每日简报

非流动性风险值AI 解读

Market efficiency relies fundamentally on stable liquidity. Consequently, forecasting liquidity dynamics is a priority for both investors and regulators. We introduce a new tail-risk metric, Illiquidity-at-Risk (IlliQaR), designed to quantify the magnitude of extreme liquidity dry-ups. Relying upon the realized Amihud (a precise illiquidity measurement derived from high-frequency data as the ratio of realized volatility to trading volume) we assess the predictive power of…

条件期望分位数的估计风险AI 解读

We establish the consistency and asymptotic normality of a two-step estimator of conditional expectiles in the context of conditional scale models. We first estimate the conditional variance parameters by quasi-maximum likelihood and then compute the unconditional expectile of the innovations using the empirical distribution of the standardized residuals. We show how replacing true innovations with standardized residuals affects the asymptotic variances of both conditional…

高维函数型时间序列的同时变点推断AI 解读

We develop a framework for simultaneous change-point inference of high-dimensional functional time series. The observations are modeled as temporally dependent vectors whose coordinates take values in possibly different separable Hilbert spaces, thereby covering a broad class of functional data. Heterogeneous mean changes may occur at coordinate-specific locations, and the contemporaneous dependence across coordinates is left unrestricted. Our procedure is based on…

分位数回归的固定平滑一致推断AI 解读

This paper develops fixed-smoothing (fixed-b, fixed-K) inference methods for time-series quantile regression that are robust to heteroskedasticity and autocorrelation. Our approach is uniformly valid over quantile levels and accounts for dependence both over time and across quantiles. It enables the construction of uniform confidence bands, Wald, and Sup-t tests for joint hypotheses, and tests of shape restrictions, providing a unified framework for assessing heterogeneity…

预期损失因子模型：共同尾部损失与预期收益AI 解读

We develop an expected shortfall factor model (ESFM) to estimate and price common variation in the severity of lower-tail losses in large panels of asset returns. Mean factor models describe common variation in average returns, while quantile factor models describe common movements in tail thresholds. ESFM instead captures common variation in the average severity of losses below those thresholds. The model combines observed risk exposures with latent common factors. We…

非递归滤波及其在金融经济学中的应用AI 解读

We develop a filter for time series, defined at each time $t$ as the minimizer of a discounted convex combination of observed and expected losses. The filter can be estimated by simulation to an arbitrary level of accuracy in $O(1)$ flops at each time point $t$ and can be run for all values $t=1,...,T$ in parallel. These methods are applied to robustly compute a preaveraged price process from the more than 1.5 million trades made on a single financial asset in a single day…

遍历基本仿射跳跃扩散中的随机跳跃强度与 Bernstein 密度估计AI 解读

This paper develops a random-effects extension of the ergodic basic affine jump-diffusion (BAJD) model for a population of independent trajectories with individual unobserved jump intensities and common structural parameters. Under continuous-time observation, each intensity is estimated by the empirical jump frequency. We establish the strong consistency and stable mixed-normal limit of this estimator as the observation horizon tends to infinity. The estimated intensities…

单因子稀疏投资组合选择的结构复杂性：精确算法、参数化困难性与受限电路下界AI 解读

We study exact-cardinality, equally weighted minimum-variance portfolio selection under a one-factor covariance model supplied in factor form. In the nonnegative homoskedastic regime, selecting the K smallest loadings is optimal. Allowing strictly positive asset-specific idiosyncratic variances makes the decision problem NP-complete even with positive integer loadings and a strictly positive-definite covariance matrix; with identity residual covariance, exactly one negative…

高维因子模型中的主成分估计误差AI 解读

In a statistical factor model, principal components (or eigenvectors) of a sample covariance matrix serve as estimates of {\it principal directions}, the true drivers of co-movement of a collection of observed variables. We write the often substantial error in these estimates as a sum of two interpretable terms, which we show have almost sure asymptotic limits as the number of variables grows with sample size bounded. This scenario is commonplace in financial economics,…

阈值原理、神经网络联系与计量经济学传承札记AI 解读

This is mostly a non-technical note, reflecting the author's philosophy and personal views on time series analysis, with references limited to only a few representatives for brevity. The Threshold Principle, formally announced in Tong (1990), modernised time series analysis by introducing a collection of sub-systems to model complex nonlinear dynamics. We explore the conceptual architecture of the Threshold Principle drawing parallels and contrasts with artificial neural…

纯跳半鞅积分波动率泛函的 Glivenko–Cantelli 定理及加密货币应用AI 解读

We develop a two-step procedure for estimating integrated volatility functionals, defined through the occupation measure of the latent spot volatility process, when the asset price is a pure-jump semimartingale. In the first step, block-based estimators formed from absolute powers of high-frequency increments uniformly approximate local averages of powers of volatility. In the second step, these estimates are aggregated into an empirical occupation measure. Since price…

利用市场信息网络建模并评估金融极端事件预测AI 解读

Modeling the joint distribution of extreme values in high-dimensional financial time series is challenging because extremes are sparse and locally extreme observations are not necessarily extreme relative to their full marginal distribution. To address this, we introduce a time-dependent network Hüsler-Reiss model in which market-informed adjacency matrices determine how strongly observations contribute to the estimation. We propose binary and weighted specifications,…

Tensor-BEKK：张量时间序列的条件协方差建模与推断AI 解读

Modern economic and financial data are increasingly organized as multiway arrays, with observations indexed simultaneously by geographic regions, industrial sectors, asset categories, and other economic characteristics. Representing such data as tensor-valued time series preserves their intrinsic multiway structure. Although substantial effort has been devoted to modeling the conditional mean of tensor-valued time series, comparatively less attention has been paid to their…

已实现相关性的稳健估计：市场贝塔日内波动的新见解AI 解读

Time-varying volatility is an inherent feature of economic time series and complicates correlation measurement at high frequencies. While the quadrant correlation estimator is robust to volatility dynamics, it has low efficiency under Gaussian sampling. We introduce a subsampled quadrant correlation estimator that improves efficiency while retaining robustness and computational simplicity. The estimator is based solely on sign information and involves no smoothing parameter…

Beta 排序组合的计量经济学性质AI 解读

Beta-sorted portfolios---portfolios comprised of assets with similar covariation with selected risk factors---are a popular tool in empirical finance to analyze models of (conditional) expected returns. Despite their widespread use, little is known of their econometric properties in contrast to comparable procedures such as two-pass regressions. We formally investigate the properties of beta-sorted portfolio returns by casting the procedure as a two-step nonparametric…

广义 Fisher 变换下相关矩阵的快速逆变换AI 解读

The generalized Fisher transformation maps a non-singular correlation matrix to an unconstrained real vector through the off-diagonal elements of its matrix logarithm. Evaluating its inverse is a computational bottleneck in dynamic correlation and multivariate volatility models. We develop a fast inversion algorithm by characterizing the unknown diagonal as the minimizer of a smooth, strictly convex, and coercive objective. An explicit Hessian and global spectral bounds…

基于扰动方法的稳健滤波与平滑AI 解读

Using a perturbation technique, we derive a new approximate filtering and smoothing methodology generalizing along different directions several existing approaches to robust filtering based on the score and the Hessian matrix of the observation density. The main advantages of the methodology can be summarized as follows: (i) it relaxes the critical assumption of a Gaussian conditional distribution for the latent states underlying such approaches; (ii) can be applied to a…

边际可能误设的 Copula 模型的贝叶斯模块化推断AI 解读

Copula models of multivariate data are popular because they allow separate specification of marginal distributions and the copula function. These components can be treated as inter-related modules in a modified Bayesian inference approach called ''cutting feedback'' that is robust to their misspecification. Recent work uses a two module approach, where all $d$ marginals form a single module, to robustify inference for the marginals against copula function misspecification,…

用收缩先验建模动态相关矩阵AI 解读

Estimating time-varying correlation matrices is challenging because existing methods may adapt slowly to structural changes, impose insufficient regularization, or produce diffuse posterior uncertainty. In moderate dimensions, an additional difficulty is summarizing the estimated evolving dependence structure for downstream decision-making tasks. We propose a Bayesian approach based on a low-rank factor representation, with latent states evolving under a dynamic shrinkage…

自回归持续时间模型的自助法AI 解读

This paper develops bootstrap methods for likelihood-based inference in autoregressive conditional duration (ACD) models, where the sample size is endogenously determined by durations observed over a fixed time span. This feature fundamentally shapes the asymptotic framework, particularly so when the durations do not have finite expectation. Building on recent limit theory for heavy-tailed and integrated ACD processes, we analyze recursive bootstrap schemes that either fix…

复杂模型中的稀疏性价值AI 解读

Sparsity or complexity? In modern high-dimensional asset pricing, these are often viewed as competing principles: recent empirical evidence favors richer models, while economic intuition has long favored parsimony. We reconcile this tension by distinguishing capacity sparsity-restrictions on effective model capacity-from factor sparsity-the parsimonious structure of priced risks. Revisiting the benchmark empirical design of Didisheim et al. (2025), we combine nonlinear…

金融中的数量方法AI 解读

These lecture notes provide a comprehensive introduction to Quantitative Methods in Finance (QMF), designed for graduate students in finance and economics with heterogeneous programming backgrounds. The material develops a unified toolkit combining probability theory, statistics, numerical methods, and empirical modeling, with a strong emphasis on implementation in Python. Core topics include random variables and distributions, moments and dependence, simulation and Monte…

用于波动率模型的稳健化高斯拟贝叶斯信息准则AI 解读

We develop a theoretical foundation for robust model comparison in a class of non-ergodic continuous volatility regression models contaminated by finite-activity jumps. Using the density-power weighting and the Hölder(-inequality)-based normalization of the conventional Gaussian quasi-likelihood function, we propose two Schwarz-type statistics and also establish their model selection consistency with respect to the minimal true parametric volatility coefficient. Numerical…

预测评分分解的统计推断AI 解读

We introduce inference methods for score decompositions, which partition scoring functions for predictive assessment into three interpretable components: miscalibration, discrimination, and uncertainty. Our estimation and inference relies on a linear recalibration of the forecasts and is applicable to general point forecasts such as means and quantiles due to its validity for non-smooth scoring functions. This approach ensures non-negative decomposition terms in finite…