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重尾时间序列的自归一化部分和AI 解读

We study the joint limit behavior of sums, maxima and $\ell^p$-type moduli for samples taken from an $\mathbb{R}^d$-valued regularly varying stationary sequence with infinite variance. As a consequence, we can determine the distributional limits for ratios of sums and maxima, studentized sums, and other self-normalized quantities in terms of hybrid characteristic functions and Laplace transforms. These transforms enable one to calculate moments of the limits and to…

基于注意力 Transformer 神经网络的通胀预测AI 解读

Inflation is a major determinant for allocation decisions and its forecast is a fundamental aim of governments and central banks. However, forecasting inflation is not a trivial task, as its prediction relies on low frequency, highly fluctuating data with unclear explanatory variables. While classical models show some possibility of predicting inflation, reliably beating the random walk benchmark remains difficult. Recently, (deep) neural networks have shown impressive…

大维因子模型的 Huber 主成分分析AI 解读

Factor models have been widely used in economics and finance. However, the heavy-tailed nature of macroeconomic and financial data is often neglected in the existing literature. To address this issue and achieve robustness, we propose an approach to estimate factor loadings and scores by minimizing the Huber loss function, which is motivated by the equivalence of conventional Principal Component Analysis (PCA) and the constrained least squares method in the factor model. We…

维度坍缩：低误差无限期预测的最优测量选择AI 解读

This work introduces a method to select linear functional measurements of a vector-valued time series optimized for forecasting distant time-horizons. By formulating and solving the problem of sequential linear measurement design as an infinite-horizon problem with the time-averaged trace of the Cramér-Rao lower bound (CRLB) for forecasting as the cost, the most informative data can be collected irrespective of the eventual forecasting algorithm. By introducing theoretical…

利用能量距离聚类多变量时间序列AI 解读

A novel methodology is proposed for clustering multivariate time series data using energy distance defined in Székely and Rizzo (2013). Specifically, a dissimilarity matrix is formed using the energy distance statistic to measure separation between the finite dimensional distributions for the component time series. Once the pairwise dissimilarity matrix is calculated, a hierarchical clustering method is then applied to obtain the dendrogram. This procedure is completely…

高维依赖数据的中心极限定理AI 解读

Motivated by statistical inference problems in high-dimensional time series data analysis, we first derive non-asymptotic error bounds for Gaussian approximations of sums of high-dimensional dependent random vectors on hyper-rectangles, simple convex sets and sparsely convex sets. We investigate the quantitative effect of temporal dependence on the rates of convergence to a Gaussian random vector over three different dependency frameworks ($α$-mixing, $m$-dependent, and…

sparseDFM：估计稀疏载荷动态因子模型的 R 包AI 解读

sparseDFM is an R package for the implementation of popular estimation methods for dynamic factor models (DFMs) including the novel Sparse DFM approach of Mosley et al. (2023). The Sparse DFM ameliorates interpretability issues of factor structure in classic DFMs by constraining the loading matrices to have few non-zero entries (i.e. are sparse). Mosley et al. (2023) construct an efficient expectation maximisation (EM) algorithm to enable estimation of model parameters using…

完全贝叶斯熵估计AI 解读

Estimating the entropy rate of discrete time series is a challenging problem with important applications in numerous areas including neuroscience, genomics, image processing and natural language processing. A number of approaches have been developed for this task, typically based either on universal data compression algorithms, or on statistical estimators of the underlying process distribution. In this work, we propose a fully-Bayesian approach for entropy estimation.…

稀疏动态因子模型：正则化准最大似然方法AI 解读

The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it is often hard to interpret the meaning of the latent factors. This paper formally introduces a class of sparse DFMs whereby the loading matrices are constrained to have few non-zero entries, thus increasing interpretability of factors. We…

贝叶斯上下文树的后验表示：抽样、估计与收敛AI 解读

We revisit the Bayesian Context Trees (BCT) modelling framework for discrete time series, which was recently found to be very effective in numerous tasks including model selection, estimation and prediction. A novel representation of the induced posterior distribution on model space is derived in terms of a simple branching process, and several consequences of this are explored in theory and in practice. First, it is shown that the branching process representation leads to a…

自协方差与互协方差无偏估计的贝塞尔校正实现AI 解读

To derive the auto-covariance function from a sampled and time-limited signal or the cross-covariance function from two such signals, the mean values must be estimated and removed from the signals. If no a priori information about the correct mean values is available and the mean values must be derived from the time series themselves, the estimates will be biased. For the estimation of the variance from independent data the appropriate correction is widely known as Bessel's…

分布值自回归与迭代运输AI 解读

We consider the problem of defining and fitting models of autoregressive time series of probability distributions on a compact interval of $\mathbb{R}$. An order-$1$ autoregressive model in this context is to be understood as a Markov chain, where one specifies a certain structure (regression) for the one-step conditional Fréchet mean with respect to a natural probability metric. We construct and explore different models based on iterated random function systems of optimal…

用于多变量重症监护数据的贝叶斯非平稳异方差时间序列模型AI 解读

We propose a multivariate GARCH model for non-stationary health time series by modifying the variance of the observations of the standard state space model. The proposed model provides an intuitive way of dealing with heteroskedastic data using the conditional nature of state space models. We follow the Bayesian paradigm to perform the inference procedure. In particular, we use Markov chain Monte Carlo methods to obtain samples from the resultant posterior distribution. Due…

Ms.FPOP：采用多尺度惩罚的精确快速分段算法AI 解读

Given a time series in $R^n$ with a piecewise constant mean and independent noises, we propose an exact dynamic programming algorithm to minimize a least square criterion with a multiscale penalty promoting well-spread changepoints. Such a penalty has been proposed in Verzelen et al. (2020), and it achieves optimal rates for changepoint detection and changepoint localization. Our proposed algorithm, named Ms.FPOP, extends functional pruning ideas of Rigaill (2015) and…

高维向量自回归中的提升法 p 值AI 解读

Assessing the statistical significance of parameter estimates is an important step in high-dimensional vector autoregression modeling. Using the least-squares boosting method, we compute the p-value for each selected parameter at every boosting step in a linear model. The p-values are asymptotically valid and also adapt to the iterative nature of the boosting procedure. Our simulation experiment shows that the p-values can keep false positive rate under control in…

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…

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 $k$…

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…

具有较弱载荷的近似因子模型AI 解读

Pervasive cross-section dependence is increasingly recognized as a characteristic of economic data and the approximate factor model provides a useful framework for analysis. Assuming a strong factor structure where $\Lop\Lo/N^α$ is positive definite in the limit when $α=1$, early work established convergence of the principal component estimates of the factors and loadings up to a rotation matrix. This paper shows that the estimates are still consistent and asymptotically…

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…