每日简报

高维时间序列的动态矩阵因子模型AI 解读

Matrix time series, which consist of matrix-valued data observed over time, are prevalent in various fields such as economics, finance, and engineering. Such matrix time series data are often observed in high dimensions. Matrix factor models are employed to reduce the dimensionality of such data, but they lack the capability to make predictions without specified dynamics in the latent factor process. To address this issue, we propose a two-component dynamic matrix factor…

降秩矩阵自回归模型：面向中等维度的方法AI 解读

Reduced-rank regressions are powerful tools used to identify co-movements within economic time series. However, this task becomes challenging when we observe matrix-valued time series, where each dimension may have a different co-movement structure. We propose reduced-rank regressions with a tensor structure for the coefficient matrix to provide new insights into co-movements within and between the dimensions of matrix-valued time series. Moreover, we relate the co-movement…

函数型时间序列中的渐进变化AI 解读

We consider the problem of detecting gradual changes in the sequence of mean functions from a not necessarily stationary functional time series. Our approach is based on the maximum deviation (calculated over a given time interval) between a benchmark function and the mean functions at different time points. We speak of a gradual change of size $Δ$, if this quantity exceeds a given threshold $Δ>0$. For example, the benchmark function could represent an average of yearly…

高维向量与张量时间序列的重尾稳健因子建模AI 解读

We study the problem of factor modelling vector- and tensor-valued time series in the presence of heavy tails in the data, which produce extreme observations with non-negligible probability. We propose to combine a two-step procedure for tensor decomposition with data truncation, which is easy to implement and does not require an iterative search for a numerical solution. Departing away from the light-tail assumptions often adopted in the time series factor modelling…

主成分因子置信区域构造中的特异成分横截面相关处理AI 解读

In this paper, we propose a computationally simple estimator of the asymptotic covariance matrix of the Principal Components (PC) factors valid in the presence of cross-correlated idiosyncratic components. The proposed estimator of the asymptotic Mean Square Error (MSE) of PC factors is based on adaptive thresholding the sample covariances of the id iosyncratic residuals with the threshold based on their individual variances. We compare the nite sample performance of…

特定因子模型样本相关矩阵有界与发散特征值的渐近位置及成分保留规则AI 解读

Let the dimension $N$ of data and the sample size $T$ tend to $\infty$ with $N/T \to c > 0$. The spectral properties of a sample correlation matrix $\mathbf{C}$ and a sample covariance matrix $\mathbf{S}$ are asymptotically equal whenever the population correlation matrix $\mathbf{R}$ is bounded (El Karoui 2009). We demonstrate this also for general linear models for unbounded $\mathbf{R}$, by examining the behavior of the singular values of multiplicatively perturbed…

通胀即时预测中的 MIDAS 与 Lag-Llama 模型比较AI 解读

Inflation is one of the most important economic indicators closely watched by both public institutions and private agents. This study compares the performance of a traditional econometric model, Mixed Data Sampling regression, with one of the newest developments from the field of Artificial Intelligence, a foundational time series forecasting model based on a Long short-term memory neural network called Lag-Llama, in their ability to nowcast the Harmonized Index of Consumer…

平稳时间序列模型创新项正态性的信息矩阵检验AI 解读

This study focuses on the problem of testing for normality of innovations in stationary time series models.To achieve this, we introduce an information matrix (IM) based test. While the IM test was originally developed to test for model misspecification, our study addresses that the test can also be used to test for the normality of innovations in various time series models. We provide sufficient conditions under which the limiting null distribution of the test statistics…

通过高维贝叶斯协整构建低波动股票组合AI 解读

We employ a Bayesian modelling technique for high dimensional cointegration estimation to construct low volatility portfolios from a large number of stocks. The proposed Bayesian framework effectively identifies sparse and important cointegration relationships amongst large baskets of stocks across various asset spaces, resulting in portfolios with reduced volatility. Such cointegration relationships persist well over the out-of-sample testing time, providing practical…

多元自回归二元模型的理论与推断：生态出现数据应用AI 解读

We introduce a general class of autoregressive models for studying the dynamic of multivariate binary time series with stationary exogenous covariates. Using a high-level set of assumptions, we show that existence of a stationary path for such models is almost automatic and does not require parameter restrictions when the noise term is not compactly supported. We then study in details statistical inference in a dynamic version of a multivariate probit type model, as a…

具有双向门限的矩阵自回归模型AI 解读

Recently, matrix-valued time series data have attracted significant attention in the literature with the recognition of threshold nonlinearity representing a significant advance. However, given the fact that a matrix is a two-array structure, it is unfortunate, perhaps even unusual, for the threshold literature to focus on using the same threshold variable for the rows and the columns. In fact, evidence in economic, financial, environmental and other data shows advantages of…

JANET：时间序列联合自适应预测区域估计AI 解读

Conformal prediction provides machine learning models with prediction sets that offer theoretical guarantees, but the underlying assumption of exchangeability limits its applicability to time series data. Furthermore, existing approaches struggle to handle multi-step ahead prediction tasks, where uncertainty estimates across multiple future time points are crucial. We propose JANET (Joint Adaptive predictioN-region Estimation for Time-series), a novel framework for…

LETS-C：利用文本嵌入进行时间序列分类AI 解读

Recent advancements in language modeling have shown promising results when applied to time series data. In particular, fine-tuning pre-trained large language models (LLMs) for time series classification tasks has achieved state-of-the-art (SOTA) performance on standard benchmarks. However, these LLM-based models have a significant drawback due to the large model size, with the number of trainable parameters in the millions. In this paper, we propose an alternative approach…

稀疏渐近主成分分析：识别高维时间序列中跨时间的稀疏潜在因子AI 解读

This paper introduces a novel sparse latent factor modeling framework using sparse asymptotic Principal Component Analysis (APCA) to analyze the co-movements of high-dimensional panel data over time. Unlike existing methods based on sparse PCA, which assume sparsity in the loading matrices, our approach posits sparsity in the factor processes while allowing non-sparse loadings. This is motivated by the fact that financial returns typically exhibit universal and non-sparse…

极端事件中的格兰杰因果关系AI 解读

We introduce a rigorous mathematical framework for Granger causality in extremes, designed to identify causal links from extreme events in time series. Granger causality plays a pivotal role in uncovering directional relationships among time-varying variables. While this notion gains heightened importance during extreme and highly volatile periods, state-of-the-art methods primarily focus on causality within the body of the distribution, often overlooking causal mechanisms…

高维函数型时间序列的因子建模AI 解读

Many economic and scientific problems involve the analysis of high-dimensional functional time series, where the number of functional variables $p$ diverges as the number of serially dependent observations $n$ increases. In this paper, we present a novel functional factor model for high-dimensional functional time series that maintains and makes use of the functional and dynamic structure to achieve great dimension reduction and find the latent factor structure. To estimate…

检验因子增强回归中的稀疏特异成分AI 解读

We propose a novel bootstrap test of a dense model, namely factor regression, against a sparse plus dense alternative augmenting model with sparse idiosyncratic components. The asymptotic properties of the test are established under time series dependence and polynomial tails. We outline a data-driven rule to select the tuning parameter and prove its theoretical validity. In simulation experiments, our procedure exhibits high power against sparse alternatives and low power…