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VAR 与局部投影:向量自回归、局部投影与脉冲响应。
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Identification and estimation of non-Gaussian structural vector autoregressions

非高斯结构向量自回归的识别与估计

Conventional structural vector autoregressive (SVAR) models with Gaussian errors are not identified, and additional identifying restrictions are needed in applied work. We show that the Gaussian case is an exception in that a SVAR model whose error vector consists of independent non-Gaussian components is, without any additional restrictions, identified and leads to essentially unique impulse responses. Building upon this result, we introduce an identification scheme under…

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Statistical inference for independent component analysis: Application to structural VAR models

独立成分分析的统计推断及其结构 VAR 应用

The well-known problem of non-identifiability of structural VAR models disappears if the structural shocks are independent and if at most one of them is Gaussian. In that case, the relevant estimation technique is the Independent Component Analysis (ICA). Since the introduction of ICA by Comon (1994), various semi-parametric estimation methods have been proposed for “orthogonalizing” the error terms. These methods include pseudo maximum likelihood (PML) approaches and…

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Impulse response matching estimators for DSGE models

DSGE 模型的脉冲响应匹配估计

The existing asymptotic theory for VAR-based impulse response matching estimators of the structural parameters of DSGE models does not cover situations in which the number of impulse responses exceeds the number of VAR model parameters. We establish the consistency of the estimator in this situation, we derive its asymptotic distribution, and we show how this distribution can be approximated by bootstrap methods. We also demonstrate that under our assumptions special care is…

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Forecasting cointegrated nonstationary time series with time-varying variance

时变方差下协整非平稳时间序列的预测

In cointegrated vector autoregressive (VAR) models, error correction terms often have indeterminate effects on forecasting, thus we are concerned with inclusion or exclusion of the cointegration relation in forecast. This paper considers the model averaging strategies for cointegrated VAR models with heterogeneous variance or variance breaks. The estimated cointegration rank along with other data information are used to formulate the model averaging weights. This specific…

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Modeling and Forecasting Large Realized Covariance Matrices and Portfolio Choice

大型已实现协方差矩阵的建模、预测与投资组合选择

Summary We consider modeling and forecasting large realized covariance matrices by penalized vector autoregressive models. We consider Lasso‐type estimators to reduce the dimensionality and provide strong theoretical guarantees on the forecast capability of our procedure. We show that we can forecast realized covariance matrices almost as precisely as if we had known the true driving dynamics of these in advance. We next investigate the sources of these driving dynamics as…

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Forecasting Tail Risks

尾部风险预测

Summary This paper presents an early warning system as a set of multi‐period forecasts of indicators of tail real and financial risks obtained using a large database of monthly US data for the period 1972:1–2014:12. Pseudo‐real‐time forecasts are generated from: (a) sets of autoregressive and factor‐augmented vector autoregressions (VARs), and (b) sets of autoregressive and factor‐augmented quantile projections. Our key finding is that forecasts obtained with AR and…

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Marginalized Predictive Likelihood Comparisons of Linear Gaussian State‐Space Models with Applications to DSGE, DSGE‐VAR, and VAR Models

线性高斯状态空间模型的边缘化预测似然比较:DSGE、DSGE-VAR与VAR应用

Summary The predictive likelihood is useful for ranking models in forecast comparison exercises using Bayesian inference. We discuss how it can be estimated, by means of marzginalization, for any subset of the observables in linear Gaussian state‐space models. We compare macroeconomic density forecasts for the euro area of a DSGE model to those of a DSGE‐VAR, a BVAR and a multivariate random walk over 1999:Q1–2011:Q4. While the BVAR generally provides superior forecasts, its…

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High-dimensional and banded vector autoregressions

高维带状向量自回归模型

We consider a class of vector autoregressive models with banded coefficient matrices. This setting represents a type of sparse structure for high-dimensional time series, although the implied auto-covariance matrices are not banded. The structure is also practically meaningful when the component time series are ordered appropriately. We establish the convergence rates of the estimated banded autoregressive coefficient matrices. We also propose a Bayesian information…

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Forecasting with Global Vector Autoregressive Models: a Bayesian Approach

全球向量自回归模型的预测:贝叶斯方法

Summary This paper develops a Bayesian variant of global vector autoregressive (B‐GVAR) models to forecast an international set of macroeconomic and financial variables. We propose a set of hierarchical priors and compare the predictive performance of B‐GVAR models in terms of point and density forecasts for one‐quarter‐ahead and four‐quarter‐ahead forecast horizons. We find that forecasts can be improved by employing a global framework and hierarchical priors which induce…

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Interconnections Between Eurozone and US Booms and Busts Using a Bayesian Panel Markov‐Switching VAR Model

欧元区与美国繁荣衰退的联动:贝叶斯面板马尔可夫转换VAR模型

Summary The proposed panel Markov‐switching VAR model accommodates changes in low and high data frequencies and incorporates endogenous time‐varying transition matrices of country‐specific Markov chains, allowing for interconnections. An efficient multi‐move sampling algorithm draws time‐varying Markov‐switching chains. Using industrial production growth and credit spread data, several important data features are obtained. Three regimes appear, with slow growth becoming…

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Noncausal Bayesian Vector Autoregression

非因果贝叶斯向量自回归

Summary We consider Bayesian analysis of the noncausal vector autoregressive model that is capable of capturing nonlinearities and effects of missing variables. Specifically, we devise a fast and reliable posterior simulator that yields the predictive distribution as a by‐product. We apply the methods to postwar US inflation and GDP growth. The noncausal model is found superior in terms of both in‐sample fit and out‐of‐sample forecasting performance over its conventional…

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Combining Time Variation and Mixed Frequencies: an Analysis of Government Spending Multipliers in Italy

结合时变参数与混合频率:意大利政府支出乘数分析

Summary In this paper, we propose a time‐varying parameter vector autoregression (VAR) model with stochastic volatility which allows for estimation on data sampled at different frequencies. Our contribution is twofold. First, we extend the methodology developed by Cogley and Sargent (Drifts and volatilities: monetary policies and outcomes in the post WWII U.S. Review of Economic Studies 2005; 8 : 262–302) and Primiceri (Time varying structural vector autoregressions and…

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Estimation and Inference of FAVAR Models

因子增广向量自回归模型的估计与推断

The factor-augmented vector autoregressive (FAVAR) model is now widely used in macroeconomics and finance. In this model, observable and unobservable factors jointly follow a vector autoregressive process, which further drives the comovement of a large number of observable variables. We study the identification restrictions for FAVAR models, and propose a likelihood-based two-step method to estimate the model. The estimation explicitly accounts for factors being partially…

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Convolutional autoregressive models for functional time series

函数型时间序列的卷积自回归模型

Functional data analysis has became an increasingly popular class of problems in statistical research. However, functional data observed over time with serial dependence remains a less studied area. Motivated by Bosq (2000), who first introduced the functional autoregressive models, we propose a convolutional functional autoregressive model, where the function at time t is a result of the sum of convolutions of the past functions and a set of convolution functions, plus a…

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Determination of Long‐run and Short‐run Dynamics in EC‐VARMA Models via Canonical Correlations

通过典型相关确定误差修正 VARMA 模型的长期与短期动态

Summary This article studies a simple, coherent approach for identifying and estimating error‐correcting vector autoregressive moving average (EC‐VARMA) models. Canonical correlation analysis is implemented for both determining the cointegrating rank, using a strongly consistent method, and identifying the short‐run VARMA dynamics, using the scalar component methodology. Finite‐sample performance is evaluated via Monte Carlo simulations and the approach is applied to…

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Forecasting with Bayesian Vector Autoregressions Estimated Using Professional Forecasts

利用专业预测估计贝叶斯向量自回归并开展预测

Summary We propose a Bayesian shrinkage approach for vector autoregressions (VARs) that uses short‐term survey forecasts as an additional source of information about model parameters. In particular, we augment the vector of dependent variables by their survey nowcasts, and claim that each variable modelled in the VAR and its nowcast are likely to depend in a similar way on the lagged dependent variables. In an application to macroeconomic data, we find that the forecasts…

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Sieve-based inference for infinite-variance linear processes

无限方差线性过程的筛方法推断

We extend the available asymptotic theory for autoregressive sieve estimators to cover the case of stationary and invertible linear processes driven by independent identically distributed (i.i.d.) infinite variance (IV) innovations. We show that the ordinary least squares sieve estimates, together with estimates of the impulse responses derived from these, obtained from an autoregression whose order is an increasing function of the sample size, are consistent and exhibit…

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Macroeconomics and the reality of mixed frequency data

宏观经济学与混频数据的现实

Many time series are sampled at different frequencies. When we study co-movements between such series we usually analyze the joint process sampled at a common low frequency. This has consequences in terms of potentially mis-specifying the co-movements and hence the analysis of impulse response functions—a commonly used tool for economic policy analysis. We introduce a class of mixed frequency VAR models that allows us to measure the impact of high frequency data on low…

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Monetary, fiscal and oil shocks: Evidence based on mixed frequency structural FAVARs

货币、财政与石油冲击:混频结构 FAVAR 的证据

Large scale factor models have been often adopted both for forecasting and to identify structural shocks and their transmission mechanism. Mixed frequency factor models have been also used in a reduced form context, but not for structural applications, and in this paper we close this gap. First, we adapt a simple technique developed in a small scale mixed frequency VAR and factor context to the large scale case, and compare the resulting model with existing alternatives.…

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Testing for Granger causality in large mixed-frequency VARs

大型混频 VAR 中的格兰杰因果检验

We analyze Granger causality testing in a mixed-frequency VAR, where the difference in sampling frequencies of the variables is large, implying parameter proliferation problems in case we attempt to estimate the model unrestrictedly. We propose several tests based on reduced rank restrictions, including bootstrap versions thereof to account for factor estimation uncertainty and improve the finite sample properties of the tests, and a Bayesian VAR extended to mixed…

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A computationally efficient method for vector autoregression with mixed frequency data

混频向量自回归的计算高效方法

A linear transformation method is proposed to handle the vector autoregression with mixed frequency time series data. Temporally aggregated observations impose linear constraints on the distribution of latent variables, which are converted such that each observation replaces a latent variable. Full-sample transformation yields a closed-form simulation smoother, while partial-sample transformation leads to a computationally efficient sampler suitable for parallel computing.

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Extended Yule–Walker identification of VARMA models with single- or mixed-frequency data

单频或混频数据下 VARMA 模型的扩展 Yule–Walker 识别

Chen and Zadrozny (1998) developed the linear extended Yule–Walker (XYW) method for determining the parameters of a vector autoregressive (VAR) model with available covariances of mixed-frequency observations on the variables of the model. If the parameters are determined uniquely for available population covariances, then, the VAR model is identified. The present paper extends the original XYW method to an extended XYW method for determining all ARMA parameters of a vector…

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Econometric Methods for Modelling Systems With a Mixture of i (1) and i (0) Variables

含 I(1) 与 I(0) 变量的混合系统建模:计量方法

Summary This paper considers structural models with both I (1) and I (0) variables. The structural shocks associated with either set of variables could be permanent or transitory. We classify the shocks as (P1,P0) and (T1,T0), where P/T distinguishes permanent/transitory, while 1/0 means they are attached to structural equations with either I (1) or I (0) variables as their ‘dependent’ variable. We show that P0 shocks can affect cointegration analysis and provide a formula…

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Asymmetric Forecast Densities for U.S. Macroeconomic Variables from a Gaussian Copula Model of Cross-Sectional and Serial Dependence

基于横截面与序列依赖高斯Copula模型的美国宏观变量非对称预测密度

Most existing reduced-form macroeconomic multivariate time series models employ elliptical disturbances, so that the forecast densities produced are symmetric. In this article, we use a copula model with asymmetric margins to produce forecast densities with the scope for severe departures from symmetry. Empirical and skew t distributions are employed for the margins, and a high-dimensional Gaussian copula is used to jointly capture cross-sectional and (multivariate) serial…

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