This paper studies the joint role of long-memory dynamics,rough-volatility behavior, and persistence-based forecasting features in equity volatility modeling. We combine semiparametric long-memory estimation, rough-volatility diagnostics, and structured forecasting regressions to examine whether persistence measures contain economically meaningful forecasting information beyond conventional volatility predictors. Using a panel of 115 S&P500 constituents from November 2001 through April 2026, we document that volatility proxies exhibit substantial long-memory behavior and locally rough dynamics. The cross-sectional mean Geweke-Porter-Hudak estimate of the memory parameter is $\hat{d} = 0.226$, while the corresponding local-Whittle estimate is $\hat{d} = 0.440$, with statistical significance observed across nearly the entire panel. Rolling estimates of persistence rise substantially during the global financial crisis and the COVID period and display a positive contemporaneous association with the VIX. We then examine whether persistence-related features improve out-of-sample volatility forecasts beyond standard HAR and HAR-X benchmarks. Incorporating cross-sectional persistence aggregates, sectoral persistence measures, and persistence-by-stress interaction terms produces moderate but statistically significant forecasting improvements, particularly at longer horizons and during stress regimes. Forecast gains are strongest during periods of elevated market volatility and in volatility-managed portfolio applications. The results suggest that persistence measures may serve as useful reduced-form indicators of the duration and propagation of uncertainty in financial markets, although the paper does not claim structural identification of the economic mechanisms generating persistence.

Survival analysis aims to estimate a time-to-event distribution from data with censored observations. Many existing methods either impose structural assumptions on the hazard function or discretize the time axis, which may limit flexibility and introduce approximation errors. We propose the Survival Diffusion Probabilistic Model (SDPM), a generative approach to continuous-time survival analysis. SDPM models the conditional distribution of the survival outcome, represented by the pair of observed time and censoring indicator, $\mathbb{P}(T,δ\mid \mathbf{x})$, using a denoising diffusion model. Under the assumption of conditionally independent censoring, conditional samples generated by the model can be transformed into survival function estimates using the Kaplan-Meier estimator. This formulation avoids parametric assumptions on the event-time distribution and does not require a discretization of the output time space. The model operates in a transformed target space, using standardized log-times and a continuous Gaussian-mixture representation of the censoring indicator. We evaluate SDPM on ten real survival datasets and compare it with five strong baselines, including tree-based, boosting-based, and neural survival models. Results show that SDPM achieves competitive predictive performance across C-index, integrated time-dependent AUC, and integrated Brier score. A study on synthetic Cox-Weibull data demonstrates that SDPM can recover the shape of an underlying continuous survival distribution more accurately than a strong nonparametric baseline when sufficiently many samples are generated. An ablation study confirms the importance of the proposed target-space transformations, which improve event-rate calibration, reduce invalid generated times, and provide consistent gains in predictive discrimination. Codes implementing the proposed model are publicly available.

Deep learning methods have proved highly effective for classification and image recognition problems. In this paper, we ask whether this success can be transferred to hypothesis testing: if a neural network can distinguish, for example, an image of a handwritten digit from another, can it also distinguish an "image of a sample" (such as a scatter plot) generated under a given statistical model from one generated outside that model? Motivated by this idea, we propose a novel procedure called deep-testing, which approaches the classical inferential problem of hypothesis testing through deep learning. More specifically, the test statistic is a classification map learned by a deep neural network from simulated data satisfying the null and alternative hypotheses, leveraging its strong discriminating power to construct a highly powerful test. As a proof of concept, we apply deep-testing to the problem of independence testing, arguably one of the most important problems in statistics. In a large-scale simulation study, deep-testing achieves the highest overall power against nineteen competing methods across a broad range of complex dependence structures, confirming the viability of the proposed approach.

A.1 Notation Let T be a failure time with CDFF. T's survival function is defined by F = 1 F. We denote failure models by FθT. Let C be a censoring time with CDFG, survival function G, and model GθC. Under right-censoring, define U = min(T,C), = 1 [T C] and we observe (Xi,Ui, i). We use G(t) to denote P(C t).

Geographic context is often consider relevant to motor insurance risk, yet public actuarial datasets provide limited location identifiers, constraining how this information can be incorporated and evaluated in claim-frequency models. This study examines how geographic information from alternative data sources can be incorporated into actuarial models for Motor Third Party Liability (MTPL) claim prediction under such constraints. Using the BeMTPL97 dataset, we adopt a zone-level modeling framework and evaluate predictive performance on unseen postcodes. Geographic information is introduced through two channels: environmental indicators from OpenStreetMap and CORINE Land Cover, and orthoimagery released by the Belgian National Geographic Institute for academic use. We evaluate the predictive contribution of coordinates, environmental features, and image embeddings across three baseline models: generalized linear models (GLMs), regularized GLMs, and gradient-boosted trees, while raw imagery is modeled using convolutional neural networks. Our results show that augmenting actuarial variables with constructed geographic information improves accuracy. Across experiments, both linear and tree-based models benefit most from combining coordinates with environmental features extracted at 5 km scale, while smaller neighborhoods also improve baseline specifications. Generally, image embeddings do not improve performance when environmental features are available; however, when such features are absent, pretrained vision-transformer embeddings enhance accuracy and stability for regularized GLMs. Our results show that the predictive value of geographic information in zone-level MTPL frequency models depends less on model complexity than on how geography is represented, and illustrate that geographic context can be incorporated despite limited individual-level spatial information.

We use the discrete variablezd,t to represent the topic that thetth word is generated from.

Federated Learning (FL) iscommonly used tocollaborativelytrain models with privacypreservation. Specifically,AdaSCP evaluates the importance of parameters with the gradients in dominant timesteps of the diffusion model.

Deep learning algorithms have recently gained significant attention due to their impressive performance.