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A Bayesian Markov-Switching Correlation Model for Contagion Analysis on Exchange Rate Markets

用于汇率市场传染分析的贝叶斯马尔可夫切换相关性模型

This article develops a new Markov-switching vector autoregressive (VAR) model with stochastic correlation for contagion analysis on financial markets. The correlation and the log-volatility dynamics are driven by two independent Markov chains, thus allowing for different effects such as volatility spill-overs and correlation shifts with various degrees of intensity. We outline a suitable Bayesian inference procedure based on Markov chain Monte Carlo algorithms. We then…

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The Pruned State-Space System for Non-Linear DSGE Models: Theory and Empirical Applications

非线性DSGE模型的剪枝状态空间系统:理论与实证应用

This article studies the pruned state-space system for higher-order perturbation approximations to dynamic stochastic general equilibrium (DSGE) models. We show the stability of the pruned approximation up to third order and provide closed-form expressions for first and second unconditional moments and impulse response functions. Our results introduce generalized method of moments (GMM) estimation and impulse-response matching for DSGE models approximated up to third order…

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Pythagorean generalization of testing the equality of two symmetric positive definite matrices

检验两个对称正定矩阵相等的勾股式推广

We provide a new test for equality of two symmetric positive-definite matrices that leads to a convenient mechanism for testing specification using the information matrix equality or the sandwich asymptotic covariance matrix of the GMM estimator. The test relies on a new characterization of equality between two k dimensional symmetric positive-definite matrices A and B: the traces of AB−1 and BA−1 are equal to k if and only if A=B. Using this simple criterion, we introduce a…

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Estimation and forecasting in vector autoregressive moving average models for rich datasets

丰富数据下向量自回归移动平均模型的估计与预测

We address the issue of modelling and forecasting macroeconomic variables using rich datasets by adopting the class of Vector Autoregressive Moving Average (VARMA) models. We overcome the estimation issue that arises with this class of models by implementing an iterative ordinary least squares (IOLS) estimator. We establish the consistency and asymptotic distribution of the estimator for weak and strong VARMA(p,q) models. Monte Carlo results show that IOLS is consistent and…

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A sequential Monte Carlo approach to inference in multiple‐equation Markov‐switching models

多方程马尔可夫切换模型推断的序贯蒙特卡洛方法

Summary Vector autoregressions with Markov‐switching parameters (MS‐VARs) offer substantial gains in data fit over VARs with constant parameters. However, Bayesian inference for MS‐VARs has remained challenging, impeding their uptake for empirical applications. We show that sequential Monte Carlo (SMC) estimators can accurately estimate MS‐VAR posteriors. Relative to multi‐step, model‐specific MCMC routines, SMC has the advantages of generality, parallelizability, and…

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Alternative Asymptotics for Cointegration Tests in Large VARs

大维VAR协整检验的替代渐近分析

Johansen's (1988,1991) likelihood ratio test for cointegration rank of a vector autoregression (VAR) depends only on the squared sample canonical correlations between current changes and past levels of a simple transformation of the data. We study the asymptotic behavior of the empirical distribution of those squared canonical correlations when the number of observations and the dimensionality of the VAR diverge to infinity simultaneously and proportionally. We find that the…

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Inference Based on Structural Vector Autoregressions Identified With Sign and Zero Restrictions: Theory and Applications

符号与零限制识别的结构向量自回归推断:理论与应用

In this paper, we develop algorithms to independently draw from a family of conjugate posterior distributions over the structural parameterization when sign and zero restrictions are used to identify structural vector autoregressions (SVARs). We call this family of conjugate posteriors normal‐generalized‐normal. Our algorithms draw from a conjugate uniform‐normal‐inverse‐Wishart posterior over the orthogonal reduced‐form parameterization and transform the draws into the…

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Inference for VARs identified with sign restrictions

符号限制识别的 VAR 模型推断

There is a fast growing literature that set‐identifies structural vector autoregressions (SVARs) by imposing sign restrictions on the responses of a subset of the endogenous variables to a particular structural shock (sign‐restricted SVARs). Most methods that have been used to construct pointwise coverage bands for impulse responses of sign‐restricted SVARs are justified only from a Bayesian perspective. This paper demonstrates how to formulate the inference problem for…

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Prediction Using Several Macroeconomic Models

利用多个宏观经济模型进行预测

We establish methods that improve the predictions of macroeconometric models—dynamic factor models, dynamic stochastic general equilibrium models, and vector autoregressions—using a quarterly U.S. data set. We measure prediction quality with one-step-ahead probability densities assigned in real time. Two steps lead to substantial improvements: (a) the use of full Bayesian predictive distributions rather than conditioning on the posterior mode for parameters and (b) the use…

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Efficient estimation of Bayesian VARMAs with time‐varying coefficients

时变系数贝叶斯VARMA模型的高效估计

Summary Empirical work in macroeconometrics has been mostly restricted to using vector autoregressions (VARs), even though there are strong theoretical reasons to consider general vector autoregressive moving averages (VARMAs). A number of articles in the last two decades have conjectured that this is because estimation of VARMAs is perceived to be challenging and proposed various ways to simplify it. Nevertheless, VARMAs continue to be largely dominated by VARs,…

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Noncausal vector autoregressive process: Representation, identification and semi-parametric estimation

非因果向量自回归过程:表示、识别与半参数估计

This paper introduces a representation theorem for a mixed VAR(p) process by distinguishing its causal and noncausal components. That representation is used to discuss the advantages and limitations of second-order identification in a mixed VAR. We show that it is possible to find the numbers of causal or noncausal components of the process from its multivariate autocovariance function, while nonlinear autocovariances are needed to distinguish between them. The paper…

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Structural FECM: Cointegration in large‐scale structural FAVAR models

结构 FECM:大规模结构 FAVAR 模型中的协整

Summary Starting from the dynamic factor model for nonstationary data we derive the factor‐augmented error correction model (FECM) and its moving‐average representation. The latter is used for the identification of structural shocks and their propagation mechanisms. We show how to implement classical identification schemes based on long‐run restrictions in the case of large panels. The importance of the error correction mechanism for impulse response analysis is analyzed by…

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The cycle of violence in the Second Intifada: Causality in nonlinear vector autoregressive models

第二次巴勒斯坦大起义中的暴力循环:非线性 VAR 的因果分析

Summary We contest Jaeger and Paserman's claim (Jaeger and Paserman , 2008. The cycle of violence? An empirical analysis of fatalities in the Palestinian–Israeli conflict. American Economic Review 98 (4): 1591–1604) that Palestinians did not react to Israeli aggression during Intifada 2. We address the differences between the two sides in terms of the timing and intensity of violence, estimate nonlinear vector autoregression models that are suitable when the linear vector…

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Have Standard VARS Remained Stable Since the Crisis?

危机以来,标准 VAR 是否保持稳定?

Summary Small vector autoregressions are commonly used in macroeconomics for forecasting and evaluating shock transmission. This requires VAR parameters to be stable over the evaluation and forecast sample or modeled as time‐varying. Prior work has considered whether there were sizable parameter changes in the early 1980s and in the subsequent period until the beginning of the new century. This paper conducts a similar analysis focused on the period since the recent crisis.…

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Using Entropic Tilting to Combine BVAR Forecasts With External Nowcasts

利用熵倾斜融合贝叶斯 VAR 预测与外部即时预测

This article shows entropic tilting to be a flexible and powerful tool for combining medium-term forecasts from BVARs with short-term forecasts from other sources (nowcasts from either surveys or other models). Tilting systematically improves the accuracy of both point and density forecasts, and tilting the BVAR forecasts based on nowcast means and variances yields slightly greater gains in density accuracy than does just tilting based on the nowcast means. Hence, entropic…

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Vector Autoregressions and Macroeconomic Modeling: An Error Taxonomy

向量自回归与宏观经济建模:误差分类

In this article, we investigate the theoretical behavior of finite lag VAR(n)$\text{VAR}(n)$ models fitted to time series that in truth come from an infinite-order VAR(∞)$\text{VAR}(\infty)$ data-generating mechanism. We show that the overall error can be broken down into two basic components, an estimation error that stems from the difference between the parameter estimates and their population ensemble VAR(n)$\text{VAR}(n)$ counterparts, and an approximation error that…

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The Analytics of SVARs: A Unified Framework to Measure Fiscal Multipliers

结构向量自回归的解析:衡量财政乘数的统一框架

Do tax cuts and spending increases stimulate output? Studies that identify fiscal shocks using structural vector autoregressions (SVAR) have reached different conclusions. In this article, we show analytically that this lack of consensus reflects different assumptions on the fiscal rules that—by relating tax and spending policies to macroeconomic conditions—determine the identification of fiscal shocks and the associated fiscal multipliers. We then propose a new…

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Network vector autoregression

网络向量自回归

We consider here a large-scale social network with a continuous response observed for each node at equally spaced time points. The responses from different nodes constitute an ultra-high dimensional vector, whose time series dynamic is to be investigated. In addition, the network structure is also taken into consideration, for which we propose a network vector autoregressive (NAR) model. The NAR model assumes each node’s response at a given time point as a linear combination…

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Granger Causality and Regime Inference in Markov Switching VAR Models with Bayesian Methods

马尔可夫转换 VAR 模型的格兰杰因果与状态推断:贝叶斯方法

In this paper, we derive restrictions for Granger noncausality in MS-VAR models and show under what conditions a variable does not affect the forecast of the hidden Markov process. To assess the noncausality hypotheses, we apply Bayesian inference. The computational tools include a novel block Metropolis–Hastings sampling algorithm for the estimation of the underlying models. We analyze a system of monthly US data on money and income. The results of testing in MS-VARs…

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Fixed-effects dynamic spatial panel data models and impulse response analysis

固定效应动态空间面板模型与脉冲响应分析

Real data often have complicated correlations over cross section and time. Such correlations are of particular interests in empirical studies. This paper considers using high order spatial lags and high order time lags to model complicated correlations over cross section and time. We propose to use the quasi maximum likelihood (QML) method to estimate the model. We establish the asymptotic theory of the quasi maximum likelihood estimator (QMLE), including the consistency and…

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A New Class of Bivariate Threshold Cointegration Models

一类新的二元门限协整模型

In this article, we introduce a new class of bivariate threshold VAR cointegration models. In the models, outside a compact region, the processes are cointegrated, while in the compact region, we allow different kinds of possibilities. We show that the bivariate processes form a 1/2-null recurrent system. We also find that the convergence rate for the estimators for the coefficients in the outside regime is T$\sqrt{T}$, while the convergence rate for the estimators for the…

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Tests of Predictive Ability for Vector Autoregressions Used for Conditional Forecasting

用于条件预测的向量自回归模型预测能力检验

Summary Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments. Even though conditional forecasting is common, there has been little work on methods for evaluating conditional forecasts. This paper provides analytical, Monte Carlo and empirical evidence on tests of predictive ability for conditional forecasts from estimated models. In the empirical analysis, we examine…

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Conventional Monetary Policy Transmission During Financial Crises: An Empirical Analysis

金融危机期间常规货币政策的传导:实证分析

Summary This paper studies the effects of a conventional monetary policy shock in the USA during times of high financial stress. The analysis is carried out by introducing a smooth transition factor model where the transition between states (‘normal’ and high financial stress) depends on a financial conditions index. Employing a quarterly dataset over the period 1970:Q1 to 2008:Q4 containing 108 US macroeconomic and financial time series, I find that a monetary policy shock…

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Testing for fundamental vector moving average representations

向量移动平均表示的基本性检验

We propose a test for invertibility or fundamentalness of structural vector autoregressive moving average models generated by non-Gaussian independent and identically distributed structural shocks. We prove that in these models and under some regularity conditions the Wold innovations are a martingale difference sequence (mds) if and only if the structural shocks are fundamental. This simple but powerful characterization suggests an empirical strategy to assess…

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