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贝叶斯马尔可夫转换向量自回归过程AI 解读

This study introduces marginal density functions of the general Bayesian Markov-Switching Vector Autoregressive (MS-VAR) process. In the case of the Bayesian MS-VAR process, we provide closed-form density functions and Monte-Carlo simulation algorithms, including the importance sampling method. The Monte-Carlo simulation method departs from the previous simulation methods because it removes the duplication in a regime vector.

具有随机波动率的大型贝叶斯张量 VARAI 解读

We consider Bayesian tensor vector autoregressions (TVARs) in which the VAR coefficients are arranged as a three-dimensional array or tensor, and this coefficient tensor is parameterized using a low-rank CP decomposition. We develop a family of TVARs using a general stochastic volatility specification, which includes a wide variety of commonly-used multivariate stochastic volatility and COVID-19 outlier-augmented models. In a forecasting exercise involving 40 US quarterly…

广义脉冲响应与多期因果关系的简便稳健两阶段估计与推断AI 解读

This paper introduces a novel two-stage estimation and inference procedure for generalized impulse responses (GIRs). GIRs encompass all coefficients in a multi-horizon linear projection model of future outcomes of y on lagged values (Dufour and Renault, 1998), which include the Sims' impulse response. The conventional use of Least Squares (LS) with heteroskedasticity- and autocorrelation-consistent covariance estimation is less precise and often results in unreliable finite…

利用张量分解的向量自回归贝叶斯推断AI 解读

Vector autoregressions (VARs) are popular model for analyzing multivariate economic time series. However, VARs can be over-parameterized if the numbers of variables and lags are moderately large. Tensor VAR, a recent solution to over-parameterization, treats the coefficient matrix as a third-order tensor and estimates the corresponding tensor decomposition to achieve parsimony. In this paper, we employ the Tensor VAR structure with a CANDECOMP/PARAFAC (CP) decomposition and…

非线性结构 VAR 中的共同趋势与长期识别AI 解读

While it is widely recognised that linear (structural) VARs may fail to capture important aspects of economic time series, the use of nonlinear SVARs has to date been almost entirely confined to the modelling of stationary time series, because of a lack of understanding as to how common stochastic trends may be accommodated within nonlinear models. This has unfortunately circumscribed the range of series to which such models can be applied -- and/or required that these…

异质性时间序列的惩罚化子群划分AI 解读

Interest in the study and analysis of dynamic processes in the social, behavioral, and health sciences has burgeoned in recent years due to the increased availability of intensive longitudinal data. However, how best to model and account for the persistent heterogeneity characterizing such processes remains an open question. The multi-VAR framework, a recent methodological development built on the vector autoregressive model, accommodates heterogeneous dynamics in…

多变量计数时间序列分析的潜在空间模型AI 解读

Motivated by a dataset of burglaries in Chicago, USA, we introduce a novel framework to analyze time series of count data combining common multivariate time series models with latent position network models. This novel methodology allows us to gain a new latent variable perspective on the crime dataset that we consider, allowing us to disentangle and explain the complex patterns exhibited by the data, while providing a natural time series framework that can be used to make…

过程图上的因果推断（一）：结构方程过程表示AI 解读

When dealing with time series data, causal inference methods often employ structural vector autoregressive (SVAR) processes to model time-evolving random systems. In this work, we rephrase recursive SVAR processes with possible latent component processes as a linear Structural Causal Model (SCM) of stochastic processes on a simple causal graph, the process graph, that models every process as a single node. Using this reformulation, we generalise Wright's well-known path-rule…

过程图上的因果推断（二）：因果结构与效应识别AI 解读

A structural vector autoregressive (SVAR) process is a linear causal model for variables that evolve over a discrete set of time points and between which there may be lagged and instantaneous effects. The qualitative causal structure of an SVAR process can be represented by its finite and directed process graph, in which a directed link connects two processes whenever there is a lagged or instantaneous effect between them. At the process graph level, the causal structure of…

局部投影的推断AI 解读

Inference for impulse responses estimated with local projections presents interesting challenges and opportunities. Analysts typically want to assess the precision of individual estimates, explore the dynamic evolution of the response over particular regions, and generally determine whether the impulse generates a response that is any different from the null of no effect. Each of these goals requires a different approach to inference. In this article, we provide an overview…

对非平稳性稳健的预白化长期方差估计AI 解读

We introduce a nonparametric nonlinear VAR prewhitened long-run variance (LRV) estimator for the construction of standard errors robust to autocorrelation and heteroskedasticity that can be used for hypothesis testing in a variety of contexts including the linear regression model. Existing methods either are theoretically valid only under stationarity and have poor finite-sample properties under nonstationarity (i.e., fixed-b methods), or are theoretically valid under the…

利用随机分块网络对 VAR 精度矩阵进行贝叶斯建模AI 解读

Commonly used priors for Vector Autoregressions (VARs) induce shrinkage on the autoregressive coefficients. Introducing shrinkage on the error covariance matrix is sometimes done but, in the vast majority of cases, without considering the network structure of the shocks and by placing the prior on the lower Cholesky factor of the precision matrix. In this paper, we propose a prior on the VAR error precision matrix directly. Our prior, which resembles a standard spike and…

利用工具变量时间序列识别因果效应：辅助变量与历史依赖调整AI 解读

Instrumental variable (IV) regression relies on instruments to infer causal effects from observational data with unobserved confounding. We consider IV regression in time series models, such as vector auto-regressive (VAR) processes. Direct applications of i.i.d. techniques are generally inconsistent as they do not correctly adjust for dependencies in the past. In this paper, we outline the difficulties that arise due to time structure and propose methodology for…

多重等式与不等式约束下大型贝叶斯 VAR 的条件预测AI 解读

Conditional forecasts, i.e. projections of a set of variables of interest on the future paths of some other variables, are used routinely by empirical macroeconomists in a number of applied settings. In spite of this, the existing algorithms used to generate conditional forecasts tend to be very computationally intensive, especially when working with large Vector Autoregressions or when multiple linear equality and inequality constraints are imposed at once. We introduce a…

VARX 格兰杰分析：建模、推断与应用AI 解读

Complex systems, such as brains, markets, and societies, exhibit internal dynamics influenced by external factors. Disentangling delayed external effects from internal dynamics within these systems is often challenging. We propose using a Vector Autoregressive model with eXogenous input (VARX) to capture delayed interactions between internal and external variables. While this model aligns with Granger's statistical formalism for testing "causal relations", the connection…

向量自回归移动平均模型综述AI 解读

Vector AutoRegressive Moving Average (VARMA) models form a powerful and general model class for analyzing dynamics among multiple time series. While VARMA models encompass the Vector AutoRegressive (VAR) models, their popularity in empirical applications is dominated by the latter. Can this phenomenon be explained fully by the simplicity of VAR models? Perhaps many users of VAR models have not fully appreciated what VARMA models can provide. The goal of this review is to…

潜在因子模型协方差矩阵的结构化先验AI 解读

Factor models are widely used for dimension reduction in the analysis of multivariate data. This is achieved through decomposition of a p x p covariance matrix into the sum of two components. Through a latent factor representation, they can be interpreted as a diagonal matrix of idiosyncratic variances and a shared variation matrix, that is, the product of a p x k factor loadings matrix and its transpose. If k << p, this defines a parsimonious factorisation of the covariance…

向量自回归模型中的反事实干预AI 解读

Counterfactual reasoning allows us to explore hypothetical scenarios in order to explain the impacts of our decisions. However, addressing such inquires is impossible without establishing the appropriate mathematical framework. In this work, we introduce the problem of counterfactual reasoning in the context of vector autoregressive (VAR) processes. We also formulate the inference of a causal model as a joint regression task where for inference we use both data with and…

线性过程频域因果效应估计的渐近不确定性AI 解读

Structural vector autoregressive (SVAR) processes are commonly used time series models to identify and quantify causal interactions between dynamically interacting processes from observational data. The causal relationships between these processes can be effectively represented by a finite directed process graph - a graph that connects two processes whenever there is a direct delayed or simultaneous effect between them. Recent research has introduced a framework for…

利用两状态马尔可夫转换异方差识别贝叶斯 VEC 模型的结构冲击AI 解读

We develop a Bayesian framework for cointegrated structural VAR models identified by two-state Markovian breaks in conditional covariances. The resulting structural VEC specification with Markov-switching heteroskedasticity (SVEC-MSH) is formulated in the so-called B-parameterization, in which the prior distribution is specified directly for the matrix of the instantaneous reactions of the endogenous variables to structural innovations. We discuss some caveats pertaining to…

气候归因中的高维格兰杰因果分析AI 解读

In this paper we test for Granger causality in high-dimensional vector autoregressive models (VARs) to disentangle and interpret the complex causal chains linking radiative forcings and global temperatures. By allowing for high dimensionality in the model, we can enrich the information set with relevant natural and anthropogenic forcing variables to obtain reliable causal relations. This provides a step forward from existing climatology literature, which has mostly treated…

随机子空间局部投影AI 解读

We show how random subspace methods can be adapted to estimating local projections with many controls. Random subspace methods have their roots in the machine learning literature and are implemented by averaging over regressions estimated over different combinations of subsets of these controls. We document three key results: (i) Our approach can successfully recover the impulse response functions across Monte Carlo experiments representative of different macroeconomic…

用于动态有效连接的贝叶斯时变张量向量自回归模型AI 解读

In contemporary neuroscience, a key area of interest is dynamic effective connectivity, which is crucial for understanding the dynamic interactions and causal relationships between different brain regions. Dynamic effective connectivity can provide insights into how brain network interactions are altered in neurological disorders such as dyslexia. Time-varying vector autoregressive (TV-VAR) models have been employed to draw inferences for this purpose. However, their…

货币政策冲击的时变识别AI 解读

We propose a new Bayesian heteroskedastic Markov-switching structural vector autoregression with data-driven time-varying identification. The model selects alternative exclusion restrictions over time and, as a condition for the search, allows to verify identification through heteroskedasticity within each regime. Based on four alternative monetary policy rules, we show that a monthly six-variable system supports time variation in US monetary policy shock identification. In…