每日简报

非高斯状态空间模型的精确拒绝采样AI 解读

Rejection sampling requires a proposal that dominates the target by a known constant, generally unavailable for non-Gaussian state space models. We construct such a proposal for the latent state path, yielding independent exact smoothing draws and an unbiased likelihood estimator whose relative variance is at most $1/p-1$ per draw at acceptance probability $p$. The method covers scalar states with affine Gaussian dynamics and log-concave observation densities, including…

分位数估计的补偿模型及其在 VaR 中的应用AI 解读

Unlike the standard two-step workflow of estimating a time series distribution and extracting quantiles from it, this paper proposes a compensatory model to refine quantile estimates based on an existing fitted distribution. We embed a new penalty term in the model and theoretically characterize its ability to bound realized coverage errors, yielding an adaptive quantile estimator. Backtests on the S&P 500 and NASDAQ Composite show that the compensatory model substantially…

用于分布时间序列预测的 Wasserstein 指数平滑AI 解读

Distributional time series arise when each temporal observation is a probability distribution rather than a scalar. We propose Wasserstein exponential smoothing (WES), a one-parameter recursive forecasting method for distributional time series on $\mathbb{R}$. The method adapts the practical logic of classical exponential smoothing to probability distributions by updating forecast distributions along Wasserstein geodesics. This yields a simple filter that can be applied…

路径签名学习有多快？路径回归的统计理论与应用AI 解读

Many prediction and decision-making problems in operations research involve path-valued covariates -- data that evolve over time -- for which path signatures have become a canonical feature representation. Their use is justified by a universal approximation theorem, but this is an existence result: it guarantees that a finite-level signature can approximate any continuous path functional, without quantifying how fast the approximation error decreases as the truncation level…

高维矩阵值时间序列的时空自回归AI 解读

Motivated by predicting intraday trading volume curves, we consider two spatio-temporal autoregressive models for matrix time series, in which each column may represent daily trading volume curve of one asset, and each row captures synchronized 5-minute volume intervals across multiple assets. While traditional matrix time series focus mainly on temporal evolution, our approach incorporates both spatial and temporal dynamics, enabling simultaneous analysis of interactions…