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高频金融数据大维瞬时波动率矩阵的非参数估计AI 解读

In this paper, we consider estimating spot/instantaneous volatility matrices of high-frequency data collected for a large number of assets. We first combine classic nonparametric kernel-based smoothing with a generalised shrinkage technique in the matrix estimation for noise-free data under a uniform sparsity assumption, a natural extension of the approximate sparsity commonly used in the literature. The uniform consistency property is derived for the proposed spot…

CF-GODE：多主体动态系统的连续时间因果推断AI 解读

Multi-agent dynamical systems refer to scenarios where multiple units interact with each other and evolve collectively over time. To make informed decisions in multi-agent dynamical systems, such as determining the optimal vaccine distribution plan, it is essential for decision-makers to estimate the continuous-time counterfactual outcomes. However, existing studies of causal inference over time rely on the assumption that units are mutually independent, which is not valid…

离散化时间尺度在连续时间处理因果推断中的作用AI 解读

There are well-established methods for identifying the causal effect of a time-varying treatment applied at discrete time points. However, in the real world, many treatments are continuous or have a finer time scale than the one used for measurement or analysis. While researchers have investigated the discrepancies between estimates under varying discretization scales using simulations and empirical data, it is still unclear how the choice of discretization scale affects…

连接频率学派与贝叶斯变点方法AI 解读

We show that the two-stage minimum description length (MDL) criterion widely used to estimate linear change-point (CP) models corresponds to the marginal likelihood of a Bayesian model with a specific class of prior distributions. This allows results from the frequentist and Bayesian paradigms to be bridged together. Thanks to this link, one can rely on the consistency of the number and locations of the estimated CPs and the computational efficiency of frequentist methods,…

切换自回归低秩张量模型AI 解读

An important problem in time-series analysis is modeling systems with time-varying dynamics. Probabilistic models with joint continuous and discrete latent states offer interpretable, efficient, and experimentally useful descriptions of such data. Commonly used models include autoregressive hidden Markov models (ARHMMs) and switching linear dynamical systems (SLDSs), each with its own advantages and disadvantages. ARHMMs permit exact inference and easy parameter estimation,…

模糊动态治疗方案：强化学习方法AI 解读

A main research goal in various studies is to use an observational data set and provide a new set of counterfactual guidelines that can yield causal improvements. Dynamic Treatment Regimes (DTRs) are widely studied to formalize this process. However, available methods in finding optimal DTRs often rely on assumptions that are violated in real-world applications (e.g., medical decision-making or public policy), especially when (a) the existence of unobserved confounders…

时变波动率下泡沫日期估计精度的改进AI 解读

In this study, we consider a four-regime bubble model under the assumption of time-varying volatility and propose the algorithm of estimating the break dates with volatility correction: First, we estimate the emerging date of the explosive bubble, its collapsing date, and the recovering date to the normal market under assumption of homoskedasticity; second, we collect the residuals and then employ the WLS-based estimation of the bubble dates. We demonstrate by Monte Carlo…

基于 U 统计量与依赖野生自助法的函数时间序列稳健变点检测AI 解读

The aim of this paper is to develop a change-point test for functional time series that uses the full functional information and is less sensitive to outliers compared to the classical CUSUM test. For this aim, the Wilcoxon two-sample test is generalized to functional data. To obtain the asymptotic distribution of the test statistic, we proof a limit theorem for a process of $U$-statistics with values in a Hilbert space under weak dependence. Critical values can be obtained…

分治动态规划：高维变点检测的近线性时间方法AI 解读

We develop a novel, general and computationally efficient framework, called Divide and Conquer Dynamic Programming (DCDP), for localizing change points in time series data with high-dimensional features. DCDP deploys a class of greedy algorithms that are applicable to a broad variety of high-dimensional statistical models and can enjoy almost linear computational complexity. We investigate the performance of DCDP in three commonly studied change point settings in high…

状态空间模型的高效变分近似AI 解读

Variational Bayes methods are a potential scalable estimation approach for state space models. However, existing methods are inaccurate or computationally infeasible for many state space models. This paper proposes a variational approximation that is accurate and fast for any model with a closed-form measurement density function and a state transition distribution within the exponential family of distributions. We show that our method can accurately and quickly estimate a…

时变向量误差修正模型：估计与推断AI 解读

This paper considers a time-varying vector error-correction model that allows for different time series behaviours (e.g., unit-root and locally stationary processes) to interact with each other to co-exist. From practical perspectives, this framework can be used to estimate shifts in the predictability of non-stationary variables, test whether economic theories hold periodically, etc. We first develop a time-varying Granger Representation Theorem, which facilitates the…

动态高斯图模型的变点检测：新冠疫情期间美国股市的依赖变化AI 解读

Reliable estimates of volatility and correlation are fundamental in economics and finance for understanding the impact of macroeconomics events on the market and guiding future investments and policies. Dependence across financial returns is likely to be subject to sudden structural changes, especially in correspondence with major global events, such as the COVID-19 pandemic. In this work, we are interested in capturing abrupt changes over time in the dependence across US…

局部平稳函数型时间序列的估计AI 解读

This study develops an asymptotic theory for estimating the time-varying characteristics of locally stationary functional time series (LSFTS). We investigate a kernel-based method to estimate the time-varying covariance operator and the time-varying mean function of an LSFTS. In particular, we derive the convergence rate of the kernel estimator of the covariance operator and associated eigenvalue and eigenfunctions and establish a central limit theorem for the kernel-based…

自回归最优传输模型AI 解读

Series of univariate distributions indexed by equally spaced time points are ubiquitous in applications and their analysis constitutes one of the challenges of the emerging field of distributional data analysis. To quantify such distributional time series, we propose a class of intrinsic autoregressive models that operate in the space of optimal transport maps. The autoregressive transport models that we introduce here are based on regressing optimal transport maps on each…

动态条件分位数处理效应的评估及网约车应用AI 解读

Many modern tech companies, such as Google, Uber, and Didi, utilize online experiments (also known as A/B testing) to evaluate new policies against existing ones. While most studies concentrate on average treatment effects, situations with skewed and heavy-tailed outcome distributions may benefit from alternative criteria, such as quantiles. However, assessing dynamic quantile treatment effects (QTE) remains a challenge, particularly when dealing with data from ride-sourcing…

利用回归树对时变参数向量自回归模型进行贝叶斯建模AI 解读

In light of widespread evidence of parameter instability in macroeconomic models, many time-varying parameter (TVP) models have been proposed. This paper proposes a nonparametric TVP-VAR model using Bayesian additive regression trees (BART) that models the TVPs as an unknown function of effect modifiers. The novelty of this model arises from the fact that the law of motion driving the parameters is treated nonparametrically. This leads to great flexibility in the nature and…

低秩向量自回归过程中的变点检测AI 解读

Vector autoregressive (VAR) models are widely used in multivariate time series analysis for describing the short-time dynamics of the data. The reduced-rank VAR models are of particular interest when dealing with high-dimensional and highly correlated time series. Many results for these models are based on the stationarity assumption that does not hold in several applications when the data exhibits structural breaks. We consider a low-rank piecewise stationary VAR model with…

分析多维数字表型的混合响应状态空间模型AI 解读

Digital technologies (e.g., mobile phones) can be used to obtain objective, frequent, and real-world digital phenotypes from individuals. However, modeling these data poses substantial challenges since observational data are subject to confounding and various sources of variabilities. For example, signals on patients' underlying health status and treatment effects are mixed with variation due to the living environment and measurement noises. The digital phenotype data thus…

非平稳时间序列的自回归逼近：推断与应用AI 解读

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range dependent non-stationary and nonlinear time series can be well approximated globally by a white-noise-driven auto-regressive (AR) process of slowly diverging order. To our best knowledge, it is the first time such a structural approximation…

高维函数型时间序列的结构突变检测与估计AI 解读

In this paper, we consider detecting and estimating breaks in heterogeneous mean functions of high-dimensional functional time series which are allowed to be cross-sectionally correlated and temporally dependent. A new test statistic combining the functional CUSUM statistic and power enhancement component is proposed with asymptotic null distribution theory comparable to the conventional CUSUM theory derived for a single functional time series. In particular, the extra power…

纵向中介分析的目标最大似然估计AI 解读

Causal mediation analysis with random interventions has become an area of significant interest for understanding time-varying effects with longitudinal and survival outcomes. To tackle causal and statistical challenges due to the complex longitudinal data structure with time-varying confounders, competing risks, and informative censoring, there exists a general desire to combine machine learning techniques and semiparametric theory. In this manuscript, we focus on targeted…

载荷状态切换的高维因子模型：估计与推断AI 解读

This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix. When regime dynamics are taken into account, smoothed regime probabilities are calculated using a…

批次式多臂老虎机的渐近展开AI 解读

In bandit algorithms, the randomly time-varying adaptive experimental design makes it difficult to apply traditional limit theorems to off-policy evaluation of the treatment effect. Moreover, the normal approximation by the central limit theorem becomes unsatisfactory for lack of information due to the small sample size of the inferior arm. To resolve this issue, we introduce a backwards asymptotic expansion method and prove the validity of this scheme based on the partial…

时间序列结构变化加权检验统计量的功效AI 解读

We investigate the power of some common change-point tests as a function of the location of the change-point. The test statistics are maxima of weighted U-statistics, with the CUSUM test and the Wilcoxon change-point test as special examples. We study the power under local alternatives, where we vary both the location of the change-point and the magnitude of the change. We quantify in which way weighted versions of the tests are more powerful when the change occurs near the…