts the quantile threshold -- it cannot shift the interval center. When a base forecaster develops persistent bias after a regime change, ACI compensates by widening intervals symmetrically, producing unnecessarily conservative bands. We propose Bias-Corrected ACI (BC-ACI), which augments…

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Benign Overfitting in Economic Forecasting via Noise Regularization

通过噪声正则化实现经济预测中的良性过拟合

This paper studies linear overparameterized models in economic forecasting and highlights that including noise variables (regressors with no predictive power) regularizes the estimator. We consider a setting where both the outcome variable and the high-dimensional predictors are driven by a small number of latent factors, and show that the linear forecast model is dense rather than sparse. It turns out that a ridgeless regression augmented with noise predictors attains the…

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Forecasting Oil Prices Across the Distribution: A Quantile VAR Approach

跨分布预测油价:分位数向量自回归方法

We develop a Quantile Bayesian Vector Autoregression (QBVAR) to forecast real oil prices across different quantiles of the conditional distribution. The model allows predictor effects to vary across quantiles, capturing asymmetries that standard mean-focused approaches miss. Using monthly data from 1975 to 2025, we document three findings. First, the QBVAR improves median forecasts by 2-5\% relative to Bayesian VARs, demonstrating that quantile-specific dynamics matter even…

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A Diagnostics-First Composite Index for Macro-Financial Resilience to Socioeconomic Challenges: The Gondauri Index with Benchmarking and Scenario Evidence

宏观金融韧性的诊断优先综合指数:Gondauri 指数、基准比较与情景证据

In the face of socioeconomic challenges, this paper develops and empirically demonstrates the Gondauri Index (GI) as a reproducible diagnostics-first composite framework for benchmarking macro-financial resilience across heterogeneous economies on a unified 0-100 scale. The GI addresses a key limitation of conventional surveillance dashboards: resilience is multi-dimensional and only partially substitutable, so strength in one area cannot sustainably offset fragility in…

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StationarityToolkit: Comprehensive Time Series Stationarity Analysis in Python

StationarityToolkit:Python 时间序列平稳性综合分析工具

Time-series stationarity is a property that statistical characteristics such as trend, variance, seasonality remain constant over time. It is considered fundamental to many forecasting and analysis methods. Different tests detect different types of non-stationarity: structural breaks or deterministic trends, clustered or time-dependent variance, stochastic or deterministic seasonality. A series might pass one test while failing another; single-test approaches seldom…

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Quantum Reservoir Computing for Realized Volatility Forecasting

用于已实现波动率预测的量子储备池计算

Recent advances in quantum computing have demonstrated its potential to significantly enhance the analysis and forecasting of complex classical data. Among these, quantum reservoir computing has emerged as a particularly powerful approach, combining quantum computation with machine learning for modeling nonlinear temporal dependencies in high-dimensional time series. As with many data-driven disciplines, quantitative finance and econometrics can hugely benefit from emerging…

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Conformal Prediction with Time-Series Data via Sequential Conformalized Density Regions

通过序贯保形密度区域进行时间序列保形预测

We propose a new conformal prediction method for time-series data with a guaranteed asymptotic conditional coverage rate, Sequential Conformalized Density Regions (SCDR), which is flexible enough to produce both prediction intervals and disconnected prediction sets, signifying the emergence of bifurcations. Our approach uses existing estimated conditional highest density predictive regions to form initial predictive regions. We then use a quantile random forest conformal…

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A Nontrivial Upper Bound on the Out-of-Sample $R^2$ in Return Forecasting

收益预测样本外 R² 的非平凡上界

This study establishes a nontrivial upper bound on the out-of-sample $R^2$ ($R^2_{\text{OOS}}$) in return forecasting. In particular, we define a coin-flip oracle model that, under the same directional accuracy, theoretically outperforms practical models in terms of MSE. The $R^2_{\text{OOS}}$ of the oracle model, whose analytical expression is a quadratic function of directional accuracy, can therefore serve as a tractable upper bound on the actual $R^2_{\text{OOS}}$.…

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Dynamic Factor Stochastic Volatility-in-Mean VAR for Large Macroeconomic Panels

面向大型宏观面板的动态因子随机波动率入均值 VAR

We develop a dynamic factor stochastic volatility-in-mean (SVM) specification for vector autoregressions (VARs) that embeds an SVM component within a dynamic factor stochastic volatility structure. A small number of latent volatility factors capture common movements in conditional variances, while volatility enters the conditional mean of the VAR. This specification allows time-varying uncertainty to influence macroeconomic dynamics through both second moments and expected…

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A Dynamic Factor Model for Level and Volatility

水平与波动率的动态因子模型

This paper develops a dynamic factor model in which common level and volatility factors evolve jointly, allowing conditional means and variances to interact endogenously within a large-information setting. The joint evolution of these factors provides a tractable framework for modeling risk, as fluctuations in volatility affect both the dispersion and the location of outcomes, generating state-dependent and asymmetric tail risks in predictive distributions. Volatility is…

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Network Structure in UK Payment Flows: Evidence on Economic Interdependencies and Implications for Real-Time Measurement

英国支付流的网络结构:经济相互依赖与实时衡量

Network analysis of inter-industry payment flows reveals structural economic relationships invisible to traditional bilateral measurement approaches, with significant implications for real-time economic monitoring. Analysing 532,346 UK payment records (2017--2024) across 89 industry sectors, we demonstrate that graph-theoretic features which include centrality measures and clustering coefficients improve payment flow forecasting by 8.8 percentage points beyond traditional…

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Copula-Based Time Series for Non-Gaussian and Non-Markovian Stationary Processes

非高斯、非马尔可夫平稳过程的 Copula 时间序列模型

In the copula-based approach to univariate time series modeling, the finite dimensional temporal dependence of a stationary time series is captured by a copula. Recent studies investigate how copula-based time series models can be generalized to have long-term autoregressive effects. We study a generalization that comes from a Markov sequence of order p and a q-dependent sequence. We derive the relation of the model to Gaussian-ARMA models and to the Gaussian-GARCH(1,1)…

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Dynamic linear regression models for forecasting time series with semi long memory errors

具有半长记忆误差的动态线性回归预测模型

Dynamic linear regression models forecast the values of a time series based on a linear combination of a set of exogenous time series while incorporating a time series process for the error term. This error process is often assumed to follow a stationary autoregressive integrated moving average (ARIMA) model, or its seasonal variants, which are unable to capture a long-range dependence structure (long memory) of the error process. We propose a novel dynamic linear regression…

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Central limit theorems for the outputs of fully convolutional neural networks with time series input

时间序列输入下全卷积神经网络输出的中心极限定理

Deep learning is widely deployed for time series learning tasks such as classification and forecasting. Despite the empirical successes, only little theory has been developed so far in the time series context. In this work, we prove that if the network inputs are generated from short-range dependent linear processes, the outputs of fully convolutional neural networks (FCNs) with global average pooling (GAP) are asymptotically Gaussian and the limit is attained if the length…

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Forecast collapse of transformer-based models under squared loss in financial time series

平方损失下金融时间序列中 Transformer 模型的预测塌缩

We study trajectory forecasting under squared loss for time series with weak conditional structure, using highly expressive prediction models. Building on the classical characterization of squared-loss risk minimization, we emphasize regimes in which the conditional expectation of future trajectories is effectively degenerate, leading to trivial Bayes-optimal predictors (flat for prices and zero for returns in standard financial settings). In this regime, increased model…

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Identifying the desert decision rule to assess and achieve fairness

识别应得决策规则以评估与实现公平

We study fairness in decision-making when the data may encode systematic bias. Existing approaches typically impose fairness constraints while predicting the observed decision, which may itself be unfair. We propose a novel framework for characterising and addressing fairness issues by introducing the notion of desert decision, a latent variable representing the decision an individual rightfully deserves based on their actions, efforts, or abilities. This formulation shifts…

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Fake Date Tests: Can We Trust In-sample Accuracy of LLMs in Macroeconomic Forecasting?

伪日期检验:大语言模型宏观预测的样本内准确性可信吗?

Large language models (LLMs) are a type of machine learning tool that economists have started to apply in their empirical research. One such application is macroeconomic forecasting with backtesting of LLMs, even though they are trained on the same data that is used to estimate their forecasting performance. Can these in-sample accuracy results be extrapolated to the model's out-of-sample performance? To answer this question, we developed a family of prompt sensitivity tests…

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Parametric generalized spectrum for heavy-tailed time series

厚尾时间序列的参数化广义谱

Recently, several spectra have emerged, designed to encapsulate the distributional characteristics of non-Gaussian stationary processes. This article introduces parametric families of generalized spectra based on the characteristic function, alongside inference procedures enabling $\sqrt{n}$-consistent estimation of the unknown parameters in a broad class of parametric models. These spectra capture non-linear dependencies without requiring that the underlying stochastic…

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Diffolio: A Diffusion Model for Multivariate Probabilistic Financial Time-Series Forecasting and Portfolio Construction

Diffolio:多变量金融时序概率预测与组合构建的扩散模型

Probabilistic forecasting is crucial in multivariate financial time-series for constructing efficient portfolios that account for complex cross-sectional dependencies. In this paper, we propose Diffolio, a diffusion model designed for multivariate financial time-series forecasting and portfolio construction. Diffolio employs a denoising network with a hierarchical attention architecture, comprising both asset-level and market-level layers. Furthermore, to better reflect…

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Non-robustness of diffusion estimates on networks with measurement error

测量误差下网络扩散估计的非稳健性

Network diffusion models are used to study disease transmission, information spread, technology adoption, and other socio-economic processes. We show that estimates of these diffusions are highly non-robust to mismeasurement. First, even when the network is measured perfectly, small and local mismeasurement in the initial seed generates a large shift in the locations of the expected diffusion. Second, if instead the initial seed is known, even a vanishingly small share of…

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Integrating Complex Covariate Transformations in Generalized Additive Models

在广义可加模型中整合复杂协变量变换

Transformations of covariates are widely used in applied statistics to improve interpretability and to satisfy assumptions required for valid inference. More broadly, feature engineering encompasses a wider set of practices aimed at enhancing predictive performance, and is typically performed as part of a data pre-processing step. In contrast, this paper integrates a substantial component of the feature engineering process directly into the modelling stage. This is achieved…

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From Hawkes Processes to Attention: Time-Modulated Mechanisms for Event Sequences

从 Hawkes 过程到注意力:事件序列的时间调制机制

Marked Temporal Point Processes (MTPPs) arise naturally in medical, social, commercial, and financial domains. However, existing Transformer-based methods mostly inject temporal information only via positional encodings, relying on shared or parametric decay structures, which limits their ability to capture heterogeneous and type-specific temporal effects. Inspired by this observation, we derive a novel attention operator called Hawkes Attention from the multivariate Hawkes…

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Granger Causality in Expectiles: an M-vine copula test

期望分位数中的格兰杰因果:M-vine Copula 检验

A model-free measure of Granger causality in expectiles is proposed, generalizing the traditional mean-based measure to arbitrary positions of the conditional distribution. Expectiles are the only law-invariant risk measures that are both coherent and elicitable, making them particularly well-suited for studying distributional Granger causality where risk quantification and forecast evaluation are both relevant. Based on this measure, a test is developed using M-vine copula…

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