Composite likelihood methods for large Bayesian VARs with stochastic volatility

Adding multivariate stochastic volatility of a flexible form to large vector autoregressions (VARs) involving over 100 variables has proved challenging owing to computational considerations and overparametrization concerns. The existing literature works with either homoskedastic models or smaller models with restrictive forms for the stochastic volatility. In this paper, we develop composite likelihood methods for large VARs with multivariate stochastic volatility. These involve estimating large numbers of parsimonious models and then taking a weighted average across these models. We discuss various schemes for choosing the weights. In our empirical work involving VARs of up to 196 variables, we show that composite likelihood methods forecast much better than the most popular large VAR approach, which is computationally practical in very high dimensions: the homoskedastic VAR with Minnesota prior. We also compare our methods to various popular approaches that allow for stochastic volatility using medium and small VARs involving up to 20 variables. We find our methods to forecast appreciably better than these as well.     

Forecasting with Medium and Large Bayesian VARS

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 and large VARs and examine their forecast performance using a US macroeconomic dataset containing 168 variables. We find that Bayesian VARs do tend to forecast better than factor methods and provide an extensive comparison of the strengths and weaknesses of various approaches. Typically, we find that the simple Minnesota prior forecasts well in medium and large VARs, which makes this prior attractive relative to computationally more demanding alternatives. Our empirical results show the importance of using forecast metrics based on the entire predictive density, instead of relying solely on those based on point forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Forecasting using variational Bayesian inference in large vector autoregressions with hierarchical shrinkage

Many recent papers in macroeconomics have used large vector autoregressions (VARs) involving 100 or more dependent variables. With so many parameters to estimate, Bayesian prior shrinkage is vital to achieve reasonable results. Computational concerns currently limit the range of priors used and render difficult the addition of empirically important features such as stochastic volatility to the large VAR. In this paper, we develop variational Bayesian methods for large VARs that overcome the computational hurdle and allow for Bayesian inference in large VARs with a range of hierarchical shrinkage priors and with time-varying volatilities. We demonstrate the computational feasibility and good forecast performance of our methods in an empirical application involving a large quarterly US macroeconomic data set.     

Combining VAR and DSGE forecast densities

A popular macroeconomic forecasting strategy utilizes many models to hedge against instabilities of unknown timing; see (among others) Stock and Watson (2004), Clark and McCracken (2010), and Jore et al. (2010). Existing studies of this forecasting strategy exclude dynamic stochastic general equilibrium (DSGE) models, despite the widespread use of these models by monetary policymakers. In this paper, we use the linear opinion pool to combine inflation forecast densities from many vector autoregressions (VARs) and a policymaking DSGE model. The DSGE receives a substantial weight in the pool (at short horizons) provided the VAR components exclude structural breaks. In this case, the inflation forecast densities exhibit calibration failure. Allowing for structural breaks in the VARs reduces the weight on the DSGE considerably, but produces well-calibrated forecast densities for inflation.     

Efficient estimation of Bayesian VARMAs with time‐varying coefficients

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, particularly in terms of developing useful extensions. We address these computational challenges with a Bayesian approach. Specifically, we develop a Gibbs sampler for the basic VARMA, and demonstrate how it can be extended to models with time‐varying vector moving average (VMA) coefficients and stochastic volatility. We illustrate the methodology through a macroeconomic forecasting exercise. We show that in a class of models with stochastic volatility, VARMAs produce better density forecasts than VARs, particularly for short forecast horizons.     

Linking words in economic discourse: Implications for macroeconomic forecasts

This paper develops indicators of unstructured press information by exploiting word vector representations. A model is trained using a corpus covering 90 years of Wall Street Journal content. The information content of the indicators is assessed through business cycle forecast exercises. The vector representations can learn meaningful word associations that are exploited to construct indicators of uncertainty. In-sample and out-of-sample forecast exercises show that the indicators contain valuable information regarding future economic activity. The combination of indices associated with different subjective states (e.g., uncertainty, fear, pessimism) results in further gains in information content. The documented performance is unmatched by previous dictionary-based word counting techniques proposed in the literature.     

Modelling multi‐period inflation uncertainty using a panel of density forecasts

This paper examines the determinants of inflation forecast uncertainty using a panel of density forecasts from the Survey of Professional Forecasters (SPF). Based on a dynamic heterogeneous panel data model, we find that the persistence in forecast uncertainty is much less than what the aggregate time series data would suggest. In addition, the strong link between past forecast errors and current forecast uncertainty, as often noted in the ARCH literature, is largely lost in a multi‐period context with varying forecast horizons. We propose a novel way of estimating ‘news’ and its variance using the Kullback‐Leibler information, and show that the latter is an important determinant of forecast uncertainty. Our evidence suggests a strong relationship of forecast uncertainty with level of inflation, but not with forecaster discord or with the volatility of a number of other macroeconomic indicators. Copyright © 2006 John Wiley & Sons, Ltd.     

Impact factors

In this paper we discuss sensitivity of forecasts with respect to the information set considered in prediction; a sensitivity measure called impact factor, IF, is defined. This notion is specialized to the case of VAR processes integrated of order 0, 1 and 2. For stationary VARs this measure corresponds to the sum of the impulse response coefficients. For integrated VAR systems, the IF has a direct interpretation in terms of long-run forecasts. Various applications of this concept are reviewed; they include questions of policy effectiveness and of forecast uncertainty due to data revisions. A unified approach to inference on the IF is given, showing under what circumstances standard asymptotic inference can be conducted also in systems integrated of order 1 and 2. It is shown how the results reported here can be used to calculate similar sensitivity measures for models with a simultaneity structure.     

Forecasting with Bayesian Vector Autoregressions Estimated Using Professional Forecasts

We propose a Bayesian shrinkage approach for vector autoregressions (VARs) that uses short‐term survey forecasts as an additional source of information about model parameters. In particular, we augment the vector of dependent variables by their survey nowcasts, and claim that each variable modelled in the VAR and its nowcast are likely to depend in a similar way on the lagged dependent variables. In an application to macroeconomic data, we find that the forecasts obtained from a VAR fitted by our new shrinkage approach typically yield smaller mean squared forecast errors than the forecasts obtained from a range of benchmark methods. Copyright © 2015 John Wiley & Sons, Ltd.     

Combining survey long-run forecasts and nowcasts with BVAR forecasts using relative entropy

This paper constructs hybrid forecasts that combine forecasts from vector autoregressive (VAR) model(s) with both short- and long-term expectations from surveys. Specifically, we use the relative entropy to tilt one-step-ahead and long-horizon VAR forecasts to match the nowcasts and long-horizon forecasts from the Survey of Professional Forecasters. We consider a variety of VAR models, ranging from simple fixed-parameter to time-varying parameters. The results across models indicate meaningful gains in multi-horizon forecast accuracy relative to model forecasts that do not incorporate long-term survey conditions. Accuracy improvements are achieved for a range of variables, including those that are not tilted directly but are affected through spillover effects from tilted variables. The accuracy gains for hybrid inflation forecasts from simple VARs are substantial, statistically significant, and competitive to time-varying VARs, univariate benchmarks, and survey forecasts. We view our proposal as an indirect approach to accommodating structural change and moving end points.     

A look into the factor model black box: Publication lags and the role of hard and soft data in forecasting GDP

We derive forecast weights and uncertainty measures for assessing the roles of individual series in a dynamic factor model (DFM) for forecasting the euro area GDP from monthly indicators. The use of the Kalman smoother allows us to deal with publication lags when calculating the above measures. We find that surveys and financial data contain important information for the GDP forecasts beyond the monthly real activity measures. However, this is discovered only if their more timely publication is taken into account properly. Differences in publication lags play a very important role and should be considered in forecast evaluation.     

The relationship between forecast dispersion and forecast uncertainty: Evidence from a survey data—arch model

This paper examines empirically the relationship between measures of forecast dispersion and forecast uncertainty from data on inflation expectations from the Livingston survey series and the Survey Research Center (SRC) survey series. Because the survey series do not provide probabilistic forecasts of inflation, we derive measures of inflation uncertainty by modelling the conditional variance of the inflation forecast errors from the survey series as an autoregressive conditional heteroscedastic (ARCH) process. The analysis is complicated by the fact that the overlap of forecast horizons for the survey series does not preclude the model's disturbance terms from displaying autocorrelation, and also places a restriction on the specification for the ARCH measures of inflation uncertainty. We estimate the model using Hansen's (1982) generalized method of moments (GMM) procedure to account for the presence of serial correlation and conditional heteroscedasticity in the disturbance terms. The results generally support the hypothesis that the measures of forecast dispersion across survey respondents are positively and statistically significantly associated with the measures of inflation uncertainty. However, the appropriateness of using forecast dispersion measures as proxies for inflation uncertainty is sensitive to the choice of the survey series.     

Bayesian doubly adaptive elastic-net Lasso for VAR shrinkage

We develop a novel Bayesian doubly adaptive elastic-net Lasso (DAELasso) approach for VAR shrinkage. DAELasso achieves variable selection and coefficient shrinkage in a data-based manner. It deals constructively with explanatory variables which tend to be highly collinear by encouraging the grouping effect. In addition, it also allows for different degrees of shrinkage for different coefficients. Rewriting the multivariate Laplace distribution as a scale mixture, we establish closed-form conditional posteriors that can be drawn from a Gibbs sampler. An empirical analysis shows that the forecast results produced by DAELasso and its variants are comparable to those from other popular Bayesian methods, which provides further evidence that the forecast performances of large and medium sized Bayesian VARs are relatively robust to prior choices, and, in practice, simple Minnesota types of priors can be more attractive than their complex and well-designed alternatives.     

Forecast-error-based estimation of forecast uncertainty when the horizon is increased

Past forecast errors are employed frequently in the estimation of the unconditional forecast uncertainty, and several institutions have increased their forecast horizons in recent times. This work addresses the question of how forecast-error-based estimation can be performed if there are very few errors available for the new forecast horizons. It extends the results of Knüppel (2014) in order to relax the condition on the data structure that is required for the SUR estimator to be independent of unknown quantities. It turns out that the SUR estimator of the forecast uncertainty, which estimates the forecast uncertainty for all horizons jointly, tends to deliver large efficiency gains relative to the OLS estimator (i.e., the sample mean of the squared forecast errors for each individual horizon) in the case of increased forecast horizons. The SUR estimator is applied to the forecast errors of the Bank of England, the US Survey of Professional Forecasters, and the FOMC.     

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

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 freedom from reliance on particular analytical relationships between prior and likelihood. We use SMC's flexibility to demonstrate that model selection among MS‐VARs can be highly sensitive to the choice of prior.     

Efficient estimation of forecast uncertainty based on recent forecast errors

Multi-step-ahead forecasts of the forecast uncertainty of an individual forecaster are often based on the horizon-specific sample means of his recent squared forecast errors, where the number of past forecast errors available decreases one-to-one with the forecast horizon. In this paper, the efficiency gains from the joint estimation of forecast uncertainty for all horizons in such samples are investigated. If the forecast uncertainty is estimated by seemingly unrelated regressions, it turns out that the covariance matrix of the squared forecast errors does not have to be estimated, but simply needs to have a certain structure, which is a very useful property in small samples. Considering optimal and non-optimal forecasts, it is found that the efficiency gains can be substantial for longer horizons in small samples. The superior performance of the seemingly-unrelated-regressions approach is confirmed in several empirical applications.     

我国长三角制造业上市公司财务预警实证研究

文章设计了适合长三角制造业的引入"技术创新指标"和"人力资本指标"的"新型化"预警指标体系,通过T检验和主成分分析法筛选出显著性指标,并建立BP神经网络预警模型。     

An investigation of the effects of decisional guidance and cognitive ability on decision-making involving uncertainty data

In their roles as users and providers of uncertainty data, decision-makers are confronted with choosing among a plethora of data formats offered by the decision support systems on most personal computers, but are offered little in the way of decisional guidance for choosing the most effective display format. This research investigated when and why decisional guidance should be provided. We found that in tasks involving uncertainty data, the decision-makers were more accurate and responded faster when symbolic tasks were matched with tabular displays and spatial tasks were matched with graphical displays. We also found that when subjects were provided with both matched and unmatched display formats, field independent individuals were more accurate for both spatial and symbolic tasks. When decisional guidance restricted the display formats to match the task types, field dependency did not significantly affect performance. This suggests that cognitive ability or field dependency is not a factor when the mental representation formulated is consistent with the problem representation.     

Research and Development,Uncertainty, and Analysts’ Forecasts: The Case of IAS 38

This study analyzes the consequences of the capitalization of development expenditures under IAS 38 on analysts’ earnings forecasts. We use unique hand‐collected data in a sample of highly research and development (R&D)‐intensive German‐listed firms over the period 2000–2007. We find that the capitalization of development costs is significantly associated with both higher individual analysts’ forecast errors and forecast dispersion. This suggests that the increasing complexity surrounding the capitalization of development costs negatively impacts forecast accuracy. However, for firms with high underlying environmental uncertainty, forecast errors are negatively associated with capitalized development expenditures. This indicates that the negative impact of increased complexity on forecast accuracy can be outweighed by the information contained in the signals from capitalized development costs when the underlying environmental uncertainty is high. The findings contribute to the ongoing controversial debate on the accounting for self‐generated intangible assets. Our results provide useful insights on the link between capitalization of development costs, environmental uncertainty, and analysts’ forecasts for accounting academics and practitioners alike.     

Forecasting Tail Risks

This paper presents an early warning system as a set of multi‐period forecasts of indicators of tail real and financial risks obtained using a large database of monthly US data for the period 1972:1–2014:12. Pseudo‐real‐time forecasts are generated from: (a) sets of autoregressive and factor‐augmented vector autoregressions (VARs), and (b) sets of autoregressive and factor‐augmented quantile projections. Our key finding is that forecasts obtained with AR and factor‐augmented VAR forecasts significantly underestimate tail risks, while quantile projections deliver fairly accurate forecasts and reliable early warning signals for tail real and financial risks up to a 1‐year horizon. Copyright © 2016 John Wiley & Sons, Ltd.