每日简报

无需截断的函数自回归：连续正则化方法AI 解读

Functional autoregressive models of order one (FAR(1)) are predominantly estimated by projecting curves onto leading functional principal components and fitting a vector autoregression in score space, requiring a discrete truncation level $K$ chosen by an \emph{ad hoc} variance threshold. We demonstrate via Monte Carlo experiments that the truncation choice is both consequential and highly regime dependent: the optimal $K$ can differ by an order of magnitude across…

含潜在因子的密度值向量自回归模型AI 解读

We propose a density-valued vector autoregressive model with latent factors for multivariate time series of density functions. Motivated by weekly regional distributions of SARS-CoV-2 cycle threshold (Ct) values in Brazil, we study their distributional dynamics across regions. The Ct value is the number of amplification cycles required for the viral signal to cross a detection threshold (lower Ct values correspond to higher viral load). We estimate each regional density by a…

零常返动态中的自组织状态切换AI 解读

Based on discrete observations $X_0,X_Δ,\dots, X_{nΔ}$ for $Δ=n^{-γ}$ with $γ\in [0,1)$ of the null-recurrent dynamic $dX_t = σ(X_t)dW_t$ with a Brownian motion $W$ and $σ(x)=α\mathbb{1}\{x<ρ\} + β\mathbb{1}\{x\geq ρ\}$, we derive rate of convergence and limiting distribution of the profile MLE for $ρ$. This includes low-frequency asymptotics ($γ=0$) for which the observations form a null-recurrent Markov chain. The derived non-standard limit is the argsup over a doubly…

用于因果推断与模型发现的连续时间集合 Kalman–Bucy 平滑器AI 解读

Data assimilation (DA) integrates observational information with model predictions to improve state estimation in complex systems. While filtering provides the basis for online forecasts by using only past and present observations, it can exhibit delays and biases when the underlying dynamics evolve rapidly or undergo regime transitions. Smoothing, which additionally incorporates future observations, provides a natural pipeline for hindcasting and reanalysis that yields an…

指数加权目标与指数族：滤波、预测和平滑AI 解读

We propose using a discounted version of a convex combination of the log-likelihood with the corresponding expected log-likelihood such that when they are maximized they yield a filter, predictor and smoother for time series. This paper then focuses on working out the implications of this in the case of the canonical exponential family. The results are simple exact filters, predictors and smoothers with linear recursions. A theory for these models is developed and the models…