Forecasting and turning point predictions in a Bayesian panel VAR model

We provide methods for forecasting variables and predicting turning points in panel Bayesian VARs. We specify a flexible model, which accounts for both interdependencies in the cross section and time variations in the parameters. Posterior distributions for the parameters are obtained for hierarchical and for Minnesota-type priors. Formulas for multistep, multiunit point and average forecasts are provided. An application to the problem of forecasting the growth rate of output and of predicting turning points in the G-7 illustrates the approach. A comparison with alternative forecasting methods is also provided.     

贝叶斯视角下时变参数VAR建模——兼论“斜率之谜”

中国渐进式的改革实践要求中国宏观时间序列的建模能够允许参数平滑变化,而传统的VAR模型对此无能为力。本文详细阐述了在贝叶斯估计框架下,如何利用MCMC算法,建立时变参数VAR模型的过程,并利用该模型对徐高(2008)的数据重新进行了拟合,发现其文中提出的斜率之谜现象不复存在,因此时变参数VAR模型在拟合中国宏观时间序列方面更为精准。     

Forecasting the UK economy with a medium-scale Bayesian VAR

We estimate a Bayesian VAR (BVAR) for the UK economy and assess its performance in forecasting GDP growth and CPI inflation in real time relative to forecasts from COMPASS, the Bank of England’s DSGE model, and other benchmarks. We find that the BVAR outperformed COMPASS when forecasting both GDP and its expenditure components. In contrast, their performances when forecasting CPI were similar. We also find that the BVAR density forecasts outperformed those of COMPASS, despite under-predicting inflation at most forecast horizons. Both models over-predicted GDP growth at all forecast horizons, but the issue was less pronounced in the BVAR. The BVAR’s point and density forecast performances are also comparable to those of a Bank of England in-house statistical suite for both GDP and CPI inflation, as well as to the official Inflation Report projections. Our results are broadly consistent with the findings of similar studies for other advanced economies.     

面板数据的贝叶斯Lasso分位回归方法

文章讨论了含有随机效应的面板数据模型,通过引入条件Laplace先验,文章构造了一种新的贝叶斯Lasso分位回归法。与一般贝叶斯分位回归法不同的是,该方法能够更大程度的将模型中非重要解释变量系数压缩至0,从而在估计系数的同时也起到了变量选择的作用。利用积分恒等式,文章构造了一种易于实施的参数估计的切片Gibbs抽样算法。模拟结果显示,在模型含有较多变量时,新方法排除“噪声”变量的能力明显高于现有文献中其他方法。文章最后对我国各地区多个宏观经济指标的面板数据进行了建模分析,演示了新方法估计参数与挑选变量的能力。     

风险测量VAR及其原理

用公式可表示为:Prob(△P>VAR}=1-a(其中Prob表示:资产价值损失小于可能损失上限的概率;△P表示:某一金融资产在一定持有期△t的价值失额;VAR表示:给定置信水平a下的在险价值,即可能的损失上限;a表示:给定的置信水平。)     

The transmission of foreign shocks to South Eastern European economies: A Bayesian VAR approach

The paper analyses the macroeconomic effects of foreign shocks in three South-East European (SEE) economies: Croatia, Macedonia and Bulgaria. In this regard, we investigate the transmission of several eurozone shocks (output gap, money market rates and inflation) on various macroeconomic variables in the aforementioned countries (output, inflation, money market rates and budget deficits). We trace the effects of foreign shocks on the basis of impulse response functions obtained from the Bayesian Vector Auto Regressions (VARs) separately for each country. The main findings from our study are: first, economic expansion in the eurozone has strong output and inflation effects on SEE economies, implying some degree of synchronization of business cycles; second, eurozone inflation is instantly and to a great extent transmitted to domestic inflation, suggesting that inflation in the SEE economies is mostly driven by foreign inflation; third, domestic money market rates are not closely linked with eurozone money markets; fourth, monetary policy in the SEE countries does not seem to be responsive to eurozone inflation shocks; and fifth, the fiscal authorities attempt to offset the spillover effects from both economic expansion and monetary tightening in the eurozone.     

Bayesian stochastic search for VAR model restrictions

We propose a Bayesian stochastic search approach to selecting restrictions for vector autoregressive (VAR) models. For this purpose, we develop a Markov chain Monte Carlo (MCMC) algorithm that visits high posterior probability restrictions on the elements of both the VAR regression coefficients and the error variance matrix. Numerical simulations show that stochastic search based on this algorithm can be effective at both selecting a satisfactory model and improving forecasting performance. To illustrate the potential of our approach, we apply our stochastic search to VAR modeling of inflation transmission from producer price index (PPI) components to the consumer price index (CPI).     

Network VAR models to measure financial contagion

Financial contagion among countries can arise from different channels, the most important of which are financial markets and bank lending. The paper aims to build an econometric network approach to understand the extent to which contagion spillovers (from one country to another) aris from financial markets, from bank lending, or from both. To achieve this aim we consider a model specification strategy which combines Vector Autoregressive models with network models. The paper contributes to the contagion literature with a model that can consider bank exposures and financial market prices, jointly and not only separately. From an empirical viewpoint, our results show that both bilateral exposures and market prices act as contagion channels in the transmission of shocks arising from a country to other countries.     

RISE OF VAR MODELLING APPROACH*

Abstract This paper surveys the rise of the Vector AutoRegressive (VAR) approach from a historical perspective. It shows that the VAR approach arises from a fusion of the Cowles Commission tradition and time series statistical methods, catalysed by the rational expectations (RE) movement, that the approach offers a systematic solution to the issue of ‘model choice’ bypassed by Cowles researchers, hence essentially inheriting and enhancing the Cowles legacy rather than abandoning or opposing it. By tackling model choice, however, the VAR approach helps reform econometrics by shifting the research focus from measurement of given theories to identification/verification of data‐coherent theories.     

风险价值法及其在证券投资中的应用

我国证券市场是我国社会主义市场经济的重要组成部分。随着我国证券市场的日趋完善和活跃,大量的投资者蜂拥而至,证券投资中的风险也有了放大效应。通过介绍目前市场上最流行的风险价值法,从投资者的角度来运用该法进行风险控制并予以回测,并进而从其他角度来系统探讨其在证券投资中的应用。     

Macroeconomic forecasting with large Bayesian VARs: Global-local priors and the illusion of sparsity

A class of global-local hierarchical shrinkage priors for estimating large Bayesian vector autoregressions (BVARs) has recently been proposed. We question whether three such priors: Dirichlet-Laplace, Horseshoe, and Normal-Gamma, can systematically improve the forecast accuracy of two commonly used benchmarks (the hierarchical Minnesota prior and the stochastic search variable selection (SSVS) prior), when predicting key macroeconomic variables. Using small and large data sets, both point and density forecasts suggest that the answer is no. Instead, our results indicate that a hierarchical Minnesota prior remains a solid practical choice when forecasting macroeconomic variables. In light of existing optimality results, a possible explanation for our finding is that macroeconomic data is not sparse, but instead dense.     

基于VAR的房地产投资风险度量方法研究

主要论述了VAR方法在房地产投资风险中的应用。首先分析了应用VAR在我国房地产投资风险中的必要性,再通过计算VAR的方法给出了如何在房地产投资项目中应用VAR度量风险,最后对房地产业应用VAR的前景进行了分析。     

基于风险价值(VAR)模型在股市中的实证分析

近年来随着股市的下跌,国内各证券公司的自营风险逐步暴露出来。这也为我国证券业风险管理提出新的课题。本文主要对VAR方法介绍,以及VAR在股票市场上的应用分析,以供投资者借鉴。     

基于VAR模型的区域物流与经济增长的关系研究

从区域物流与经济增长的关系出发,研究物流对经济增长的促进机制以及经济增长对区域物流的拉动作用建立VAR模型对区域物流与经济增长的关系进行研究,验证了两者的互动的协同关系。     

MIDAS vs. mixed-frequency VAR: Nowcasting GDP in the euro area

This paper compares the mixed-data sampling (MIDAS) and mixed-frequency VAR (MF-VAR) approaches to model specification in the presence of mixed-frequency data, e.g. monthly and quarterly series. MIDAS leads to parsimonious models which are based on exponential lag polynomials for the coefficients, whereas MF-VAR does not restrict the dynamics and can therefore suffer from the curse of dimensionality. However, if the restrictions imposed by MIDAS are too stringent, the MF-VAR can perform better. Hence, it is difficult to rank MIDAS and MF-VAR a priori, and their relative rankings are better evaluated empirically. In this paper, we compare their performances in a case which is relevant for policy making, namely nowcasting and forecasting quarterly GDP growth in the euro area on a monthly basis, using a set of about 20 monthly indicators. It turns out that the two approaches are more complements than substitutes, since MIDAS tends to perform better for horizons up to four to five months, whereas MF-VAR performs better for longer horizons, up to nine months.     

Asymmetries and Markov-switching structural VAR

The development of nonlinear representations and of generalized IRFs favored the study of the variables behavior in response to an economically identified shock as regards (i) the state of the system when the shock occurs, (ii) the size of the shock and (iii) the sign of the shock. Generalized IRFs are widely used in threshold representations to illustrate and even test the presence of asymmetries (Potter, 1995, van Dijk et al., 2007). However, GIRF have known no comparable development in Markov-switching VAR. I show that whether IRF and GIRF recently developed in this framework impose sign and size symmetries or display poor properties. In this paper, I propose a new GIRF for general Markov-switching structural VAR with fixed transition probabilities. In a simulation framework inspired from Rubio-Ramirez et al. (2005), I relax the assumption of perfect knowledge of the regime and introduce the updating step proposed by Camacho and Perez-Quiros (2013). As a consequence, sign/size asymmetries can now be examined in MSIAH-VAR and the GIRF now incorporates the dependence on future shocks without extra complexity. Visited regimes can now differ endogenously between the shocked and baseline trajectories due to the initial and future shocks but the only exogenous difference in the simulated trajectories relies on the initial structural shock. I use this approach to implement a test for sign and size asymmetries on US aggregate gross job flows.     

Bayesian median autoregression for robust time series forecasting

We develop a Bayesian median autoregressive (BayesMAR) model for time series forecasting. The proposed method utilizes time-varying quantile regression at the median, favorably inheriting the robustness of median regression in contrast to the widely used mean-based methods. Motivated by a working Laplace likelihood approach in Bayesian quantile regression, BayesMAR adopts a parametric model bearing the same structure as autoregressive models by altering the Gaussian error to Laplace, leading to a simple, robust, and interpretable modeling strategy for time series forecasting. We estimate model parameters by Markov chain Monte Carlo. Bayesian model averaging is used to account for model uncertainty, including the uncertainty in the autoregressive order, in addition to a Bayesian model selection approach. The proposed methods are illustrated using simulations and real data applications. An application to U.S. macroeconomic data forecasting shows that BayesMAR leads to favorable and often superior predictive performance compared to the selected mean-based alternatives under various loss functions that encompass both point and probabilistic forecasts. The proposed methods are generic and can be used to complement a rich class of methods that build on autoregressive models.     

商业银行市场风险管理中的VAR模型

巴塞尔新资本协议规定金融机构满足资本充足率的要求,并将风险分为信用风险、市场风险和操作风险。针对市场风险的管理,本文着重介绍VAR模型的概念、VAR的种类以及主要特点,并指出VAR面临的主要问题及其在我国金融应用的前景。     

Minnesota-type adaptive hierarchical priors for large Bayesian VARs

Large Bayesian VARs with stochastic volatility are increasingly used in empirical macroeconomics. The key to making these highly parameterized VARs useful is the use of shrinkage priors. We develop a family of priors that captures the best features of two prominent classes of shrinkage priors: adaptive hierarchical priors and Minnesota priors. Like adaptive hierarchical priors, these new priors ensure that only ‘small’ coefficients are strongly shrunk to zero, while ‘large’ coefficients remain intact. At the same time, these new priors can also incorporate many useful features of the Minnesota priors such as cross-variable shrinkage and shrinking coefficients on higher lags more aggressively. We introduce a fast posterior sampler to estimate BVARs with this family of priors—for a BVAR with 25 variables and 4 lags, obtaining 10,000 posterior draws takes about 3 min on a standard desktop computer. In a forecasting exercise, we show that these new priors outperform both adaptive hierarchical priors and Minnesota priors.     

外商直接投资与经济增长:基于动态VAR模型的分析

外商直接投资与经济增长的关系一直是国内外学者研究的热点。本文运用向量自回归(VAR)模型、脉冲响应函数、方差分解等计量经济学方法,基于2002年至2011年的季度数据,对外商直接投资与经济增长的关系进行了实证研究。结果表明:从长期来看,外商直接投资的增加有助于促进经济增长,但是短期这种促进作用并不明显;经济增长有助于外商直接投资的增加。