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自适应 Lasso 解路径单位根检验的自助法改进AI 解读

We propose sieve wild bootstrap analogues to the adaptive Lasso solution path unit root tests of Arnold and Reinschlüssel (2024) arXiv:2404.06205 to improve finite sample properties and extend their applicability to a generalised framework, allowing for non-stationary volatility. Numerical evidence shows the bootstrap to improve the tests' precision for error processes that promote spurious rejections of the unit root null, depending on the detrending procedure. The…

ARMA 过程谱密度函数的分解AI 解读

Quasi-periodic oscillations are characterized by fitting Lorentzian functions to a nonparametric estimate of the power spectral density, a two-step procedure that separates estimation from modeling and does not accommodate measurement error. We develop a parametric alternative based on autoregressive moving-average (ARMA) processes observed with measurement error. We derive an exact decomposition of the ARMA spectral density into real-valued components, one for each class of…

检测Copula结构变化的平滑检验方法AI 解读

This paper develops novel smooth tests for structural changes in the innovation copula of multivariate dynamic models. We characterize deviations from copula constancy through a collection of generalized Fourier coefficients and test their joint significance. Under the null hypothesis, estimation of the dynamic parameters and the unknown marginals has no first-order estimation effect on the proposed statistics. Consequently, the feasible tests based on estimated residuals…

标量对函数回归中的函数型预测变量选择与平滑系数估计AI 解读

In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing accurate smooth (or, more generally, regular) estimates of the functional coefficients. We suppose that the functional predictors belong to a real separable Hilbert space, while the functional coefficients belong to a specific subspace of…

高维非线性因子模型的最优估计AI 解读

This paper studies optimal estimation of large-dimensional nonlinear factor models. The key challenge is that the observed variables are possibly nonlinear functions of some latent variables, with the functional forms left unspecified. A local principal component analysis method combining K-nearest neighbors matching and principal component analysis is proposed to estimate the factor structure and recover information on latent variables and latent functions. Large-sample…

时间序列的高斯过程建模AI 解读

Gaussian processes (GPs) provide a flexible nonparametric framework for modeling time series through appropriately chosen kernel functions. This chapter introduces the basic formulation of Gaussian processes, commonly used kernels, GP regression, hyperparameter estimation, and model evaluation using in-sample and out-of-sample criteria. Applications to stationary, quasi-periodic, and seasonal time series illustrate how individual and composite kernels can represent different…

对象值时间序列中的长程依赖度量AI 解读

Object-valued time series, including distributions, covariance matrices, networks, and compositions, lack the linear structure required by conventional autocovariance-based definitions of long memory. We develop an intrinsic framework for defining and estimating long memory in metric spaces of negative type. An isometric embedding yields a centered Hilbert-valued process, and the trace of its lag-covariance operator provides a signed, additive measure of temporal dependence.…

观察性时间序列动态因果效应的半参数推断AI 解读

In observational time series, statistical inference for dynamic causal effects of a one-time intervention across horizons is complicated by high-dimensional observed pre-treatment information, unmeasured confounding, and serial dependence. To address these challenges, we develop a semiparametric framework for inference from a single serially dependent time series, integrating debiased machine learning with instrumental variables through buffered block cross-fitting. Under…

具有 Cholesky 随机波动率的大型 VAR：贝叶斯推断、在线预测与模型选择AI 解读

We consider $K$-dimensional Bayesian vector autoregressions (BVARs) with Cholesky stochastic volatility (SV), in which the innovation covariance matrix is a lower-triangular linear transform of $K$ independent univariate SV processes. Such models are widely used in empirical macroeconomics to capture time-varying uncertainty and improve forecast accuracy, but the cost of posterior simulation is the binding constraint on the size of the system, and a major bottleneck for…

局部差分隐私下利用交互机制进行非参数谱密度估计AI 解读

We study the problem of estimating the spectral density of a centered stationary Gaussian time series under local differential privacy constraints. Specifically, we propose new interactive privacy mechanisms for three tasks: recovering a single covariance coefficient, recovering the spectral density at a fixed frequency, and global recovery. Our approach achieves faster rates through a two-stage process: we first apply the Laplace mechanism to the truncated value, and then…

通过条件中心化进行非线性 Granger 因果的 RKHS 推断AI 解读

Granger causality is commonly formulated through linear prediction in vector autoregressive models, limiting its ability to detect nonlinear predictive relationships. We propose a reproducing kernel Hilbert space (RKHS)-based test for nonlinear Granger non-causality in conditional mean for nonlinear autoregressive processes. The key idea is a conditional-centering decomposition of the target regression function into an own-history component and an orthogonal component…

马尔可夫链混合模型中最优匹配聚类的一致性AI 解读

We study clustering of categorical sequences using the Optimal Matching (OM) distance under finite mixtures of finite-state Markov chains. We show that the normalized OM distance between two independent chains converges almost surely to a deterministic population quantity, concentrates exponentially around its finite-horizon mean, and admits an $O(\sqrt{\log n/n})$ convergence rate when the two chains have the same transition kernel. These population quantities yield a…

时间序列中的条件独立检验AI 解读

We consider the problem of testing Granger causality in time series, specifically, whether the future outcome $Y_{t+1}$ and the exposure history $\bar X_t$ are conditionally independent given the history of $\bar Y_t$ and a set of confounding variables $\bar Z_t$ up to time $t$. This testing procedure distinguishes true causal effects from associations driven by common external processes, supporting reliable decision-makings in applications such as finance, neuroscience, and…

弱依赖非线性时间序列模型准似然估计量的一致高斯近似AI 解读

We study estimation and inference for a semiparametric class of time series models that specify only the conditional expectation, which is a known link function applied to a linear combination of past observations and covariates. The class covers count, binary, bounded and conditionally heteroskedastic responses within a single formulation, and the parameter is estimated by a quasi-likelihood estimating equation based on the first conditional moment. Under stationarity and a…

因果状态依赖局部投影AI 解读

State-dependent local projections (LPs) are widely used to study how causal effects vary as a function of economic states, but shock exogeneity alone does not identify this response function. We show that identification follows when the underlying conditional mean is linear in the shock with a state-dependent coefficient, a condition satisfied in canonical micro-macro environments, including first-order perturbation solutions of heterogeneous-agent and macro-finance models.…

具有分组边效应的降秩网络自回归AI 解读

We propose the Edge-Grouped Reduced-Rank Network Autoregressive model (Edge-Grouped RRNAR) for multivariate time series observed over a network. The model allows transmission effects to vary across prespecified and economically interpretable groups of edges, while using a low-rank structure to capture cross-variable dynamics. This structure separates where network transmission occurs from which variables transmit and respond. We develop a topology-aware and block-specific…

度量空间时间序列的在线分布变化检测AI 解读

We propose an online testing framework for detecting distributional changes in serially dependent data with values in a separable metric space. Based on two-sample $U$-statistics, the framework encompasses sequential analogs of energy distance and maximum mean discrepancy (MMD) procedures while accommodating temporal dependence. We establish asymptotic theory for finite and open-ended monitoring horizons that characterizes the full asymptotic run-length distribution under $H_0$…

广义岭回归与卷积LASSOAI 解读

We derive the complete duality theory underlying the Hodrick--Prescott filter, whose rank-deficient second-difference penalty admits infinitely many equivalent trend representations via generalized inverses. Constructing two canonical choices---the Moore--Penrose-based \emph{B-representation} and an alternative \emph{A-representation}---we prove that the extracted trend is invariant across representations, obtain a closed-form Bregman-type divergence quantifying their…

SCAN：通过自适应非参数推断依次检测变点AI 解读

Modern time series are often long, serially dependent, and non-stationary. Existing change-point methods either target specific changes or become computationally intensive when using nonparametric costs on long series. Many also require thresholds to be carefully calibrated under serial dependence. We introduce SCAN, an offline method for detecting multiple distributional change-points in long, serially dependent univariate time series. SCAN compares adjacent windows using…

非欧对象值时间序列的周期性量化AI 解读

Non-Euclidean object-valued time series are playing a growing role in modern data analysis, and periodicity is a fundamental characteristic of many time series. However, quantifying periodicity in general non-Euclidean random objects remains largely unexplored. In this work, we introduce a novel nonparametric framework for quantifying periodicity in random objects within a general metric space that lacks Euclidean structure. Our approach formulates periodicity estimation as…

含未知趋势与周期成分的球面嵌入时间序列AI 解读

Spherically embedded time series are time series with values naturally residing on or can be equivalently mapped to the sphere. Despite their ubiquity in diverse scientific fields, these data frequently exhibit complex non-stationarity driven by latent trend and periodic components. Traditional Euclidean time series methods fail to account for the intrinsic non-Euclidean geometry of the sphere, leaving a critical gap in rigorous methodologies for modelling and forecasting…

聚类与弱依赖数据下 U 统计量的极限理论AI 解读

This paper develops asymptotic theory and feasible inference for unbounded-kernel order-k U-statistics under clustered sampling and weakly dependent time-series. The analysis first builds the complete order-2 pipeline, moving from clustered data to exact $m$-dependence and then to near-epoch dependence. The same logic is subsequently extended to general order k greater or equal to 2. Under clustered sampling, the theory allows arbitrary within-cluster dependence and growing,…

二次型统计量的随机不变性检验及自相关应用AI 解读

Randomization testing with permutations is a very common nonparametric approach to hypothesis testing. However, randomization testing can be done with other group transformations including random rotations. In this work, we consider the problem of invariance in quadratic form statistics under a unified framework with closed form p-values. In particular, we propose a nonparametric variant of the classic Durbin-Watson test for testing for autocorrelation in time series data at…

利用多分位数稳健检验多变量波动率的结构变化AI 解读

We propose an omnibus nonparametric test for structural changes in the multivariate volatility matrix. The test aggregates bounded generalized quantile scores over a range of quantile levels and has a weighted leave-$q$-out $U$-statistic representation. Deleting nearby index pairs renders the centering effect induced by serial dependence asymptotically negligible. All quantities required for implementation, including the variance estimator used for standardization, are…