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高维线性过程的 Bernstein 型不等式及稳健时间序列回归应用AI 解读

Time series regression models are commonly used in time series analysis. However, in modern real-world applications, serially correlated data with an ultra-high dimension and fat tails are prevalent. This presents a challenge in developing new statistical tools for time series analysis. In this paper, we propose a novel Bernstein-type inequality for high-dimensional linear processes and apply it to investigate two high-dimensional robust estimation problems: (1) time series…

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…

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…

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…

含缺失数据的高维条件高斯状态空间模型AI 解读

We develop an efficient sampling approach for handling complex missing data patterns and a large number of missing observations in conditionally Gaussian state space models. Two important examples are dynamic factor models with unbalanced datasets and large Bayesian VARs with variables in multiple frequencies. A key insight underlying the proposed approach is that the joint distribution of the missing data conditional on the observed data is Gaussian. Moreover, the inverse…

高维时间序列的时变网络估计AI 解读

We explore time-varying networks for high-dimensional locally stationary time series, using the large VAR model framework with both the transition and (error) precision matrices evolving smoothly over time. Two types of time-varying graphs are investigated: one containing directed edges of Granger causality linkages, and the other containing undirected edges of partial correlation linkages. Under the sparse structural assumption, we propose a penalised local linear method…

共识型与分歧型不确定性AI 解读

When agents' information is imperfect and dispersed, existing measures of macroeconomic uncertainty based on the forecast error variance have two distinct drivers: the variance of the economic shock and the variance of the information dispersion. The former driver increases uncertainty and reduces agents' disagreement (agreed uncertainty). The latter increases both uncertainty and disagreement (disagreed uncertainty). We use these implications to identify empirically the…

多维动态因子模型AI 解读

This paper generalises dynamic factor models for multidimensional dependent data. In doing so, it develops an interpretable technique to study complex information sources ranging from repeated surveys with a varying number of respondents to panels of satellite images. We specialise our results to model microeconomic data on US households jointly with macroeconomic aggregates. This results in a powerful tool able to generate localised predictions, counterfactuals and impulse…

基于因子调整向量自回归的高维时间序列分段AI 解读

Vector autoregressive (VAR) models are popularly adopted for modelling high-dimensional time series, and their piecewise extensions allow for structural changes in the data. In VAR modelling, the number of parameters grow quadratically with the dimensionality which necessitates the sparsity assumption in high dimensions. However, it is debatable whether such an assumption is adequate for handling datasets exhibiting strong serial and cross-sectional correlations. We propose…

结合协方差选择与阶数选择的因果向量自回归AI 解读

A causal vector autoregressive (CVAR) model is introduced for weakly stationary multivariate processes, combining a recursive directed graphical model for the contemporaneous components and a vector autoregressive model longitudinally. Block Cholesky decomposition with varying block sizes is used to solve the model equations and estimate the path coefficients along a directed acyclic graph (DAG). If the DAG is decomposable, i.e. the zeros form a reducible zero pattern (RZP)…

利用非高斯性估计因果有向无环图过程AI 解读

Numerous approaches have been proposed to discover causal dependencies in machine learning and data mining; among them, the state-of-the-art VAR-LiNGAM (short for Vector Auto-Regressive Linear Non-Gaussian Acyclic Model) is a desirable approach to reveal both the instantaneous and time-lagged relationships. However, all the obtained VAR matrices need to be analyzed to infer the final causal graph, leading to a rise in the number of parameters. To address this issue, we…

多项式尾部下稀疏高维时间序列的稳健估计AI 解读

High dimensional Vector Autoregressions (VAR) have received a lot of interest recently due to novel applications in health, engineering, finance and the social sciences. Three issues arise when analyzing VAR's: (a) The high dimensional nature of the model in the presence of many time series that poses challenges for consistent estimation of its parameters; (b) the presence of temporal dependence introduces additional challenges for theoretical analysis of various estimation…

高斯过程向量自回归与宏观经济不确定性AI 解读

We develop a non-parametric multivariate time series model that remains agnostic on the precise relationship between a (possibly) large set of macroeconomic time series and their lagged values. The main building block of our model is a Gaussian process prior on the functional relationship that determines the conditional mean of the model, hence the name of Gaussian process vector autoregression (GP-VAR). A flexible stochastic volatility specification is used to provide…

多元非平稳时间序列的逆协方差算子AI 解读

For multivariate stationary time series many important properties, such as partial correlation, graphical models and autoregressive representations are encoded in the inverse of its spectral density matrix. This is not true for nonstationary time series, where the pertinent information lies in the inverse infinite dimensional covariance matrix operator associated with the multivariate time series. This necessitates the study of the covariance of a multivariate nonstationary…

分数过程导数向分数布朗运动导数的弱收敛AI 解读

It is well known that, under suitable regularity conditions, the normalized fractional process with fractional parameter $d$ converges weakly to fractional Brownian motion for $d>1/2$. We show that, for any non-negative integer $M$, derivatives of order $m=0,1,\dots,M$ of the normalized fractional process with respect to the fractional parameter $d$, jointly converge weakly to the corresponding derivatives of fractional Brownian motion. As an illustration we apply the…

加密货币对数收益预测：LASSO-VAR 与情绪方法AI 解读

Cryptocurrencies have become a trendy topic recently, primarily due to their disruptive potential and reports of unprecedented returns. In addition, academics increasingly acknowledge the predictive power of Social Media in many fields and, more specifically, for financial markets and economics. In this paper, we leverage the predictive power of Twitter and Reddit sentiment together with Google Trends indexes and volume to forecast the log returns of ten cryptocurrencies.…

高维重尾时间序列的最优稀疏估计AI 解读

Recently, high dimensional vector auto-regressive models (VAR), have attracted a lot of interest, due to novel applications in the health, engineering and social sciences. The presence of temporal dependence poses additional challenges to the theory of penalized estimation techniques widely used in the analysis of their iid counterparts. However, recent work (e.g., [Basu and Michailidis, 2015, Kock and Callot, 2015]) has established optimal consistency of $\ell_1$-LASSO…

邻域 VAR：利用邻域信息高效估计多元时间序列AI 解读

In data science, vector autoregression (VAR) models are popular in modeling multivariate time series in the environmental sciences and other applications. However, these models are computationally complex with the number of parameters scaling quadratically with the number of time series. In this work, we propose a so-called neighborhood vector autoregression (NVAR) model to efficiently analyze large-dimensional multivariate time series. We assume that the time series have…

贝叶斯混频分位数向量自回归：刻画美国月度 GDP 尾部风险AI 解读

Timely characterizations of risks in economic and financial systems play an essential role in both economic policy and private sector decisions. However, the informational content of low-frequency variables and the results from conditional mean models provide only limited evidence to investigate this problem. We propose a novel mixed-frequency quantile vector autoregression (MF-QVAR) model to address this issue. Inspired by the univariate Bayesian quantile regression…

大型贝叶斯 VAR 的随机波动率设定比较AI 解读

Large Bayesian vector autoregressions with various forms of stochastic volatility have become increasingly popular in empirical macroeconomics. One main difficulty for practitioners is to choose the most suitable stochastic volatility specification for their particular application. We develop Bayesian model comparison methods -- based on marginal likelihood estimators that combine conditional Monte Carlo and adaptive importance sampling -- to choose among a variety of…

融合机器学习的时变参数全球向量自回归：经济动态解释与预测AI 解读

The paper proposes a time-varying parameter global vector autoregressive (TVP-GVAR) framework for predicting and analysing developed region economic variables. We want to provide an easily accessible approach for the economy application settings, where a variety of machine learning models can be incorporated for out-of-sample prediction. The LASSO-type technique for numerically efficient model selection of mean squared errors (MSEs) is selected. We show the convincing…

具有因子随机波动率的大型贝叶斯 VAR：识别、排序不变性与结构分析AI 解读

Vector autoregressions (VARs) with multivariate stochastic volatility are widely used for structural analysis. Often the structural model identified through economically meaningful restrictions--e.g., sign restrictions--is supposed to be independent of how the dependent variables are ordered. But since the reduced-form model is not order invariant, results from the structural analysis depend on the order of the variables. We consider a VAR based on the factor stochastic…

用于向量自回归的灵活贝叶斯乘积混合模型AI 解读

Bayesian non-parametric methods based on Dirichlet process mixtures have seen tremendous success in various domains and are appealing in being able to borrow information by clustering samples that share identical parameters. However, such methods can face hurdles in heterogeneous settings where objects are expected to cluster only along a subset of axes or where clusters of samples share only a subset of identical parameters. We overcome such limitations by developing a…

用于高效估计多元时变自回归模型的贝叶斯循环格型滤波器AI 解读

Nonstationary time series data exist in various scientific disciplines, including environmental science, biology, signal processing, econometrics, among others. Many Bayesian models have been developed to handle nonstationary time series. The time-varying vector autoregressive (TV-VAR) model is a well-established model for multivariate nonstationary time series. Nevertheless, in most cases, the large number of parameters presented by the model results in a high computational…