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VAR FORECASTING USING BAYESIAN VARIABLE SELECTION

利用贝叶斯变量选择进行VAR预测

SUMMARY This paper develops methods for automatic selection of variables in Bayesian vector autoregressions (VARs) using the Gibbs sampler. In particular, I provide computationally efficient algorithms for stochastic variable selection in generic linear and nonlinear models, as well as models of large dimensions. The performance of the proposed variable selection method is assessed in forecasting three major macroeconomic time series of the UK economy. Data‐based…

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Forecasting with Medium and Large Bayesian VARS

中大型贝叶斯VAR的预测

SUMMARY This paper is motivated by the recent interest in the use of Bayesian VARs for forecasting, even in cases where the number of dependent variables is large. In such cases factor methods have been traditionally used, but recent work using a particular prior suggests that Bayesian VAR methods can forecast better. In this paper, we consider a range of alternative priors which have been used with small VARs, discuss the issues which arise when they are used with medium…

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Macroeconomic forecasting and structural change

宏观经济预测与结构变化

SUMMARY The aim of this paper is to assess whether modeling structural change can help improving the accuracy of macroeconomic forecasts. We conduct a simulated real‐time out‐of‐sample exercise using a time‐varying coefficients vector autoregression (VAR) with stochastic volatility to predict the inflation rate, unemployment rate and interest rate in the USA. The model generates accurate predictions for the three variables. In particular, the forecasts of inflation are much…

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Stochastic search variable selection in vector error correction models with an application to a model of the UK macroeconomy

向量误差修正模型中的随机搜索变量选择及英国宏观应用

SUMMARY This paper develops methods for stochastic search variable selection (currently popular with regression and vector autoregressive models) for vector error correction models where there are many possible restrictions on the cointegration space. We show how this allows the researcher to begin with a single unrestricted model and either do model selection or model averaging in an automatic and computationally efficient manner. We apply our methods to a large UK…

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Fiscal Foresight and Information Flows

财政预见与信息流

Fiscal foresight --the phenomenon that legislative and implementation lags ensure that private agents receive clear signals about the tax rates they face in the future --is intrinsic to the tax policy process.This paper develops an analytical framework to study the econometric implications of fiscal foresight.Simple theoretical examples show that foresight produces equilibrium time series with nonfundamental representations, which misalign the agents' and the…

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Confronting model misspecification in macroeconomics

应对宏观经济模型的误设

We estimate a Markov-switching mixture of two familiar macroeconomic models: A richly parameterized DSGE model and a corresponding BVAR model. We show that the Markov-switching mixture model dominates both individual models and improves the fit considerably. Our estimation indicates that the DSGE model plays an important role only in the late 1970s and the early 1980s. We show how to use the mixture model as a data filter for estimation of the DSGE model when the BVAR model…

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Information criteria for impulse response function matching estimation of DSGE models

DSGE模型脉冲响应匹配估计的信息准则

We propose new information criteria for impulse response function matching estimators (IRFMEs). These estimators yield sampling distributions of the structural parameters of dynamic stochastic general equilibrium (DSGE) models by minimizing the distance between sample and theoretical impulse responses. First, we propose an information criterion to select only the responses that produce consistent estimates of the true but unknown structural parameters: the Valid Impulse…

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Persistence-robust surplus-lag Granger causality testing

对持续性稳健的增广滞后 Granger 因果检验

Previous literature has introduced causality tests with conventional limiting distributions in I(0)/I(1) vector autoregressive (VAR) models with unknown integration orders, based on an additional surplus lag in the specification of the estimated equation, which is not included in the tests. By extending this surplus lag approach to an infinite order VARX framework, we show that it can provide a highly persistence-robust Granger causality test that accommodates i.a…

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Comparison of misspecified calibrated models: The minimum distance approach

误设校准模型的比较:最小距离方法

This paper proposes several testing procedures for comparison of misspecified calibrated models. The proposed tests are of the Vuong-type (Vuong, 1989; Rivers and Vuong, 2002). In our framework, the econometrician selects values for model’s parameters in order to match some characteristics of data with those implied by the theoretical model. We assume that all competing models are misspecified, and suggest a test for the null hypothesis that they provide equivalent fit to…

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Testing for rational bubbles in a coexplosive vector autoregression

共爆炸向量自回归中的理性泡沫检验

We derive the parameter restrictions that a standard equity market model implies for a bivariate vector autoregression for stock prices and dividends, and we show how to test these restrictions using likelihood ratio tests. The restrictions, which imply that stock returns are unpredictable, are derived both for a model without bubbles and for a model with a rational bubble. In both cases we show how the restrictions can be tested through standard chi-squared inference. The…

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UNIT ROOTS IN WHITE NOISE

白噪声中的单位根

We show that the empirical distribution of the roots of the vector autoregression (VAR) of order p fitted to T observations of a general stationary or nonstationary process converges to the uniform distribution over the unit circle on the complex plane, when both T and p tend to infinity so that (ln T )/ p → 0 and p 3 / T → 0. In particular, even if the process is a white noise, nearly all roots of the estimated VAR will converge by absolute value to unity. For fixed p , we…

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Probabilistic forecasting of output growth, inflation and the balance of trade in a GVAR framework

GVAR 框架下产出增长、通胀与贸易差额的概率预测

SUMMARY We apply a global vector autoregressive (GVAR) model to the analysis of inflation, output growth and global imbalances among a group of 33 countries (26 regions). We account for structural instability by use of country‐specific intercept shifts, the timings of which are identified taking into account both statistical evidence and our knowledge of historic economic conditions and events. Using this model, we compute both central forecasts and scenario‐based…

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Real-Time Forecasts of the Real Price of Oil

实际油价的实时预测

We construct a monthly real-time dataset consisting of vintages for 1991.1–2010.12 that is suitable for generating forecasts of the real price of oil from a variety of models. We document that revisions of the data typically represent news, and we introduce backcasting and nowcasting techniques to fill gaps in the real-time data. We show that real-time forecasts of the real price of oil can be more accurate than the no-change forecast at horizons up to 1 year. In some cases,…

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VAR Estimation and Forecasting When Data Are Subject to Revision

数据修订条件下的 VAR 估计与预测

We show that Howrey’s method for producing economic forecasts when data are subject to revision is easily generalized to handle the case where data are produced by a sophisticated statistical agency. The proposed approach assumes that government estimates are efficient with a finite lag. It takes no stand on whether earlier revisions are the result of “news” or of reductions in “noise.” We present asymptotic performance results in the scalar case and illustrate the technique…

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Estimation for spatial dynamic panel data with fixed effects: The case of spatial cointegration

固定效应空间动态面板的估计:空间协整情形

Yu et al. (2008) establish asymptotic properties of quasi-maximum likelihood estimators for a stable spatial dynamic panel model with fixed effects when both the number of individuals n and the number of time periods T are large. This paper investigates unstable cases where there are unit roots generated by temporal and spatial correlations. We focus on the spatial cointegration model where some eigenvalues of the data generating process are equal to 1 and the outcomes of…

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Using Conditional Kernel Density Estimation for Wind Power Density Forecasting

利用条件核密度估计进行风电功率密度预测

Of the various renewable energy resources, wind power is widely recognized as one of the most promising. The management of wind farms and electricity systems can benefit greatly from the availability of estimates of the probability distribution of wind power generation. However, most research has focused on point forecasting of wind power. In this article, we develop an approach to producing density forecasts for the wind power generated at individual wind farms. Our…

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Likelihood Inference for a Fractionally Cointegrated Vector Autoregressive Model

分数协整向量自回归模型的似然推断

We consider model based inference in a fractionally cointegrated (or cofractional) vector autoregressive model with a restricted constant term, ¿, based on the Gaussian likelihood conditional on initial values. The model nests the I(d) VAR model. We give conditions on the parameters such that the process X_{t} is fractional of order d and cofractional of order d-b; that is, there exist vectors ß for which ß'X_{t} is fractional of order d-b, and no other fractionality order…

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What's News in Business Cycles

商业周期中的预期冲击

In the context of a dynamic, stochastic, general equilibrium model, we perform classical maximum likelihood and Bayesian estimations of the contribution of anticipated shocks to business cycles in the postwar United States. Our identification approach relies on the fact that forward-looking agents react to anticipated changes in exogenous fundamentals before such changes materialize. It further allows us to distinguish changes in fundamentals by their anticipation horizon.…

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Bootstrap Determination of the Co-Integration Rank in Vector Autoregressive Models

向量自回归模型中协整秩的自助法确定

This paper discusses a consistent bootstrap implementation of the likelihood ratio (LR) co-integration rank test and associated sequential rank determination procedure of Johansen (1996). The bootstrap samples are constructed using the restricted parameter estimates of the underlying vector autoregressive (VAR) model that obtain under the reduced rank null hypothesis. A full asymptotic theory is provided that shows that, unlike the bootstrap procedure in Swensen (2006) where…

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One-Dimensional Inference in Autoregressive Models With the Potential Presence of a Unit Root

可能存在单位根的自回归模型中的一维推断

This paper examines the problem of testing and confidence set construction for one-dimensional functions of the coefficients in autoregressive (AR(p)) models with potentially persistent time series. The primary example concerns inference on impulse responses. A new asymptotic framework is suggested and some new theoretical properties of known procedures are demonstrated. I show that the likelihood ratio (LR) and LR± statistics for a linear hypothesis in an AR(p) can be…

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Bayesian inference in a time varying cointegration model

时变协整模型的贝叶斯推断

There are both theoretical and empirical reasons for believing that the parameters of macroeconomic models may vary over time. However, work with time-varying parameter models has largely involved vector autoregressions (VARs), ignoring cointegration. This is despite the fact that cointegration plays an important role in informing macroeconomists on a range of issues. In this paper, we develop a new time varying parameter model which permits cointegration. We use a…

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A bootstrap algorithm for testing cointegration rank in VAR models in the presence of stationary variables

含平稳变量的 VAR 模型中协整秩检验的自助法算法

In this paper, a bootstrap algorithm for a reduced rank vector autoregressive (VAR) model which also includes stationary regressors, is analyzed. It is shown that the bootstrap distribution for estimating the rank converges to the distribution derived from the usual asymptotic framework. Because the asymptotic distribution will typically depend on unknown parameters, bootstrap distributions are of considerable interest in this context. The result of an application and some…

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How Reliable Are Local Projection Estimators of Impulse Responses?

局部投影脉冲响应估计量有多可靠?

We compare the finite-sample performance of impulse response confidence intervals based on local projections (LPs) and vector autoregressive (VAR) models in linear stationary settings. We find that in small samples, the asymptotic LP interval often is less accurate than the bias-adjusted bootstrap VAR interval, notwithstanding its excessive average length. Although the asymptotic LP interval has adequate coverage in sufficiently large samples, its average length still far…

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Are the responses of the U.S. economy asymmetric in energy price increases and decreases?

美国经济对能源价格上涨与下跌的反应是否不对称?

How much does real gross domestic product (GDP) respond to unanticipated changes in the real price of oil? Commonly used censored oil price vector autoregressive models suggest a substantial decline in real GDP in response to unexpected increases in the real price of oil, yet no response to unexpected declines. We show that these estimates are invalid. Based on a structural model that encompasses both symmetric and asymmetric models as special cases, correctly computed…

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