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基于函数主成分混合模型的物候曲线估计AI 解读

Vegetation phenology consists of studying synchronous stationary events, such as the vegetation green up and leaves senescence, that can be construed as adaptive responses to climatic constraints. In this paper, we propose a method to estimate the annual phenology curve from multi-annual observations of time series of vegetation indices derived from satellite images. We fitted the classical harmonic regression model to annual-based time series in order to construe the…

弱依赖函数型时间序列的自适应估计AI 解读

The local regularity of functional time series is studied under $L^p-m-$appro\-ximability assumptions. The sample paths are observed with error at possibly random design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric mean and autocovariance functions estimators that adapt to the regularity and the design, which can be sparse or dense. We also derive the asymptotic normality of the mean…

经济固定事件预测的预测区间AI 解读

The fixed-event forecasting setup is common in economic policy. It involves a sequence of forecasts of the same (`fixed') predictand, so that the difficulty of the forecasting problem decreases over time. Fixed-event point forecasts are typically published without a quantitative measure of uncertainty. To construct such a measure, we consider forecast postprocessing techniques tailored to the fixed-event case. We develop regression methods that impose constraints motivated…

营销时间序列的多重分形小波动态模态分解建模AI 解读

Marketing is the way we ensure our sales are the best in the market, our prices the most accessible, and our clients satisfied, thus ensuring our brand has the widest distribution. This requires sophisticated and advanced understanding of the whole related network. Indeed, marketing data may exist in different forms such as qualitative and quantitative data. However, in the literature, it is easily noted that large bibliographies may be collected about qualitative studies,…

kDGLM：广义动态线性模型贝叶斯分析的 R 包AI 解读

This paper introduces kDGLM, an R package designed for Bayesian analysis of Generalized Dynamic Linear Models (GDLM), with a primary focus on both uni- and multivariate exponential families. Emphasizing sequential inference for time series data, the kDGLM package provides comprehensive support for fitting, smoothing, monitoring, and feed-forward interventions. The methodology employed by kDGLM, as proposed in Alves et al. (2024), seamlessly integrates with well-established…

利用累积量生成函数进行时间序列推断AI 解读

We introduce innovative inference procedures for analyzing time series data. Our methodology enables density approximation and composite hypothesis testing based on Whittle's estimator, a widely applied M-estimator in the frequency domain. Its core feature involves the (general Legendre transform of the) cumulant generating function of the Whittle likelihood score, as obtained using an approximated distribution of the periodogram ordinates. We present a testing algorithm…

因果变化点的检测与定位AI 解读

Detecting and localizing change points in sequential data is of interest in many areas of application. Various notions of change points have been proposed, such as changes in mean, variance, or the linear regression coefficient. In this work, we consider settings in which a response variable $Y$ and a set of covariates $X=(X^1,\ldots,X^{d+1})$ are observed over time and aim to find changes in the causal mechanism generating $Y$ from $X$. More specifically, we assume $Y$ depen…

变量组因果发现的理论基础AI 解读

Discovering causal relationships from observational data is a challenging task that relies on assumptions connecting statistical quantities to graphical or algebraic causal models. In this work, we focus on widely employed assumptions for causal discovery when objects of interest are (multivariate) groups of random variables rather than individual (univariate) random variables, as is the case in a variety of problems in scientific domains such as climate science or…

密集纵向计数数据的贝叶斯多层泊松对数正态隐马尔可夫模型AI 解读

Hidden Markov models (HMMs) are probabilistic methods in which observations are seen as realizations of a latent Markov process with discrete states that switch over time. Moving beyond standard statistical tests, HMMs offer a statistical environment to optimally exploit the information present in multivariate time series, uncovering the latent dynamics that rule them. Here, we extend the Poisson HMM to the multilevel framework, accommodating variability between individuals…

面向高维数据的高效张量回归AI 解读

Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater than four or five. However, for the simplest tensor autoregression in handling time series data, its coefficient tensor already has the order of six. This paper revises a newly proposed tensor train (TT) decomposition and then applies it…

机器学习预测不确定性估计综述AI 解读

Predictions and forecasts of machine learning models should take the form of probability distributions, aiming to increase the quantity of information communicated to end users. Although applications of probabilistic prediction and forecasting with machine learning models in academia and industry are becoming more frequent, related concepts and methods have not been formalized and structured under a holistic view of the entire field. Here, we review the topic of predictive…

基于反射布朗运动的重复事件模型及其低血糖应用AI 解读

Patients with type 2 diabetes need to closely monitor blood sugar levels as their routine diabetes self-management. Although many treatment agents aim to tightly control blood sugar, hypoglycemia often stands as an adverse event. In practice, patients can observe hypoglycemic events more easily than hyperglycemic events due to the perception of neurogenic symptoms. We propose to model each patient's observed hypoglycemic event as a lower-boundary crossing event for a…

利用非抽取小波包特征与 Transformer 模型进行时间序列预测AI 解读

This article combines wavelet analysis techniques with machine learning methods for univariate time series forecasting, focusing on three main contributions. Firstly, we consider the use of Daubechies wavelets with different numbers of vanishing moments as input features to both non-temporal and temporal forecasting methods, by selecting these numbers during the cross-validation phase. Secondly, we compare the use of both the non-decimated wavelet transform and the…

高维向量误差修正模型的贝叶斯分析AI 解读

Vector Error Correction Model (VECM) is a classic method to analyse cointegration relationships amongst multivariate non-stationary time series. In this paper, we focus on high dimensional setting and seek for sample-size-efficient methodology to determine the level of cointegration. Our investigation centres at a Bayesian approach to analyse the cointegration matrix, henceforth determining the cointegration rank. We design two algorithms and implement them on simulated…

带加性噪声的周期自回归模型：估计与检验的实证研究AI 解读

Periodic autoregressive (PAR) time series with finite variance is considered as one of the most common models of second-order cyclostationary processes. However, in the real applications, the signals with periodic characteristics may be disturbed by additional noise related to measurement device disturbances or to other external sources. Thus, the known estimation techniques dedicated for PAR models may be inefficient for such cases. When the variance of the additive noise…

样本分割与时间序列拟合优度评估AI 解读

A fundamental and often final step in time series modeling is to assess the quality of fit of a proposed model to the data. Since the underlying distribution of the innovations that generate a model is often not prescribed, goodness-of-fit tests typically take the form of testing the fitted residuals for serial independence. However, these fitted residuals are inherently dependent since they are based on the same parameter estimates and thus standard tests of serial…

利用可变带通周期块自助法研究美国新冠死亡的季节与周期模式AI 解读

Since the emergence of the SARS-CoV-2 virus, research into the existence, extent, and pattern of seasonality has been of the highest importance for public health preparation. This study uses a novel bandpass bootstrap approach called the Variable Bandpass Periodic Block Bootstrap (VBPBB) to investigate the periodically correlated (PC) components including seasonality within US COVID-19 mortality. Bootstrapping to produce confidence intervals (CI) for periodic characteristics…

含噪声且异步的高频数据下因子型瞬时波动率矩阵估计AI 解读

We propose a new estimator of high-dimensional spot volatility matrices satisfying a low-rank plus sparse structure from noisy and asynchronous high-frequency data collected for an ultra-large number of assets. The noise processes are allowed to be temporally correlated, heteroskedastic, asymptotically vanishing and dependent on the efficient prices. We define a kernel-weighted pre-averaging method to jointly tackle the microstructure noise and asynchronicity issues, and we…

分组时变网络向量自回归模型的估计AI 解读

This paper introduces a flexible time-varying network vector autoregressive model framework for large-scale time series. A latent group structure is imposed on the heterogeneous and node-specific time-varying momentum and network spillover effects so that the number of unknown time-varying coefficients to be estimated can be reduced considerably. A classic agglomerative clustering algorithm with nonparametrically estimated distance matrix is combined with a ratio criterion…

灵活的全局预测组合AI 解读

Forecast combination -- the aggregation of individual forecasts from multiple experts or models -- is a proven approach to economic forecasting. To date, research on economic forecasting has concentrated on local combination methods, which handle separate but related forecasting tasks in isolation. Yet, it has been known for over two decades in the machine learning community that global methods, which exploit task-relatedness, can improve on local methods that ignore it.…

使用稀疏性排序 Lasso 进行快速、有效且一致的时间序列建模AI 解读

The sparsity-ranked lasso (SRL) has been developed for model selection and estimation in the presence of interactions and polynomials. The main tenet of the SRL is that an algorithm should be more skeptical of higher-order polynomials and interactions *a priori* compared to main effects, and hence the inclusion of these more complex terms should require a higher level of evidence. In time series, the same idea of ranked prior skepticism can be applied to the possibly…

指数平滑的新理论框架AI 解读

Simple Exponential Smoothing is a classical technique used for smoothing time series data by assigning exponentially decreasing weights to past observations through a recursive equation; it is sometimes presented as a rule of thumb procedure. We introduce a novel theoretical perspective where the recursive equation that defines simple exponential smoothing occurs naturally as a stochastic gradient ascent scheme to optimize a sequence of Gaussian log-likelihood functions.…

多元响应的回归 Copula 模型AI 解读

We propose a novel distributional regression model for a multivariate response vector based on a copula process over the covariate space. It uses the implicit copula of a Gaussian multivariate regression, which we call a ``regression copula''. To allow for large covariate vectors their coefficients are regularized using a novel multivariate extension of the horseshoe prior. Bayesian inference and distributional predictions are evaluated using efficient variational inference…

用两次交叉验证确定共同函数因子的数量AI 解读

The semiparametric factor model serves as a vital tool to describe the dependence patterns in the data. It recognizes that the common features observed in the data are actually explained by functions of specific exogenous variables.Unlike traditional factor models, where the focus is on selecting the number of factors, our objective here is to identify the appropriate number of common functions, a crucial parameter in this model. In this paper, we develop a novel data-driven…