每日简报

基于稳健逐对角线低秩近似的多变量奇异谱分析AI 解读

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and engineering. However, MSSA lacks robustness against outliers because it relies on the singular value decomposition, which is very sensitive to the presence of anomalous values. MSSA can then give biased results and lead to erroneous…

结构向量自回归与高阶矩：小样本挑战及解决方法AI 解读

Generalized method of moments estimators based on higher-order moment conditions derived from independent shocks can be used to identify and estimate the simultaneous interaction in structural vector autoregressions. This study highlights two problems that arise when using these estimators in small samples. First, imprecise estimates of the asymptotically efficient weighting matrix and the asymptotic variance lead to volatile estimates and inaccurate inference. Second, many…

时变跨价格溢出的贝叶斯马尔可夫转换空间自回归模型AI 解读

The spatial autoregressive (SAR) model is extended by introducing a Markov switching dynamics for the weight matrix and spatial autoregressive parameter. The framework enables the identification of regime-specific connectivity patterns and strengths and the study of the spatiotemporal propagation of shocks in a system with a time-varying spatial multiplier matrix. The proposed model is applied to disaggregated CPI data from 15 EU countries to examine cross-price…

打开黑箱：基于神经网络的美国衰退实时预测AI 解读

Long short-term memory (LSTM) and gated recurrent unit (GRU) are used to model US recessions from 1967 to 2021. Their predictive performances are compared to those of the traditional linear models. The out-of-sample performance suggests the application of LSTM and GRU in recession forecasting, especially for longer-term forecasts. The Shapley additive explanations (SHAP) method is applied to both groups of models. The SHAP-based different weight assignments imply the…

重新审视 ARMA 模型推断：拟合改进与置信区间比较AI 解读

Autoregressive moving average (ARMA) models are widely used for analyzing time series data. However, standard likelihood-based inference methodology for ARMA models has avoidable limitations. We show that currently accepted standards for ARMA likelihood maximization frequently lead to sub-optimal parameter estimates. Existing algorithms have theoretical support, but can result in parameter estimates that correspond to a local optimum. While this possibility has been…

学习非马尔可夫行为的极限：费舍尔信息率与超额信息AI 解读

We address the fundamental limits of learning unknown parameters of any stochastic process from time-series data, and discover exact closed-form expressions for how optimal inference scales with observation length. Given a parametrized class of candidate models, the Fisher information of observed sequence probabilities lower-bounds the variance in model estimation from finite data. As sequence-length increases, the minimal variance scales as the square inverse of the length…

用数论将无限时间序列图投影为有限边际图AI 解读

In recent years, a growing number of method and application works have adapted and applied the causal-graphical-model framework to time series data. Many of these works employ time-resolved causal graphs that extend infinitely into the past and future and whose edges are repetitive in time, thereby reflecting the assumption of stationary causal relationships. However, most results and algorithms from the causal-graphical-model framework are not designed for infinite graphs.…

贝叶斯向量自回归与随机波动AI 解读

Bayesian vector autoregressions (BVARs) are the workhorse in macroeconomic forecasting. Research in the last decade has established the importance of allowing time-varying volatility to capture both secular and cyclical variations in macroeconomic uncertainty. This recognition, together with the growing availability of large datasets, has propelled a surge in recent research in building stochastic volatility models suitable for large BVARs. Some of these new models are also…

面向单通道应用的潜变量模型谱正则化框架AI 解读

Latent variable models (LVMs) are commonly used to capture the underlying dependencies, patterns, and hidden structure in observed data. Source duplication is a by-product of the data hankelisation pre-processing step common to single channel LVM applications, which hinders practical LVM utilisation. In this article, a Python package titled spectrally-regularised-LVMs is presented. The proposed package addresses the source duplication issue via the addition of a novel…

捕捉潜在波动信息的分解集成时间序列预测框架AI 解读

Time series forecasting represents a significant and challenging task across various fields. Recently, methods based on mode decomposition have dominated the forecasting of complex time series because of the advantages of capturing local characteristics and extracting intrinsic modes from data. Unfortunately, most models fail to capture the implied volatilities that contain significant information. To enhance the prediction of contemporary diverse and complex time series, we…

亚稳态金融市场AI 解读

Metastability is a phenomenon observed in stochastic systems which stay in a false-equilibrium within a region of its state space until the occurrence of a sequence of rare events that leads to an abrupt transition to a different region. This paper presents financial markets as metastable systems and shows that, under this assumption, financial time series evolve as hidden Markov models. In special, we propose a theory that outlines an explicit causal relation between a…

谱 Rényi 散度的稳健性AI 解读

This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $α$-Rényi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to highlight both information-theoretic and statistical properties of spectral $α$-Rényi divergences. We reveal the connection between the spectral $α$-Rényi divergence and the $γ$-divergence in robust statistics, and a variational representation of the…

利用经验能量距离检测函数型数据的变点AI 解读

We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints, including the "classical" case of changes in the mean, and even changes in the whole distribution. Our statistics are based on a generalisation of the empirical energy distance; we propose weighted functionals of the energy distance process,…

非独立同分布创新下高维向量自回归时间序列的统计推断AI 解读

Independent or i.i.d. innovations is an essential assumption in the literature for analyzing a vector time series. However, this assumption is either too restrictive for a real-life time series to satisfy or is hard to verify through a hypothesis test. This paper performs statistical inference on a sparse high-dimensional vector autoregressive time series, allowing its white noise innovations to be dependent, even non-stationary. To achieve this goal, it adopts a…

高维投影样本协方差的极值渐近理论及金融与卷积网络应用AI 解读

Maximum-type statistics of certain functions of the sample covariance matrix of high-dimensional vector time series are studied to statistically confirm or reject the null hypothesis that a data set has been collected under normal conditions. The approach generalizes the case of the maximal deviation of the sample autocovariances function from its assumed values. Within a linear time series framework it is shown that Gumbel-type extreme value asymptotics holds true. As…

含协变量计数时间序列模型的设定检验AI 解读

We propose a goodness-of-fit test for a class of count time series models with covariates which includes the Poisson autoregressive model with covariates (PARX) as a special case. The test criteria are derived from a specific characterization for the conditional probability generating function and the test statistic is formulated as a $L_2$ weighting norm of the corresponding sample counterpart. The asymptotic properties of the proposed test statistic are provided under the…

泊松计数时间序列AI 解读

This paper reviews and compares popular methods, some old and some very recent, that produce time series having Poisson marginal distributions. The paper begins by narrating ways where time series with Poisson marginal distributions can be produced. Modeling nonstationary series with covariates motivates consideration of methods where the Poisson parameter depends on time. Here, estimation methods are developed for some of the more flexible methods. The results are used in…

多条相依异方差时间序列的新模型AI 解读

Functional magnetic resonance imaging or functional MRI (fMRI) is a very popular tool used for differing brain regions by measuring brain activity. It is affected by physiological noise, such as head and brain movement in the scanner from breathing, heart beats, or the subject fidgeting. The purpose of this paper is to propose a novel approach to handling fMRI data for infants with high volatility caused by sudden head movements. Another purpose is to evaluate the volatility…

混合因果—非因果、可逆—不可逆模型的谱识别与估计AI 解读

This paper introduces new techniques for estimating, identifying and simulating mixed causal-noncausal invertible-noninvertible models. We propose a framework that integrates high-order cumulants, merging both the spectrum and bispectrum into a single estimation function. The model that most adequately represents the data under the assumption that the error term is i.i.d. is selected. Our Monte Carlo study reveals unbiased parameter estimates and a high frequency with which…

动态因子模型的谱系AI 解读

Dynamic factor models have been developed out of the need of analyzing and forecasting time series in increasingly high dimensions. While mathematical statisticians faced with inference problems in high-dimensional observation spaces were focusing on the so-called spiked-model-asymptotics, econometricians adopted an entirely and considerably more effective asymptotic approach, rooted in the factor models originally considered in psychometrics. The so-called dynamic factor…

用于脑电活动分析的分层随机效应状态空间模型AI 解读

Mental disorders present challenges in diagnosis and treatment due to their complex and heterogeneous nature. Electroencephalogram (EEG) has shown promise as a potential biomarker for these disorders. However, existing methods for analyzing EEG signals have limitations in addressing heterogeneity and capturing complex brain activity patterns between regions. This paper proposes a novel random effects state-space model (RESSM) for analyzing large-scale multi-channel…

时间序列的在线自助法AI 解读

Resampling methods such as the bootstrap have proven invaluable in the field of machine learning. However, the applicability of traditional bootstrap methods is limited when dealing with large streams of dependent data, such as time series or spatially correlated observations. In this paper, we propose a novel bootstrap method that is designed to account for data dependencies and can be executed online, making it particularly suitable for real-time applications. This method…

大衰退与新冠衰退的实时预测AI 解读

This paper uses standard and penalized logistic regression models to predict the Great Recession and the Covid-19 recession in the US in real time. It examines the predictability of various macroeconomic and financial indicators with respect to the NBER recession indicator. The findings strongly support the use of penalized logistic regression models in recession forecasting. These models, particularly the ridge logistic regression model, outperform the standard logistic…

错设 Copula 模型中的反馈切断AI 解读

In copula models the marginal distributions and copula function are specified separately. We treat these as two modules in a modular Bayesian inference framework, and propose conducting modified Bayesian inference by "cutting feedback". Cutting feedback limits the influence of potentially misspecified modules in posterior inference. We consider two types of cuts. The first limits the influence of a misspecified copula on inference for the marginals, which is a Bayesian…