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Delay-SDE-net：兼顾记忆与不确定性估计的时间序列深度学习AI 解读

To model time series accurately is important within a wide range of fields. As the world is generally too complex to be modelled exactly, it is often meaningful to assess the probability of a dynamical system to be in a specific state. This paper presents the Delay-SDE-net, a neural network model based on stochastic delay differential equations (SDDEs). The use of SDDEs with multiple delays as modelling framework makes it a suitable model for time series with memory effects,…

局部平稳时间序列的自动预测：疫情冲击下英国增加值应用AI 解读

Accurate forecasting of the U.K. gross value added (GVA) is fundamental for measuring the growth of the U.K. economy. A common nonstationarity in GVA data, such as the ABML series, is its increase in variance over time due to inflation. Transformed or inflation-adjusted series can still be challenging for classical stationarity-assuming forecasters. We adopt a different approach that works directly with the GVA series by advancing recent forecasting methods for locally…

函数型数据中随机偏微分方程实现协变差的可行中心极限定理AI 解读

This article establishes an asymptotic theory for volatility estimation in an infinite-dimensional setting. We consider mild solutions of semilinear stochastic partial differential equations and derive a stable central limit theorem for the semigroup adjusted realised covariation (SARCV), which is a consistent estimator of the integrated volatility and a generalisation of the realised quadratic covariation to Hilbert spaces. Moreover, we introduce semigroup adjusted…

分布向量自回归：刻画宏观与金融依赖关系AI 解读

Vector autoregression is an essential tool in empirical macroeconomics and finance for understanding the dynamic interdependencies among multivariate time series. In this study, we expand the scope of vector autoregression by incorporating a multivariate distributional regression framework and introducing a distributional impulse response function, providing a comprehensive view of dynamic heterogeneity. We propose a straightforward yet flexible estimation method and…

时变线性模型的长程依赖检测AI 解读

We consider the problem of testing for long-range dependence in time-varying coefficient regression models, where the covariates and errors are locally stationary, allowing complex temporal dynamics and heteroscedasticity. We develop KPSS, R/S, V/S, and K/S-type statistics based on the nonparametric residuals. Under the null hypothesis, the local alternatives as well as the fixed alternatives, we derive the limiting distributions of the test statistics. As the four types of…

时间序列的条件极端值AI 解读

Accurate modelling of the joint extremal dependence structure within a stationary time series is a challenging problem that is important in many applications.\ Several previous approaches to this problem are only applicable to certain types of extremal dependence in the time series such as asymptotic dependence, or Markov time series of finite order.\ In this paper, we develop statistical methodology for time series extremes based on recent probabilistic results that allow…

以最小预测损失保护时间序列数据AI 解读

Forecasting could be negatively impacted due to anonymization requirements in data protection legislation. To measure the potential severity of this problem, we derive theoretical bounds for the loss to forecasts from additive exponential smoothing models using protected data. Following the guidelines of anonymization from the General Data Protection Regulation (GDPR) and California Consumer Privacy Act (CCPA), we develop the $k$-nearest Time Series ($k$-nTS) Swapping and $k$…

HAR–Itô 模型与高频数据的高维 HAR 建模AI 解读

It is an important task to model realized volatilities for high-frequency data in finance and economics and, as arguably the most popular model, the heterogeneous autoregressive (HAR) model has dominated the applications in this area. However, this model suffers from three drawbacks: (i.) its heterogeneous volatility components are linear combinations of daily realized volatilities with fixed weights, which limit its flexibility for different types of assets, (ii.) it is…

eCDANs：从自相关与非平稳数据中高效发现时序因果关系（学生摘要）AI 解读

Conventional temporal causal discovery (CD) methods suffer from high dimensionality, fail to identify lagged causal relationships, and often ignore dynamics in relations. In this study, we present a novel constraint-based CD approach for autocorrelated and non-stationary time series data (eCDANs) capable of detecting lagged and contemporaneous causal relationships along with temporal changes. eCDANs addresses high dimensionality by optimizing the conditioning sets while…

通过凸规划选择多个自回归过程的滞后阶并估计稳定参数AI 解读

Motivated by a variety of applications, high-dimensional time series have become an active topic of research. In particular, several methods and finite-sample theories for individual stable autoregressive processes with known lag have become available very recently. We, instead, consider multiple stable autoregressive processes that share an unknown lag. We use information across the different processes to simultaneously select the lag and estimate the parameters. We prove…

全球温度不确定性的 ARMA 模型构建与分析AI 解读

Temperature uncertainty models for land and sea surfaces can be developed based on statistical methods. In this paper, we developed a novel time series temperature uncertainty model which is the Auto-regressive Moving Average (ARMA)(1, 1) model. The model was developed for observed annual mean temperature anomaly X(t) which is a combination of true (latent) global anomaly Y (t) for a year (t) and normal variable w(t). The uncertainty is taken as the variance of w(t) which…

具有光滑特征值的多维平稳时间序列谱密度分解AI 解读

The aim of this paper to give a multidimensional version of the classical one-dimensional case of smooth spectral density. A smooth spectral density gives an explicit method to factorize the spectral density and compute the constituents of the Wold representation of a regular weakly stationary time series. These constituents are important to give the best linear predictions of the time series.

弱条件下时间序列二阶参数的同时统计推断AI 解读

Strict stationarity is a common assumption used in the time series literature in order to derive asymptotic distributional results for second-order statistics, like sample autocovariances and sample autocorrelations. Focusing on weak stationarity, this paper derives the asymptotic distribution of the maximum of sample autocovariances and sample autocorrelations under weak conditions by using Gaussian approximation techniques. The asymptotic theory for parameter estimation…

连续时间整数值 Trawl 过程的推断与预测AI 解读

This paper develops likelihood-based methods for estimation, inference, model selection, and forecasting of continuous-time integer-valued trawl processes. The full likelihood of integer-valued trawl processes is, in general, highly intractable, motivating the use of composite likelihood methods, where we consider the pairwise likelihood in lieu of the full likelihood. Maximizing the pairwise likelihood of the data yields an estimator of the parameter vector of the model,…

DeepCAR：含变点时间序列的预测方法AI 解读

Many methods for time-series forecasting are known in classical statistics, such as autoregression, moving averages, and exponential smoothing. The DeepAR framework is a novel, recent approach for time-series forecasting based on deep learning. DeepAR has shown very promising results already. However, time series often have change points, which can degrade the DeepAR's prediction performance substantially. This paper extends the DeepAR framework by detecting and including…

基于线性高斯状态空间混合模型与 EM 算法的时间序列聚类AI 解读

In this paper, we consider the task of clustering a set of individual time series while modeling each cluster, that is, model-based time series clustering. The task requires a parametric model with sufficient flexibility to describe the dynamics in various time series. To address this problem, we propose a novel model-based time series clustering method with mixtures of linear Gaussian state space models, which have high flexibility. The proposed method uses a new…

合成控制的识别与推断：近端因果推断框架AI 解读

Synthetic control (SC) methods are commonly used to estimate the treatment effect on a single treated unit in panel data settings. An SC is a weighted average of control units built to match the treated unit, with weights typically estimated by regressing (summaries of) pre-treatment outcomes and measured covariates of the treated unit to those of the control units. However, it has been established that in the absence of a good fit, such regression estimator will generally…

奇异谱分析中不同对象的自动识别AI 解读

Approaches to automated grouping in singular spectrum analysis are considered. A new method for the identification of periodic components is proposed. The possibilities of extensions to multivariate time series and images are discussed.

无限变差跳跃与相关市场微观结构噪声下的瞬时波动率估计AI 解读

Jumps and market microstructure noise are stylized features of high-frequency financial data. It is well known that they introduce bias in the estimation of volatility (including integrated and spot volatilities) of assets, and many methods have been proposed to deal with this problem. When the jumps are intensive with infinite variation, the efficient estimation of spot volatility under serially dependent noise is not available and is thus in need. For this purpose, we…

聚合自适应模型的低成本多地电力负荷日前预测AI 解读

We focus on day-ahead electricity load forecasting of substations of the distribution network in France; therefore, our problem lies between the instability of a single consumption and the stability of a countrywide total demand. Moreover, we are interested in forecasting the loads of over one thousand substations; consequently, we are in the context of forecasting multiple time series. To that end, we rely on an adaptive methodology that provided excellent results at a…

通过强自适应在线学习改进在线共形预测AI 解读

We study the problem of uncertainty quantification via prediction sets, in an online setting where the data distribution may vary arbitrarily over time. Recent work develops online conformal prediction techniques that leverage regret minimization algorithms from the online learning literature to learn prediction sets with approximately valid coverage and small regret. However, standard regret minimization could be insufficient for handling changing environments, where…

CUTS：从不规则时间序列中进行神经网络因果发现AI 解读

Causal discovery from time-series data has been a central task in machine learning. Recently, Granger causality inference is gaining momentum due to its good explainability and high compatibility with emerging deep neural networks. However, most existing methods assume structured input data and degenerate greatly when encountering data with randomly missing entries or non-uniform sampling frequencies, which hampers their applications in real scenarios. To address this issue,…

多元因子随机波动率模型的序贯估计AI 解读

We provide a simple method to estimate the parameters of multivariate stochastic volatility models with latent factor structures. These models are very useful as they alleviate the standard curse of dimensionality, allowing the number of parameters to increase only linearly with the number of the return series. Although theoretically very appealing, these models have only found limited practical application due to huge computational burdens. Our estimation method is simple…

基于张量积 B 样条的多元隐马尔可夫模型非参数估计AI 解读

For multivariate time series driven by underlying states, hidden Markov models (HMMs) constitute a powerful framework which can be flexibly tailored to the situation at hand. However, in practice it can be challenging to choose an adequate emission distribution for multivariate observation vectors. For example, the marginal data distribution may not immediately reveal the within-state distributional form, and also the different data streams may operate on different supports,…