Vector autoregression and causality: a theoretical overview and simulation study

This paper provides a theoretical overview of Wald tests for Granger causality in levels vector autoregressions (VAR's) and Johansen-type error correction models (ECM's). The theory is based on results in Toda and Phillips (1991a) and allows for stochastic and deterministic trends as well as arbitrary degrees of cointegration. We recommend some operational procedures for conducting Granger causality tests that are based on the Gaussian maximum likelihood estimation of ECM's. These procedures are applicable in the important practical case of testing the causal effects of one variable on another group of variables and vice versa. This paper also investigates the sampling properties of these testing procedures through simulation exercises. Three sequential causality tests in ECM's are compared with conventional causality tests in levels and differences VAR's.     

Linear and nonlinear causality tests in an LSTAR model: wavelet decomposition in a nonlinear environment

In this paper, we use simulated data to investigate the power of different causality tests in a two-dimensional vector autoregressive (VAR) model. The data are presented in a nonlinear environment that is modelled using a logistic smooth transition autoregressive function. We use both linear and nonlinear causality tests to investigate the unidirection causality relationship and compare the power of these tests. The linear test is the commonly used Granger causality F test. The nonlinear test is a non-parametric test based on Baek and Brock [A general test for non-linear Granger causality: Bivariate model. Tech. Rep., Iowa State University and University of Wisconsin, Madison, WI, 1992] and Hiemstra and Jones [Testing for linear and non-linear Granger causality in the stock price–volume relation, J. Finance 49(5) (1994), pp. 1639–1664]. When implementing the nonlinear test, we use separately the original data, the linear VAR filtered residuals, and the wavelet decomposed series based on wavelet multiresolution analysis. The VAR filtered residuals and the wavelet decomposition series are used to extract the nonlinear structure of the original data. The simulation results show that the non-parametric test based on the wavelet decomposition series (which is a model-free approach) has the highest power to explore the causality relationship in nonlinear models.     

Granger因果关系检验的模型选择与相关策略研究

运用Granger因果关系检验识别确定经济变量间因果关系是经济研究中极为常见的分析模式,然而在具体应用时,Granger因果关系检验的功效会受到模型形式选择与检验策略因素的影响,为此,解析了Granger因果关系检验的水平型VAR、差分型VAR、VEC三种模型形式选择的基本原理,探讨了与模型选择相关的四大检验策略,即变量个数选择、滞后阶数选择、变量单整性检验、协整空间维数选择,并给出了Granger因果关系检验相对稳妥的实践操作程序。     

Vector autoregressive models with measurement errors for testing Granger causality

This paper develops a method for estimating the parameters of a vector autoregression (VAR) observed in white noise. The estimation method assumes that the noise variance matrix is known and does not require any iterative process. This study provides consistent estimators and the asymptotic distribution of the parameters required for conducting tests of Granger causality. Methods in the existing statistical literature cannot be used for testing Granger causality, since under the null hypothesis the model becomes unidentifiable. Measurement error effects on parameter estimates were evaluated by using computational simulations. The results suggest that the proposed approach produces empirical false positive rates close to the adopted nominal level (even for small samples) and has a satisfactory performance around the null hypothesis. The applicability and usefulness of the proposed approach are illustrated using a functional magnetic resonance imaging dataset.     

非线性Granger因果检验方法的检验功效及有限样本性质的模拟分析

为了克服传统Granger因果检验方法因忽略经济变量的非线性特征而导致结论出现显著偏差的局限性,非线性Granger因果检验方法在近年来正逐步成为经济学研究领域的重要分析工具。然而,迄今为止,学术界仍较少对非线性Granger因果检验方法在不同非线性模型中的有限样本性质展开系统性的比较与分析,因此,本文通过数据生成过程（DGP）,结合Monte Carlo模拟对Diks和Panchenko（2006）等主流的非线性Granger因果检验方法的检验功效、过度拒绝等问题展开比较研究,并对共同滞后阶数、带宽参数的不同设置可能引发结论敏感性变化进行深入分析,在此基础上我们从动态非线性滚动分析的角度对其有限样本性质展开进一步的讨论,并提出对未来非线性应用研究具有实际指导价值的若干建议。     

中国粮价与通货膨胀关系的协整分析：2001-2005

文章利用2001~2005年CPI和批发粮价的月度数据进行协整分析,并构建均衡修正模型,实证检验了二者的关系。实证结果说明无论长短期通货膨胀对粮价都具有Granger因果关系,验证了通货膨胀通过改变粮食市场参与主体的预期影响粮价的假说;在长期粮价对通货膨胀具有Granger因果关系,粮价长期高位运行会导致通货膨胀,但在短期内粮价对通货膨胀的影响较弱,不支持粮价上涨短期内即会引发通货膨胀的观点。     

Panel—Data下Granger因果检验的理论和应用发展综述

Panel-Data下Granger因果检验的相关理论是最近几年才发展起来的,现有的研究提出了关于Panel-Data下Granger因果检验的四个基本假设:同质无因果关系假设(HNCH)、同质因果关系假设(HCH)、异质因果关系假设(HECH)以及异质无因果关系假设(HENCH),根据检验参数的特点给出三种类型的检验模型:固定系数模型、随机系数模型和混合固定随机系数模型。目前,还只有固定系数模型的相关理论较为完善,另外两种模型的检验还都存在一定的难度。因此,只有从理论研究和实际应用两个方面对该理论进行阐述,并对现有的理论进行简要的评述,才可指出其存在的不足及可能的改进方向。     

Granger Causality Test in the Presence of Spillover Effects

In this article, we investigate the effect of spillover (i.e., causality in variance) on the reliability of Granger causality test based on ordinary least square estimates. We studied eight different versions of the test both, with and without Whites heteroskedasticity consistent covariance matrix (HCCME). The properties of the tests are investigated by means of a Monte Carlo experiment where 21 different data generating processes (DGP) are used and a number of factors that might affect the test are varied. The result shows that the best choice to test for Granger causality under the presence of spillover is the Lagrange Multiplier test with HCCME.     

A Wavelet-Based Approach of Testing for Granger Causality in the Presence of GARCH Effects

The size and power of the most commonly used tests and a new wavelet-based approach of testing for Granger causality is evaluated by means of a Monte Carlo study in which the error term follows a generalized autoregressive conditional heteroscedasticity consistent (GARCH) process. In the simulation study it is shown that the commonly used causality tests tend to overreject the true null hypothesis in the presence of GARCH errors and that the new wavelet-based approach improves the size properties of the Granger causality test for all of the different situations evaluated.     

Tests for noncorrelation of two multivariate ARMA time series

In many situations, we want to verify the existence of a relationship between multivariate time series. In this paper, we generalize the procedure developed by Haugh (1976) for univariate time series in order to test the hypothesis of noncorrelation between two multivariate stationary ARMA series. The test statistics are based on residual cross-correlation matrices. Under the null hypothesis of noncorrelation, we show that an arbitrary vector of residual cross-correlations asymptotically follows the same distribution as the corresponding vector of cross-correlations between the two innovation series. From this result, it follows that the test statistics considered are asymptotically distributed as chi-square random variables. Two test procedures are described. The first one is based on the residual cross-correlation matrix at a particular lag, whilst the second one is based on a portmanteau type statistic that generalizes Haugh's statistic. We also discuss how the procedures for testing noncorrelation can be adapted to determine the directions of causality in the sense of Granger (1969) between the two series. An advantage of the proposed procedures is that their application does not require the estimation of a global model for the two series. The finite-sample properties of the statistics introduced were studied by simulation under the null hypothesis. It led to modified statistics whose upper quantiles are much better approximated by those of the corresponding chi-square distribution. Finally, the procedures developed are applied to two different sets of economic data.     

格兰杰伪因果关系检验的小样本性质研究

基于MC模拟方法研究了格兰杰伪因果关系的小样本性质,结果表明伪因果关系的发生概率会随着数据过程持久性的增强而增大,但会随着样本容量的增加而减少,且由于检验式的设定使得经Newey-West修正的检验方法并没有明显优势。通过解释变量和被解释变量的持久性对伪因果关系的影响以及与OLS估计的伪回归比较分析,表明随机干扰项的自相关或异方差是产生伪因果关系的主要原因,这为解决伪回归和伪因果关系问题提供了统一研究框架。     

A Dynamic Analysis of Prices in the U.S. Rice Marketing Channel

Granger causality tests and dynamic multipliers are used to explore the dynamic relationship among prices in the U.S. rice marketing channel. The dynamic multipliers provide information about the speed and magnitude of dynamic price adjustments that is not provided by the Granger causality tests. This information is shown to be useful in explaining the underlying economic relationship among the time series of prices.     

中国银行信贷、房地产价格与宏观经济互动关系研究——基于VAR模型的实证分析

银行信贷在近几年有了飞速发展,但是有相当一部分资金流向了房地产业,而房地产业是国计民生的重要产业之一,在推动宏观经济增长方面起到了重要作用。在建立VAR模型的基础上综合运用协整检验、Granger因果关系检验等方法,对中国银行信贷、房地产价格与宏观经济间的互动关系进行研究,结果表明银行信贷、房地产价格与宏观经济三者之间确实存在互动关系。     

格兰杰因果检验的有效性及其应用

在经济分析中,常常要对经济变量之间的因果关系作出判断。例如,在制定货币政策时,就需要对可供选择的不同的政策方案的有效性作出评价,而判明货币变量与名义收入和通货膨胀等变量之间的因果关系,则是这种政策有效性评价中的一个重要组成部分。尽管人们可以根据经济理论对变量间的因果关系作出初步判断,但由于不同的经济理论所依据的前提假设不一致,使得有时单凭经济理论很难作出合理的判断,甚至有可能会给同一对变量间的因果关系作出近乎完全相反的判断。因此,用统计推断的方法,从实际观测数据中得出变量间因果关系的经验判断,这…     

Adaptive estimation of vector autoregressive models with time-varying variance: Application to testing linear causality in mean

Linear vector autoregressive (VAR) models where the innovations could be unconditionally heteroscedastic are considered. The volatility structure is deterministic and quite general, including breaks or trending variances as special cases. In this framework we propose ordinary least squares (OLS), generalized least squares (GLS) and adaptive least squares (ALS) procedures. The GLS estimator requires the knowledge of the time-varying variance structure while in the ALS approach the unknown variance is estimated by kernel smoothing with the outer product of the OLS residual vectors. Different bandwidths for the different cells of the time-varying variance matrix are also allowed. We derive the asymptotic distribution of the proposed estimators for the VAR model coefficients and compare their properties. In particular we show that the ALS estimator is asymptotically equivalent to the infeasible GLS estimator. This asymptotic equivalence is obtained uniformly with respect to the bandwidth(s) in a given range and hence justifies data-driven bandwidth rules. Using these results we build Wald tests for the linear Granger causality in mean which are adapted to VAR processes driven by errors with a nonstationary volatility. It is also shown that the commonly used standard Wald test for the linear Granger causality in mean is potentially unreliable in our framework (incorrect level and lower asymptotic power). Monte Carlo experiments illustrate the use of the different estimation approaches for the analysis of VAR models with time-varying variance innovations.     

Linear bootstrap methods for vector autoregressive moving-average models

We provide the theoretical justification of bootstrapping stationary invertible echelon vector autoregressive moving-average (VARMA) models using linear methods. The asymptotic validity of the bootstrap is established with strong white noise under parametric and nonparametric assumptions. Our methods are practical and useful for building reliable simulation-based inference and forecasting without implementing nonlinear estimation techniques such as ML which is usually burdensome, time demanding or impractical, particularly in big or highly persistent systems. The relevance of our procedures is more pronounced in the context of dynamic simulation-based techniques such as maximized Monte Carlo (MMC) tests [see Dufour J-M. Monte Carlo tests with nuisance parameters: a general approach to finite-sample inference and nonstandard asymptotics in econometrics. J Econom. 2006;133(2):443–477 and Dufour J-M, Jouini T. Finite-sample simulation-based tests in VAR models with applications to Granger causality testing. J Econom. 2006;135(1–2):229–254 for the VAR case]. Simulation evidence shows that, compared with conventional asymptotics, our bootstrap methods have good finite-sample properties in approximating the actual distribution of the studentized echelon VARMA parameter estimates, and in providing echelon parameter confidence sets with satisfactory coverage.     

Granger-causal analysis of GARCH models: A Bayesian approach

A multivariate GARCH model is used to investigate Granger causality in the conditional variance of time series. Parametric restrictions for the hypothesis of noncausality in conditional variances between two groups of variables, when there are other variables in the system as well, are derived. These novel conditions are convenient for the analysis of potentially large systems of economic variables. To evaluate hypotheses of noncausality, a Bayesian testing procedure is proposed. It avoids the singularity problem that may appear in the Wald test, and it relaxes the assumption of the existence of higher-order moments of the residuals required in classical tests.     

北京市能源消费与经济增长关系研究

 本文利用面板协整理论和基于面板误差修正模型的Granger因果关系检验分析了北京市能源消费和经济增长的关系。面板协整检验表明北京市能源消费和经济增长之间存在长期协整关系,进一步基于面板误差修正模型的Granger因果关系检验表明北京市短期存在能源消费到经济增长的单向因果关系,长期能源消费和经济增长之间存在双向的因果关系。因此北京市在进行节能减排的工作时,必须考虑到能源消费减少对经济增长的负作用,尽可能采取提高能源利用效率的措施,包括利用财政税收优惠政策鼓励节能技术的研发,在政府采购时要求产品在生产过程中采用节能技术,更关键也是更重要的是积极探索能源价格机制改革,通过价格手段促进企业真正具备节能意识,主动节约能源,提高利用效率。     

公共投资与社会福利的动态相关性：1978—2008年——基于VAR模型的分析及检验

基于VAR模型,利用1978—2008年的样本数据分析公共投资与社会福利的动态相关性。通过协整检验、VECM模型、Granger因果检验及方差分解分析,结果表明：福利（W）与生产性投资（PI）、消费性投资（CI）间存在长期稳定的均衡关系;基于W、PI和CI的VECM模型具体较好的误差修正机制;PI、CI与福利间有Granger因果关系,反向关系成立,但PI与CI间不成立;W自身的冲击对W的贡献率最大,CI次之,PI的贡献率最小。     

对外贸易影响中国经济增长的动态分析

运用计量经济学方法对中国1980-2007年相关经济变量时间序列数据的平稳性进行ADF检验,对修正后表现平稳的变量进行协整分析,研究在长期内是否存在稳定的均衡关系。通过构建协整方程、误差修正模型和Granger因果关系式分析各经济变量在长期均衡和短期波动中相互因果关系的影响。研究结果表明：在短期内经济增长更多受制于需求,而长期内取决于生产效率的提高。因此在继续重视出口贸易创造市场作用的前提下,要充分发挥外贸在增加要素供给和创造市场需求两个方面的作用。