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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.…

多个密度值时间序列的预测AI 解读

Density-valued time series are common in practice. However, since these functions are non-negative and must integrate to one, they do not form a linear vector space, which complicates the direct application of standard time-series methods. To address these constraints, we introduce two transformations, based on the centered log-ratio transformation and the cumulative distribution function, for modeling and forecasting balanced panel data represented by multiple densities.…

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…

通过预过滤筛式自助法校正函数型时间序列长记忆估计偏差AI 解读

We investigate a bias correction procedure based on sieve bootstrapping to estimate the long-memory parameter d in stationary or nonstationary fractionally integrated processes. The resampling method implements a sieve bootstrap method on data prefiltered by a preliminary estimate of the long-memory parameter. For the initial estimate, we recommend the local polynomial Whittle with noise (LPWN) estimator in Frederiksen et al. (2012) to reduce bias, especially in the presence…

预测协调与成分数据分析：意大利分死因死亡年龄研究AI 解读

We introduce a novel approach that integrates compositional data analysis (CoDA) in the forecasting of hierarchical and grouped time series and apply it to improve mortality forecasts. By leveraging the inherent decomposition of mortality data by cause of death and sex, our framework addresses key challenges in mortality forecasting, ensuring internal coherence across different levels of aggregation while maintaining high predictive accuracy. Our empirical results on Italian…

高维函数型时间序列预测的可解释模型AI 解读

We study the modeling and forecasting of high-dimensional functional time series, which can be temporally dependent and cross-sectionally correlated. Central to our implementation is a functional analysis of variance by decomposing high-dimensional functional time series, such as subnational age- and sex-specific mortality observed over years, into two distinct components: a deterministic mean structure and a residual process varying over time. Unlike purely statistical…

比例时间序列的 Beta-GAM 隐 Markov 模型AI 解读

We propose a hidden Markov model for univariate proportion time series taking values in (0,1), where regime switching captures latent structural changes and the emission distribution belongs to the Beta family. In each latent state, the Beta mean is linked to covariates through a generalized additive model (GAM) with spline-based smooth functions, while the Beta precision is state-specific, enabling flexible modeling of both nonlinear covariate effects and regime-dependent…

高维函数型时间序列中伪因子的来源分解AI 解读

This article explores a general factor structure for high-dimensional nonstationary functional time series, encompassing a wide range of factor models studied in the existing literature. We investigate the asymptotic spectral behaviors of the sample covariance operator under this general data structure. A novel fundamental sufficient condition, formulated in terms of a newly introduced effective rank tailored to this setup, is established under which empirical eigen-analysis…

高维函数型时间序列的共形预测：地方死亡率应用AI 解读

In statistics, forecast uncertainty is often quantified using a specified statistical model, though such approaches may be vulnerable to model misspecification, selection bias, and limited finite-sample validity. While bootstrapping can potentially mitigate some of these concerns, it is often computationally demanding. Instead, we take a model-agnostic and distribution-free approach, namely conformal prediction, to construct prediction intervals in high-dimensional…

函数型时间序列的整数单整检验AI 解读

We develop a statistical testing procedure to examine whether the curve-valued time series of interest is integrated of order d for an integer d. The proposed procedure can distinguish between integer-integrated time series and fractionally-integrated ones, and it has broad applicability in practice. Monte Carlo simulation experiments show that the proposed testing procedure performs reasonably well. We apply our methodology to Canadian yield curve data and French…

高维时间序列的自回归筛自助法AI 解读

This paper proposes a new AR-sieve bootstrap approach to high-dimensional time series. The major challenge of classical bootstrap methods on high-dimensional time series is two-fold: curse of dimensionality and temporal dependence. To address such a difficulty, we utilize factor modeling to reduce dimension and capture temporal dependence simultaneously. A factor-based bootstrap procedure is constructed, which performs an AR-sieve bootstrap on the extracted low-dimensional…

分析高维函数型时间序列的可解释加性模型AI 解读

High-dimensional functional time series offers a powerful framework for extending functional time series analysis to settings with multiple simultaneous dimensions, capturing both temporal dynamics and cross-sectional dependencies. We propose a novel, interpretable additive model tailored for such data, designed to deliver both high predictive accuracy and clear interpretability. The model features bivariate coefficient surfaces to represent relationships across panel…

生命表死亡人数建模与预测的加权成分函数型数据分析AI 解读

Age-specific life-table death counts observed over time are examples of densities. Non-negativity and summability are constraints that sometimes require modifications of standard linear statistical methods. The centered log-ratio transformation presents a mapping from a constrained to a less constrained space. With a time series of densities, forecasts are more relevant to the recent data than the data from the distant past. We introduce a weighted compositional functional…

空间标量对函数分位数回归模型AI 解读

This paper introduces a novel spatial scalar-on-function quantile regression model that extends classical scalar-on-function models to account for spatial dependence and heterogeneous conditional distributions. The proposed model incorporates spatial autocorrelation through a spatially lagged response and characterizes the entire conditional distribution of a scalar outcome given a functional predictor. To address the endogeneity induced by the spatial lag term, we develop…

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…

日内颗粒物粒径数量分布预测：函数型时间序列方法AI 解读

Particulate matter data now include various particle sizes, which often manifest as a collection of curves observed sequentially over time. When considering 51 distinct particle sizes, these curves form a high-dimensional functional time series observed over equally spaced and densely sampled grids. While high dimensionality poses statistical challenges due to the curse of dimensionality, it also offers a rich source of information that enables detailed analysis of temporal…

函数型 GARCH 方法的日内外汇波动率曲线预测AI 解读

This paper seeks to forecast intraday volatility curves for major foreign exchange (FX) currencies using functional GARCH models. Intraday return curves are observed at a daily frequency, yet preserve the full high-frequency trading structure, enabling volatility analysis at the intraday level. We demonstrate that the USD/EUR, USD/GBP, and USD/JPY intraday return curves exhibit strong cross-dependence, while individually they are serially uncorrelated but display long-range…

结合偏态正态分布与隐马尔可夫模型扩展时间序列有限混合模型AI 解读

We introduce an extension of finite mixture models by incorporating skew-normal distributions within a Hidden Markov Model framework. By assuming a constant transition probability matrix and allowing emission distributions to vary according to hidden states, the proposed model effectively captures dynamic dependencies between variables. Through the estimation of state-specific parameters, including location, scale, and skewness, the proposed model enables the detection of…

为死亡年龄分布构造预测区间AI 解读

We introduce a model-agnostic procedure to construct prediction intervals for the age distribution of deaths. The age distribution of deaths is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation and a cumulative distribution function transformation are used to remove the two constraints, where the latter transformation can also handle the presence of zero counts. Our general procedure divides data…

生命表死亡人数年龄分布的自助预测区间AI 解读

We introduce a nonparametric bootstrap procedure based on a dynamic factor model to construct pointwise prediction intervals for period life-table death counts. The age distribution of death counts is an example of constrained data, which are nonnegative and have a constrained integral. A centered log-ratio transformation is used to remove the constraints. With a time series of unconstrained data, we introduce our bootstrap method to construct prediction intervals, thereby…

洛伦兹曲线时间序列预测：单因素函数型方差分析AI 解读

The Lorenz curve is a fundamental tool for analysing income and wealth distribution and inequality at national and regional levels. We utilise a one-way functional analysis of variance to decompose a time series of Lorenz curves and develop a method for producing one-step-ahead point and interval forecasts. The one-way functional analysis of variance is easily interpretable by decomposing an array into a functional grand effect, a functional row effect and residual…

基于依赖结构的函数型时间序列模糊聚类AI 解读

Time series clustering is essential in scientific applications, yet methods for functional time series, collections of infinite-dimensional curves treated as random elements in a Hilbert space, remain underdeveloped. This work presents clustering approaches for functional time series that combine the fuzzy $C$-medoids and fuzzy $C$-means procedures with a novel dissimilarity measure tailored for functional data. This dissimilarity is based on an extension of the quantile…

密度值函数型面板数据的预测AI 解读

We introduce a statistical method for modeling and forecasting functional panel data represented by multiple densities. Density functions are nonnegative and have a constrained integral and thus do not constitute a linear vector space. We implement a center log-ratio transformation to transform densities into unconstrained functions. These functions exhibit cross-sectional correlation and temporal dependence. Via a functional analysis of variance decomposition, we decompose…

非平稳函数型时间序列预测AI 解读

We propose a nonstationary functional time series forecasting method with an application to age-specific mortality rates observed over the years. The method begins by taking the first-order differencing and estimates its long-run covariance function. Through eigen-decomposition, we obtain a set of estimated functional principal components and their associated scores for the differenced series. These components allow us to reconstruct the original functional data and compute…