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大型贝叶斯 VAR 中的共同时变波动率AI 解读

The general pattern of estimated volatilities of macroeconomic and financial variables is often broadly similar. We propose two models in which conditional volatilities feature comovement and study them using U.S. macroeconomic data. The first model specifies the conditional volatilities as driven by a single common unobserved factor, plus an idiosyncratic component. We label this model BVAR with general factor stochastic volatility (BVAR-GFSV) and we show that the loss in…

测量误差下的漂移与波动率：评估过去一个世纪的货币政策冲击AI 解读

How much have the dynamics of U.S. time series changed over the last century? Has the evolution of the Federal Reserve as an institution over the 100 years altered the transmission of monetary policy shocks? To tackle these questions, we build a multivariate time series model with time-varying parameters and stochastic volatility that features measurement errors in observables. We find substantial changes in the structure of the economy. There is also large variation in the…

利用采购经理指数预测产出增长的多国方法AI 解读

This paper derives new theoretical results for forecasting with Global VAR (GVAR) models. It is shown that the presence of strong unobserved common factors can lead to an undetermined GVAR model. To solve this problem, we propose augmenting the GVAR with additional proxy equations for the strong factors and establish conditions under which forecasts from the augmented GVAR model (AugGVAR) uniformly converge in probability (as the panel dimensions N,T→j∞) to the infeasible…

多元自回归指数模型的结构分析AI 解读

We address the issue of parameter dimensionality reduction in Vector Autoregressive models (VARs) for many variables by imposing specific reduced rank restrictions on the coefficient matrices that simplify the VARs into Multivariate Autoregressive Index (MAI) models. We derive the Wold representation implied by the MAIs and show that it is closely related to that associated with dynamic factor models. Then, the theoretical analysis is extended to the case of general rank…

大型贝叶斯 VARMA 模型AI 解读

Vector Autoregressive Moving Average (VARMA) models have many theoretical properties which should make them popular among empirical macroeconomists. However, they are rarely used in practice due to over-parameterization concerns, difficulties in ensuring identification and computational challenges. With the growing interest in multivariate time series models of high dimension, these problems with VARMAs become even more acute, accounting for the dominance of VARs in this…

宏观建模中的 VARMA 识别：一种新方法AI 解读

This paper develops a new methodology for identifying the structure of VARMA time series models. The analysis proceeds by examining the echelon form and presents a fully automatic, strongly consistent, data driven approach to model specification. A novel feature of the inferential procedures developed here is that they work in terms of a canonical representation based on the Kronecker invariants in which the variables are expressed in the form of scalar dynamic structural…

高斯混合向量自回归AI 解读

This paper proposes a new nonlinear vector autoregressive (VAR) model referred to as the Gaussian mixture vector autoregressive (GMVAR) model. The GMVAR model belongs to the family of mixture vector autoregressive models and is designed for analyzing time series that exhibit regime-switching behavior. The main difference between the GMVAR model and previous mixture VAR models lies in the definition of the mixing weights that govern the regime probabilities. In the GMVAR…

结构脉冲响应的联合置信集AI 解读

Many questions of economic interest in structural VAR analysis involve estimates of multiple impulse response functions. Other questions relate to the shape of a given impulse response function. Answering these questions requires joint inference about sets of structural impulse responses, allowing for dependencies across time as well as across response functions. Such joint inference is complicated by the fact that the joint distribution of the structural impulse response…

未知时点可能存在趋势断点时的 VAR 协整秩检验AI 解读

In this paper we consider the problem of testing for the co-integration rank of a vector autoregressive process in the case where a trend break may potentially be present in the data. It is known that un-modelled trend breaks can result in tests which are incorrectly sized under the null hypothesis and inconsistent under the alternative hypothesis. Extant procedures in this literature have attempted to solve this inference problem but require the practitioner to either…

异方差向量自回归中的协整参数推断AI 解读

We consider estimation and hypothesis testing on the coefficients of the co-integrating relations and the adjustment coefficients in vector autoregressions driven by shocks which display both conditional and unconditional heteroskedasticity of a quite general and unknown form. We show that the conventional results in Johansen (1996) for the maximum likelihood estimators and associated likelihood ratio tests derived under homoskedasticity do not in general hold under…

未知形式条件异方差下的VAR推断AI 解读

We consider a framework for asymptotically valid inference in stable vector autoregressive (VAR) models with conditional heteroskedasticity of unknown form. A joint central limit theorem for the LS estimators of both the VAR slope parameters as well as the unconditional innovation variance parameters is obtained from a weak vector autoregressive moving average model set-up recently proposed in the literature. Our results are important for correct inference on VAR statistics…

结构向量自回归过程的贝叶斯图模型AI 解读

Summary This paper proposes a Bayesian, graph‐based approach to identification in vector autoregressive (VAR) models. In our Bayesian graphical VAR (BGVAR) model, the contemporaneous and temporal causal structures of the structural VAR model are represented by two different graphs. We also provide an efficient Markov chain Monte Carlo algorithm to estimate jointly the two causal structures and the parameters of the reduced‐form VAR model. The BGVAR approach is shown to be…

稀疏高维时间序列模型中的正则化估计AI 解读

Many scientific and economic problems involve the analysis of high-dimensional time series datasets. However, theoretical studies in high-dimensional statistics to date rely primarily on the assumption of independent and identically distributed (i.i.d.) samples. In this work, we focus on stable Gaussian processes and investigate the theoretical properties of $\ell_{1}$-regularized estimates in two important statistical problems in the context of high-dimensional time series:…

多元时间序列变化检测及其脑电数据应用AI 解读

The primary contributions of this article are rigorously developed novel statistical methods for detecting change points in multivariate time series. We extend the class of score type change point statistics considered in 2007 by Hušková, Prášková, and Steinebach to the vector autoregressive (VAR) case and the epidemic change alternative. Our proposed procedures do not require the observed time series to actually follow the VAR model. Instead, following the strategy…

使用混频 VAR 进行实时预测AI 解读

This article develops a vector autoregression (VAR) for time series which are observed at mixed frequencies—quarterly and monthly. The model is cast in state-space form and estimated with Bayesian methods under a Minnesota-style prior. We show how to evaluate the marginal data density to implement a data-driven hyperparameter selection. Using a real-time dataset, we evaluate forecasts from the mixed-frequency VAR and compare them to standard quarterly frequency VAR and to…

小型 DSGE 模型的频率学派评估AI 解读

This article proposes a new evaluation approach for the class of small-scale “hybrid” new Keynesian dynamic stochastic general equilibrium (NK-DSGE) models typically used in monetary policy and business cycle analysis. The empirical assessment of the NK-DSGE model is based on a conditional sequence of likelihood-based tests conducted in a vector autoregressive (VAR) system, in which both the low- and high-frequency implications of the model are addressed in a coherent…

用于 VaR 的 VAR：以多元回归分位数衡量尾部依赖AI 解读

This paper proposes methods for estimation and inference in multivariate, multi-quantile models. The theory can simultaneously accommodate models with multiple random variables, multiple confidence levels, and multiple lags of the associated quantiles. The proposed framework can be conveniently thought of as a vector autoregressive (VAR) extension to quantile models. We estimate a simple version of the model using market equity returns data to analyze spillovers in the…

二次卡尔曼滤波器AI 解读

We propose a new filtering and smoothing technique for non-linear state-space models. Observed variables are quadratic functions of latent factors following a Gaussian VAR. Stacking the vector of factors with its vectorized outer-product, we form an augmented state vector whose first two conditional moments are known in closed-form. We also provide analytical formulae for the unconditional moments of this augmented vector. Our new Quadratic Kalman Filter (Qkf) exploits these…

过度识别、非递归与时变系数结构向量自回归的估计AI 解读

This paper provides a general procedure to estimate structural vector autoregressions. The algorithm can be used in constant or time-varying coefficient models, and in the latter case, the law of motion of the coefficients can be linear or nonlinear. It can deal in a unified way with just-identified (recursive or nonrecursive) or overidentified systems where identification restrictions are of linear or of nonlinear form. We study the transmission of monetary policy shocks in…

高维向量自回归的 oracle 不等式AI 解读

This paper establishes non-asymptotic oracle inequalities for the prediction error and estimation accuracy of the LASSO in stationary vector autoregressive models. These inequalities are used to establish consistency of the LASSO even when the number of parameters is of a much larger order of magnitude than the sample size. We also state conditions under which no relevant variables are excluded.

向量误差修正模型的自动化估计AI 解读

Model selection and associated issues of post-model selection inference present well known challenges in empirical econometric research. These modeling issues are manifest in all applied work but they are particularly acute in multivariate time series settings such as cointegrated systems where multiple interconnected decisions can materially affect the form of the model and its interpretation. In cointegrated system modeling, empirical estimation typically proceeds in a…

We bring together some recent advances in the literature on vector autoregressive moving-average models, creating a simple specification and estimation strategy for the cointegrated case. We show that in this case with fixed initial values there exists a so-called final moving-average representation. We prove that the specification strategy is consistent. The performance of the proposed method is investigated via a Monte Carlo study and a forecasting exercise for US interest…

不同时变波动率设定下的宏观经济预测表现AI 解读

This paper compares alternative models of time-varying volatility on the basis of the accuracy of real-time point and density forecasts of key macroeconomic time series for the USA. We consider Bayesian autoregressive and vector autoregressive models that incorporate some form of time-varying volatility, precisely random walk stochastic volatility, stochastic volatility following a stationary AR process, stochastic volatility coupled with fat tails, GARCH and mixture of…

基于回归的协整系统分析AI 解读

Two estimation procedures dominate the cointegration literature: Johansen’s maximum likelihood inference on vector autoregressive error correction models and estimation of Phillips’ triangular forms. This latter methodology is essentially semiparametric, focusing on estimating long run parameters by means of cointegrating regressions. However, it is less used in practice than Johansen’s approach, since its implementation requires prior knowledge of features such as the…