每日简报

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…

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…

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…

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…

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…

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…

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…

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…

通过序贯假设检验检测 Granger 因果关系AI 解读

Most of the metrics used for detecting a causal relationship among multiple time series ignore the effects of practical measurement impairments, such as finite sample effects, undersampling and measurement noise. It has been shown that these effects significantly impair the performance of the underlying causality test. In this paper, we consider the problem of sequentially detecting the causal relationship between two time series while accounting for these measurement…

经典谱估计量的非渐近逐点与最坏情形误差界AI 解读

Spectrum estimation is a fundamental methodology in the analysis of time-series data, with applications including medicine, speech analysis, and control design. The asymptotic theory of spectrum estimation is well-understood, but the theory is limited when the number of samples is fixed and finite. This paper gives non-asymptotic error bounds for a broad class of spectral estimators, both pointwise (at specific frequencies) and in the worst case over all frequencies. The…

高斯与计数预测经协调后的分布性质AI 解读

Reconciliation enforces coherence between hierarchical forecasts, in order to satisfy a set of linear constraints. While most works focus on the reconciliation of the point forecasts, we consider probabilistic reconciliation and we analyze the properties of the distributions reconciled via conditioning. We provide a formal analysis of the variance of the reconciled distribution, treating separately the case of Gaussian forecasts and count forecasts. We also study the…

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…

不确定的短期限制与统计识别的结构向量自回归AI 解读

This study proposes a combination of a statistical identification approach with potentially invalid short-run zero restrictions. The estimator shrinks towards imposed restrictions and stops shrinkage when the data provide evidence against a restriction. Simulation results demonstrate how incorporating valid restrictions through the shrinkage approach enhances the accuracy of the statistically identified estimator and how the impact of invalid restrictions decreases with the…

高维动态因子模型下的多重检验AI 解读

Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously distorts error rate control in large-scale inference. In this manuscript, we propose a new multiple testing procedure under dynamic factor models that is robust to nonlinear serial dependence. The idea is to integrate a new sample-splitting…

动态网络可分离模型的变点检测AI 解读

This paper studies the unsupervised change point detection problem in time series of networks using the Separable Temporal Exponential-family Random Graph Model (STERGM). Inherently, dynamic network patterns are complex due to dyadic and temporal dependence, and change points detection can identify the discrepancies in the underlying data generating processes to facilitate downstream analysis. In particular, the STERGM that utilizes network statistics and nodal attributes to…

区分宏观数据因子模型中的结构突变AI 解读

We develop a projection-based decomposition to disentangle structural breaks in the factor variance and factor loadings. Our approach yields test statistics that can be compared against standard distributions commonly used in the structural break literature. Because standard methods for estimating factor models in macroeconomics normalize the factor variance, they do not distinguish between breaks of the factor variance and factor loadings. Applying our procedure to U.S.…

缺失数据下的长记忆模型估计：插补还是直接估计？AI 解读

Among the most important models for long-range dependent time series is the class of ARFIMA$(p,d,q)$ (Autoregressive Fractionally Integrated Moving Average) models. Estimating the long-range dependence parameter $d$ in ARFIMA models is a well-studied problem, but the literature regarding the estimation of $d$ in the presence of missing data is very sparse. There are two basic approaches to dealing with the problem: missing data can be imputed using some plausible method, and…

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…

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…

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…

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…

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.…

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 $k$…

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…