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

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 dependence. The copula parameter matrix is given by the correlation matrix of a latent stationary and Markov vector autoregression (VAR). We show that the likelihood can be evaluated efficiently using the unique partial correlations, and estimate the copula using Bayesian methods. We examine the forecasting performance of the model for four U.S. macroeconomic variables between 1975:Q1 and 2011:Q2 using quarterly real-time data. We find that the point and density forecasts from the copula model are competitive with those from a Bayesian VAR. During the recent recession the forecast densities exhibit substantial asymmetry, avoiding some of the pitfalls of the symmetric forecast densities from the Bayesian VAR. We show that the asymmetries in the predictive distributions of GDP growth and inflation are similar to those found in the probabilistic forecasts from the Survey of Professional Forecasters. Last, we find that unlike the linear VAR model, our fitted Gaussian copula models exhibit nonlinear dependencies between some macroeconomic variables. This article has online supplementary material.     

Dynamic Forecasts of Qualitative Variables

This article presents a new Qual VAR model for incorporating information from qualitative and/or discrete variables in vector autoregressions. With a Qual VAR, it is possible to create dynamic forecasts of the qualitative variable using standard VAR projections. Previous forecasting methods for qualitative variables, in contrast, produce only static forecasts. I apply the Qual VAR to forecasting the 2001 business recession out of sample and to analyzing the Romer and Romer narrative measure of monetary policy contractions as an endogenous variable in a VAR. Out of sample, the model predicts the timing of the 2001 recession quite well relative to the recession probabilities put forth at the time by professional forecasters. Qual VARs—which include information about the qualitative variable—can also enhance the quality of density forecasts of the other variables in the system.     

Real-Time Forecasts of the Real Price of Oil

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, real-time mean squared prediction error (MSPE) reductions may be as high as 25% 1 month ahead and 24% 3 months ahead. This result is in striking contrast to related results in the literature for asset prices. In particular, recursive vector autoregressive (VAR) forecasts based on global oil market variables tend to have lower MSPE at short horizons than forecasts based on oil futures prices, forecasts based on autoregressive (AR) and autoregressive moving average (ARMA) models, and the no-change forecast. In addition, these VAR models have consistently higher directional accuracy.     

INDEX TO VOLUME 8 (1 990)

This article provides a simple shrinkage representation that describes the operational characteristics of various forecasting methods designed for a large number of orthogonal predictors (such as principal components). These methods include pretest methods, Bayesian model averaging, empirical Bayes, and bagging. We compare empirically forecasts from these methods with dynamic factor model (DFM) forecasts using a U.S. macroeconomic dataset with 143 quarterly variables spanning 1960–2008. For most series, including measures of real economic activity, the shrinkage forecasts are inferior to the DFM forecasts. This article has online supplementary material.     

Rational Expectations and Macroeconomic Forecasts

The article presents extensive results from testing for bias and serially correlated errors in a collection of time series of quarterly multiperiod forecasts for six variables including real GNP growth, inflation, and unemployment. The analysis covers responses by 79 frequent participants in economic outlook surveys conducted regularly since 1968. It shows much greater incidence of apparently systematic errors for inflation than for the other variables. Also, the tests are more favorable to composite group forecasts than to most of the individual forecast sets.     

Bayesian averaging of classical estimates in asymmetric vector autoregressive models

The estimated vector autoregressive (VAR) model is sensitive to model misspecifications, resulting to biased and inconsistent parameter estimates. This article extends the Bayesian averaging of classical estimates, a robustness procedure in cross-section data, to a vector time-series that is estimated using a large number of asymmetric VAR models. The proposed procedure was applied to simulated data from various forms of model misspecifications. The results of the simulation suggest that, under misspecification problems, particularly if an important variable and moving average (MA) terms were omitted, the proposed procedure gives robust results and better forecasts than the automatically selected equal lag-length VAR model.     

Exact joint forecast regions for vector autoregressive models

Assume that a k-element vector time series follows a vector autoregressive (VAR) model. Obtaining simultaneous forecasts of the k elements of the vector time series is an important problem. Based on the Bonferroni inequality, Lutkepohl (1991) derived the procedures which construct the conservative joint forecast regions for the VAR model. In this paper, we propose to use an exact method which provides shorter prediction intervals than does the Bonferroni method. Three illustrative examples are given for comparison of the various VAR forecasting procedures.     

Predictive Accuracy Gain From Disaggregate Sampling in ARIMA Models

We compare the forecast accuracy of autoregressive integrated moving average (ARIMA) models based on data observed with high and low frequency, respectively. We discuss how, for instance, a quarterly model can be used to predict one quarter ahead even if only annual data are available, and we compare the variance of the prediction error in this case with the variance if quarterly observations were indeed available. Results on the expected information gain are presented for a number of ARIMA models including models that describe the seasonally adjusted gross national product (GNP) series in the Netherlands. Disaggregation from annual to quarterly GNP data has reduced the variance of short-run forecast errors considerably, but further disaggregation from quarterly to monthly data is found to hardly improve the accuracy of monthly forecasts.     

Forecasting data revisions of GDP: a mixed frequency approach

Releases of GDP data undergo a series of revisions over time. These revisions have an impact on the results of macroeconometric models documented by the growing literature on real-time data applications. Revisions of U.S. GDP data can be explained and are partly predictable according to Faust et al. (J. Money Credit Bank. 37(3):403–419, 2005) or Fixler and Grimm (J. Product. Anal. 25:213–229, 2006). This analysis proposes the inclusion of mixed frequency data for forecasting GDP revisions. Thereby, the information set available around the first data vintage can be better exploited than the pure quarterly data. In-sample and out-of-sample results suggest that forecasts of GDP revisions can be improved by using mixed frequency data.     

资产配置模型的选择:回报、风险抑或二者兼具

近年来以风险平价为代表的基于风险的配置模型广为流行。这些模型的一大特点是放弃回报信息。而以均值方差模型代表的基于回报的配置模型则认为回报很重要而且默认对回报的预测是准确的。这两种做法都有问题。考虑到回报的可预测性得到了大量经验研究的支持,那么对于基于风险的配置模型而言,完全放弃回报则意味着有关回报的有用信息得不到充分利用。对于基于回报的配置模型而言,不考虑参数估计误差而且对输入参数敏感的缺点也大大抵消了它们利用回报信息带来的好处。那么,回报是否重要以及应该如何使用回报成了资产配置研究所面临的一个重大问题。为此,本文提出以风险平价为配置基准,以贝叶斯VAR回报预测为主观观点的Black-Litterman(贝叶斯BL)模型回答这一命题。利用1952-2016年的美国股票和债券季度数据,本文将贝叶斯BL模型与现有配置模型进行比较研究。实证结果表明,相比基于回报的配置模型,贝叶斯BL模型降低了组合风险;相比基于风险的配置模型,贝叶斯BL模型增强了组合回报。这些特性来自于它既能利用回报可预测性带来的有用信息,又能够发挥基于风险的配置模型在控制风险方面的优势。因此该模型表现出增强回报和控制风险兼具的特点,是一条具有潜力的资产配置新方案。     

人民币升值与国民收入变动对中美贸易的影响

运用1999-2013年中美两国贸易的季度数据,通过建立VAR模型以及对模型的协整检验,拟合了人民币兑美元实际有效汇率、中美两国收入水平及美国对中国贸易逆差的相关关系,发现美国贸易逆差并非由人民币低估引起。通过建立美国进口需求模型和美国对中国出口模型,结果显示:美国国民收入每增加1亿元,美国从中国的进口额就会增加约174万美元,而中国国民收入每增加1亿元,中国对美国的进口额增加约192万美元,这说明美国长期的贸易逆差主要是市场供需调节的结果,人民币汇率与之相关,但并不是主要原因。     

Forecasting the Distribution of Economic Variables in a Data-Rich Environment

This article investigates the relevance of considering a large number of macroeconomic indicators to forecast the complete distribution of a variable. The baseline time series model is a semiparametric specification based on the quantile autoregressive (QAR) model that assumes that the quantiles depend on the lagged values of the variable. We then augment the time series model with macroeconomic information from a large dataset by including principal components or a subset of variables selected by LASSO. We forecast the distribution of the h-month growth rate for four economic variables from 1975 to 2011 and evaluate the forecast accuracy relative to a stochastic volatility model using the quantile score. The results for the output and employment measures indicate that the multivariate models outperform the time series forecasts, in particular at long horizons and in tails of the distribution, while for the inflation variables the improved performance occurs mostly at the 6-month horizon. We also illustrate the practical relevance of predicting the distribution by considering forecasts at three dates during the last recession.     

A Parametric approach to the Estimation of Cointegration Vectors in Panel Data

In this article, a parametric framework for estimation and inference in cointegrated panel data models is considered that is based on a cointegrated VAR(p) model. A convenient two-step estimator is suggested where, in the first step, all individual specific parameters are estimated, and in the second step, the long-run parameters are estimated from a pooled least-squares regression. The two-step estimator and related test procedures can easily be modified to account for contemporaneously correlated errors, a feature that is often encountered in multi-country studies. Monte Carlo simulations suggest that the two-step estimator and related test procedures outperform semiparametric alternatives such as the fully modified OLS approach, especially if the number of time periods is small.     

Autoregressive Forecasting of Some Functional Climatic Variations

Many variations such as the annual cycle in sea surface temperatures can be considered to be smooth functions and are appropriately described using methods from functional data analysis. This study defines a class of functional autoregressive (FAR) models which can be used as robust predictors for making forecasts of entire smooth functions in the future. The methods are illustrated and compared with pointwise predictors such as SARIMA by applying them to forecasting the entire annual cycle of climatological El Nino–Southern Oscillation (ENSO) time series one year ahead. Forecasts for the period 1987–1996 suggest that the FAR functional predictors show some promising skill, compared to traditional scalar SARIMA forecasts which perform poorly.     

Generalizing the Bayesian Vector Autoregression Approach for Regional Interindustry Employment Forecasting

The Bayesian vector autoregression (BVAR) employment-forecasting approach is generalized using data for the state of Georgia. This study advances previous regional BVAR approaches by (a) incorporating regional input-output coefficients instead of national coefficients, (b) using the coefficients both to specify the prior means in one model and to weight the variances of a Minnesota-type prior in a second model, and (c) including final-demand effects and links to national and world economies. Out-of-sample forecasts produced by the generalized BVAR models are compared to forecasts produced from an autoregressive model, an unconstrained VAR model, and a Minnesota BVAR model.     

FORECASTING VOLATILITY IN THE PRESENCE OF MODEL INSTABILITY

Recent advances in financial econometrics have allowed for the construction of efficient ex post measures of daily volatility. This paper investigates the importance of instability in models of realised volatility and their corresponding forecasts. Testing for model instability is conducted with a subsampling method. We show that removing structurally unstable data of a short duration has a negligible impact on the accuracy of conditional mean forecasts of volatility. In contrast, it does provide a substantial improvement in a model's forecast density of volatility. In addition, the forecasting performance improves, often dramatically, when we evaluate models on structurally stable data.     

Temporal Disaggregation of Economic Time Series using Artificial Neural Networks

Several methods based on smoothing or statistical criteria have been used for deriving disaggregated values compatible with observed annual totals. The present method is based on the artificial neural networks. This article evaluates the use of artificial neural networks (ANNs) for the disaggregation of annual US GDP data to quarterly time increments. A feed-forward neural network with back-propagation algorithm for learning was used. An ANN model is introduced and evaluated in this paper. The proposed method is considered as a temporal disaggregation method without related series. A comparison with previous temporal disaggregation methods without related series has been done. The disaggregated quarterly GDP data compared well with observed quarterly data. In addition, they preserved all the basic statistics such as summing to the annual data value, cross correlation structure among quarterly flows, etc.     

Vector autoregression modelling and forecasting growth of South Korea

In this paper, we have estimated vector autoregression (VAR), Bayesian vector autoregression (BVAR) and vector error-correction models (VECMs) using annual time-series data of South Korea for 1950-94. We find evidence supporting the view that growth of real per-capita income has been aided by income, investment and export growth, as well as government spending and exchange rate policies. The VECMs provide better forecasts of growth than do the VAR and BVAR models for both short-term and long-term predictions.     

Error models for official mortality forecasts

"The Office of the Actuary, U.S. Social Security Administration, produces alternative forecasts of mortality to reflect uncertainty about the future.... In this article we identify the components and assumptions of the official forecasts and approximate them by stochastic parametric models. We estimate parameters of the models from past data, derive statistical intervals for the forecasts, and compare them with the official high-low intervals. We use the models to evaluate the forecasts rather than to develop different predictions of the future. Analysis of data from 1972 to 1985 shows that the official intervals for mortality forecasts for males or females aged 45-70 have approximately a 95% chance of including the true mortality rate in any year. For other ages the chances are much less than 95%."     

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This article develops a new identification procedure to estimate the contemporaneous relation between monetary policy and the stock market within a vector autoregression (VAR) framework. The approach combines high-frequency data from the futures market with the VAR methodology to circumvent exclusion restrictions and achieve identification. Our analysis casts doubt on VAR models imposing a recursive structure between innovations in policy rates and stock returns. We find that a tightening in policy rates has a negative impact on stock prices and that the Federal Reserve (Fed) has responded significantly to movements in the stock market. Estimates are robust to various model specifications.