每日简报

状态空间模型的 MCMC 方法AI 解读

A state-space model is a time-series model that has an unobserved latent process from which we take noisy measurements over time. The observations are conditionally independent given the latent process and the latent process itself is Markovian. These properties lead to simplifications for the conditional distribution of the latent process given the parameters and the observations. This chapter looks at how we can leverage the properties of state-space models to construct…

高维时间序列的稀疏组因子分析AI 解读

Factor analysis is a widely used technique for dimension reduction in high-dimensional data. However, a key challenge in factor models lies in the interpretability of the latent factors. One intuitive way to interpret these factors is through their associated loadings. Liu and Wang proposed a novel framework that redefines factor models with sparse loadings to enhance interpretability. In many high-dimensional time series applications, variables exhibit natural group…

有序时间序列的二元一阶离散自回归模型AI 解读

We present a bivariate vector valued discrete autoregressive model of order $1$ (BDAR($1$)) for discrete time series. The BDAR($1$) model assumes that each time series follows its own univariate DAR($1$) model with dependent random mechanisms that determine from which component the current status occurs and dependent innovations. The joint distribution of the random mechanisms which are expressed by Bernoulli vectors are proposed to be defined through copulas. The same holds…

关于条件异方差时间序列拟极大似然估计的随机递推方法的一则注记AI 解读

Bougerol (1993) and Straumann and Mikosch (2006) gave conditions under which there exists a unique stationary and ergodic solution to the stochastic difference equation $Y_t \overset{a.s.}{=} Φ_t (Y_{t-1}), t \in \mathbb{Z}$ where $(Φ_t)_{t \in \mathbb{Z}}$ is a sequence of stationary and ergodic random Lipschitz continuous functions from $(Y,|| \cdot ||)$ to $(Y,|| \cdot ||)$ where $(Y,|| \cdot ||)$ is a complete subspace of a real or complex separable Banach space. In the…

加密货币网络数据中的张量时间序列变点检测AI 解读

Financial fraud has been growing exponentially in recent years. The rise of cryptocurrencies as an investment asset has simultaneously seen a parallel growth in cryptocurrency scams. To detect possible cryptocurrency fraud, and in particular market manipulation, previous research focused on the detection of changes in the network of trades; however, market manipulators are now trading across multiple cryptocurrency platforms, making their detection more difficult. Hence, it…

货币冲击对宏观经济星号变量的影响：SMUC-IV 框架AI 解读

This paper proposes a structural multivariate unobserved components model with external instrument (SMUC-IV) to investigate the effects of monetary policy shocks on key U.S. macroeconomic "stars"-namely, the level of potential output, the growth rate of potential output, trend inflation, and the neutral interest rate. A key feature of our approach is the use of an external instrument to identify monetary policy shocks within the multivariate unobserved components modeling…

ResCP：用于时间序列预测的储备池共形预测AI 解读

Conformal prediction offers a powerful framework for building distribution-free prediction intervals for exchangeable data. Existing methods that extend conformal prediction to sequential data rely on fitting a relatively complex model to capture temporal dependencies. However, these methods can fail if the sample size is small and often require expensive retraining when the underlying data distribution changes. To overcome these limitations, we propose Reservoir Conformal…

超越预言机性质：近单位根解释变量下协整回归的自适应LASSOAI 解读

This paper derives new asymptotic results for the adaptive LASSO estimator in cointegrating regressions, allowing for uncertainty about whether the regressors are exact unit root processes. We study model selection probabilities, estimator consistency, and limiting distributions under standard and moving-parameter asymptotics. We further derive uniform convergence rates and the fastest local-to-zero rates detectable by the estimator under conservative and consistent tuning.…

网络依赖时间序列的频域分析：全球银行关联应用AI 解读

Financial spillovers in interconnected systems, such as global banking networks, require tools that capture temporal and frequency dynamics, while incorporating the underlying network topology. While current network time series models are developed in the time-domain, frequency-domain approaches, which reveal how cross-nodal dependencies vary across different cycles, remain under-explored. This paper develops a spectral analysis framework that accommodates flexible forms of…

离散时间滞后鞅差阵列的稳定中心极限定理及动态因果应用AI 解读

Recent work in dynamic causal inference introduced a class of discrete-time stochastic processes that generalize martingale difference sequences and arrays as follows: the random variates in each sequence have expectation zero given certain lagged filtrations but not given the natural filtration. We formalize this class of stochastic processes and prove stable central limit theorems (CLTs) via martingale-coboundary decomposition, leveraging the classical martingale CLT. We…

具有时变偏度的随机波动入均值 VAR 模型AI 解读

This paper introduces a Bayesian vector autoregression (BVAR) with stochastic volatility-in-mean and time-varying skewness. Unlike previous approaches, the proposed model allows both volatility and skewness to directly affect macroeconomic variables. We provide a Gibbs sampling algorithm for posterior inference and apply the model to quarterly data for the US and the UK. Empirical results show that skewness shocks have economically significant effects on output, inflation…

利用逐级比率估计对 trawl 过程进行基于模拟的推断AI 解读

The growing availability of large and complex datasets has increased interest in temporal stochastic processes that can capture stylized facts such as marginal skewness, non-Gaussian tails, long memory, and even non-Markovian dynamics. While such models are often easy to simulate from, parameter estimation remains challenging. Simulation-based inference (SBI) offers a promising way forward, but existing methods typically require large training datasets or complex…

HAC 估计的自动阶数与带宽选择及特征值调整缺陷AI 解读

In this paper, we propose a new heteroskedasticity and autocorrelation consistent covariance matrix estimator based on the prewhitened kernel estimator and a localized leave-one-out frequency domain cross-validation (FDCV). We adapt the cross-validated log likelihood (CVLL) function to simultaneously select the order of the prewhitening vector autoregression (VAR) and the bandwidth. The prewhitening VAR is estimated by the Burg method without eigen adjustment as we find the…

DeepVARwT：含趋势向量自回归模型的深度学习估计AI 解读

The vector autoregressive (VAR) model has been used to describe the dependence within and across multiple time series. This is a model for stationary time series which can be extended to allow the presence of a deterministic trend in each series. Detrending the data either parametrically or nonparametrically before fitting the VAR model gives rise to more errors in the latter part. In this study, we propose a new approach called DeepVARwT that employs deep learning…

密度值时间序列：非参数密度对密度回归AI 解读

This paper is concerned with forecasting probability density functions. Density functions are nonnegative and have a constrained integral; thus, they do not constitute a vector space. Implementing unconstrained functional time-series forecasting methods is problematic for such nonlinear and constrained data. A novel forecasting method is developed based on a nonparametric function-on-function regression, where both the response and the predictor are probability density…

机器学习、偏微分方程与统计中的再生核方法AI 解读

This monograph develops a unified, application-driven framework for kernel methods grounded in reproducing kernel Hilbert spaces (RKHS) and optimal transport (OT). Part I lays the theoretical and numerical foundations on positive-definite kernels; discrete and continuous RKHS; kernel engineering and scaling maps; error assessment via kernel discrepancy/maximum mean discrepancy (MMD); and a systematic operator view of kernels. In this viewpoint, projection, gradient,…