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Working Paper
12.20.2023 |
WP 23-34
This paper examines the forecasting efficacy and implications of the recently popular breakdown of core inflation into three components: goods excluding food and energy, services excluding energy and housing, and housing. A comprehensive historical evaluation of the accuracy of point and density forecasts from a range of models and approaches shows that a BVAR with stochastic volatility in aggregate core inflation, its three components, and wage growth is an effective tool for forecasting inflation's components as well as aggregate core inflation. Looking ahead, the model's baseline projection puts core inflation at 2.6 percent in 2026, well below its 2023 level but still elevated relative to the Federal Reserve's 2 percent objective. The probability that core inflation will return to 2 percent or less is much higher when conditioning on goods or non-housing services inflation slowing to pre-pandemic levels than when conditioning on these components remaining above the same thresholds. Scenario analysis indicates that slower wage growth will likely be associated with reduced inflation in all three components, especially goods and non-housing services, helping to return core inflation to near the 2 percent target by 2026.
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Working Paper
11.28.2022 |
WP 22-37
This paper presents a new approach to combining the information in point and density forecasts from the Survey of Professional Forecasters (SPF) and assesses the incremental value of the density forecasts. Our starting point is a model, developed in companion work, that constructs quarterly term structures of expectations and uncertainty from SPF point forecasts for quarterly fixed horizons and annual fixed events. We then employ entropic tilting to bring the density forecast information contained in the SPF’s probability bins to bear on the model estimates. In a novel application of entropic tilting, we let the resulting predictive densities exactly replicate the SPF’s probability bins. Our empirical analysis of SPF forecasts of GDP growth and inflation shows that tilting to the SPF’s probability bins can visibly affect our model-based predictive distributions. Yet in historical evaluations, tilting does not offer consistent benefits to forecast accuracy relative to the model-based densities that are centered on the SPF’s point forecasts and reflect the historical behavior of SPF forecast errors. That said, there can be periods in which tilting to the bin information helps forecast accuracy.
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Working Paper
11.23.2022 |
WP 22-36
We develop a model that permits the estimation of a term structure of both expectations and forecast uncertainty for application to professional forecasts such as the Survey of Professional Forecasters (SPF). Our approach exactly replicates a given data set of predictions from the SPF (or a similar forecast source) without measurement error. Our model captures fixed horizon and fixed-event forecasts, and can accommodate changes in the maximal forecast horizon available from the SPF. The model casts a decomposition of multi-period forecast errors into a sequence of forecast updates that may be partially unobserved, resulting in a multivariate unobserved components model. In our empirical analysis, we provide quarterly term structures of expectations and uncertainty bands. Our preferred specification features stochastic volatility in forecast updates, which improves forecast performance and yields model estimates of forecast uncertainty that vary over time. We conclude by constructing SPF-based fan charts for calendar-year forecasts like those published by the Federal Reserve.
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Working Paper
08.31.2022 |
WP 22-25
Quantile regression has become widely used in empirical macroeconomics, in particular for estimating and forecasting tail risks to macroeconomic indicators. In this paper we examine various choices in the specification of quantile regressions for macro applications, for example, choices related to how and to what extent to include shrinkage, and whether to apply shrinkage in a classical or Bayesian framework. We focus on forecasting accuracy, using for evaluation both quantile scores and quantile-weighted continuous ranked probability scores at a range of quantiles spanning from the left to right tail. We find that shrinkage is generally helpful to tail forecast accuracy, with gains that are particularly large for GDP applications featuring large sets of predictors and unemployment and inflation applications, and with gains that increase with the forecast horizon.
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Working Paper
07.12.2022 |
WP 21-08R
We develop multivariate time series models using Bayesian additive regression trees that posit nonlinearities among macroeconomic variables, their lags, and possibly their lagged errors. The error variances can be stable, feature stochastic volatility, or follow a nonparametric specification. We evaluate density and tail forecast performance for a set of US macroeconomic and financial indicators. Our results suggest that the proposed models improve forecast accuracy both overall and in the tails. Another finding is that when allowing for nonlinearities in the conditional mean, heteroskedasticity becomes less important. A scenario analysis reveals nonlinear relations between predictive distributions and financial conditions.
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Working Paper
03.02.2022 |
WP 22-05
The relationship between inflation and predictors such as unemployment is potentially nonlinear with a strength that varies over time, and prediction errors may be subject to large, asymmetric shocks. Inspired by these concerns, we develop a model for inflation forecasting that is nonparametric both in the conditional mean and in the error using Gaussian and Dirichlet processes, respectively. We discuss how both these features may be important in producing accurate forecasts of inflation. In a forecasting exercise involving CPI inflation, we find that our approach has substantial benefits, both overall and in the left tail, with nonparametric modeling of the conditional mean being of particular importance.
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Working Paper
02.02.2022 |
WP 22-02
In this paper we propose a hierarchical shrinkage approach for multi-country VAR models. In implementation, we consider three different scale mixtures of Normals priors — specifically, Horseshoe, Normal- Gamma, and Normal-Gamma-Gamma priors. We provide new theoretical results for the Normal-Gamma prior. Empirically, we use a quarterly data set for the G7 economies to examine how model specifications and prior choices affect the forecasting performance for GDP growth, inflation, and a short-term interest rate. We find that hierarchical shrinkage, particularly as implemented with the Horseshoe prior, is very useful in forecasting inflation. It also has the best density forecast performance for output growth and the interest rate. Adding foreign information yields benefits, as multi-country models generally improve on the forecast accuracy of single-country models.
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Working Paper
01.04.2022 |
WP 20-32R
We measure the effects of the COVID-19 outbreak on uncertainty, and we assess the consequences of the uncertainty for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. The model includes additional latent volatility states in order to accommodate outliers in volatility, to reduce the influence of extreme observations from the COVID period. Our estimates yield large increases in macroeconomic and financial uncertainty since the onset of the COVID-19 period. These increases have contributed to the downturn in economic and financial conditions, but the contributions of uncertainty are small compared to the overall movements in many macroeconomic and financial indicators. That implies that the downturn is driven more by other dimensions of the COVID crisis than shocks to aggregate uncertainty (as measured by our method).
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Working Paper
01.03.2022 |
WP 18-03C
Carriero, Clark, and Marcellino (2020, CCM2020) used large BVAR models with a factor structure to stochastic volatility to produce estimates of time-varying international macroeconomic uncertainty and assess uncertainty's effects on the global economy. The results in CCM2020 were based on an estimation algorithm that has recently been shown to be incorrect by Bognanni (2021) and fixed by Carriero, et al. (2021). In this note we use the algorithm correction of Carriero, et al. (2021) to correct the estimates of CCM2020. Although the correction has some impact on the original results, the changes are small and the key findings of CCM2020 are upheld.
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Working Paper
01.02.2022 |
WP 16-22C
Carriero, Clark, and Marcellino (2018, CCM2018) used a large BVAR with a factor structure to stochastic volatility lo produce an estimate of time-varying macroeconomic and financial uncertainty and assess uncertainty's effects on the economy. The results in CCM2018 were based on an estimation algorithm that has recently shown to be incorrect by Bognanni (2021) and fixed by Carriero, et al. (2021). In this note we use the algorithm correction of Carriero, et a1. (2021) to correct the estimates of CCM2018. Although the correction has some impact on the original results, the changes are small and the key findings of CCM2018 are upheld.
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Working Paper
12.02.2021 |
WP 16-17C
The original algorithm contained a mistake that meant the conditional distributions used for the VAR’s coefficients were missing a piece of information. We propose a new algorithm that uses the same factorization but includes the missing term. The new, correct algorithm has the same computational complexity as the old, incorrect one (i.e., O(N4)), and therefore it still allows the estimation of large VARs.
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Working Paper
08.09.2021 |
WP 21-02R
The COVID-19 pandemic has led to enormous movements in economic data that strongly affect parameters and forecasts obtained from standard VARs. One way to address these issues is to model extreme observations as random shifts in the stochastic volatility (SV) of VAR residuals. Specifically, we propose VAR models with outlier-augmented SV that combine transitory and persistent changes in volatility. The resulting density forecasts for the COVID-19 period are much less sensitive to outliers in the data than standard VARs. Evaluating forecast performance over the last few decades, we find that outlier-augmented SV schemes do at least as well as a conventional SV model. Predictive Bayes factors indicate that our outlier-augmented SV model provides the best data fit for the period since the pandemic’s outbreak, as well as for earlier subsamples of relatively high volatility.
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Working Paper
03.29.2021 |
WP 21-09
Interest rate data are an important element of macroeconomic forecasting. Projections of future interest rates are not only an important product themselves, but also typically matter for forecasting other macroeconomic and financial variables. A popular class of forecasting models is linear vector autoregressions (VARs) that include shorter- and longer-term interest rates. However, in a number of economies, at least shorter-term interest rates have now been stuck for years at or near their effective lower bound (ELB), with longer-term rates drifting toward the constraint as well. In such an environment, linear forecasting models that ignore the ELB constraint on nominal interest rates appear inept. To handle the ELB on interest rates, we model observed rates as censored observations of a latent shadow-rate process in an otherwise standard VAR setup. The shadow rates are assumed to be equal to observed rates when above the ELB. Point and density forecasts for interest rates (short term and long term) constructed from a shadow-rate VAR for the US since 2009 are superior to predictions from a standard VAR that ignores the ELB. For other indicators of financial conditions and measures of economic activity and inflation, the accuracy of forecasts from our shadow-rate specification is on par with a standard VAR that ignores the ELB.
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Working Paper
03.22.2021 |
WP 21-08
We develop novel multivariate time series models using Bayesian additive regression trees that posit nonlinear relationships among macroeconomic variables, their lags, and possibly the lags of the errors. The variance of the errors can be stable, driven by stochastic volatility (SV), or follow a novel nonparametric specification. Estimation is carried out using scalable Markov chain Monte Carlo estimation algorithms for each specification. We evaluate the real-time density and tail forecasting performance of the various models for a set of US macroeconomic and financial indicators. Our results suggest that using nonparametric models generally leads to improved forecast accuracy. In particular, when interest centers on the tails of the posterior predictive, flexible models improve upon standard VAR models with SV. Another key finding is that if we allow for nonlinearities in the conditional mean, allowing for heteroskedasticity becomes less important. A scenario analysis reveals highly nonlinear relations between the predictive distribution and financial conditions.
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Working Paper
02.02.2021 |
WP 21-02
Incoming data in 2020 posed sizable challenges for the use of VARs in economic analysis: Enormous movements in a number of series have had strong effects on parameters and forecasts constructed with standard VAR methods. We propose the use of VAR models with time-varying volatility that include a treatment of the COVID extremes as outlier observations. Typical VARs with time-varying volatility assume changes in uncertainty to be highly persistent. Instead, we adopt an outlier-adjusted stochastic volatility (SV) model for VAR residuals that combines transitory and persistent changes in volatility. In addition, we consider the treatment of outliers as missing data. Evaluating forecast performance over the last few decades in quasi-real time, we find that the outlier-augmented SV scheme does at least as well as a conventional SV model, while both outperform standard homoskedastic VARs. Point forecasts made in 2020 from heteroskedastic VARs are much less sensitive to outliers in the data, and the outlier-adjusted SV model generates more reasonable gauges of forecast uncertainty than a standard SV model. At least pre-COVID, a close alternative to the outlier-adjusted model is an SV model with t-distributed shocks. Treating outliers as missing data also generates better-behaved forecasts than the conventional SV model. However, since uncertainty about the incidence of outliers is ignored in that approach, it leads to strikingly tight predictive densities.
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Working Paper
10.23.2020 |
WP 20-32
We measure the effects of the COVID-19 outbreak on macroeconomic and financial uncertainty, and we assess the consequences of the latter for key economic variables. We use a large, heteroskedastic vector autoregression (VAR) in which the error volatilities share two common factors, interpreted as macro and financial uncertainty, in addition to idiosyncratic components. Macro and financial uncertainty are allowed to contemporaneously affect the macroeconomy and financial conditions, with changes in the common component of the volatilities providing contemporaneous identifying information on uncertainty. We also consider an extended version of the model, based on a latent state approach to accommodating outliers in volatility, to reduce the influence of extreme observations from the COVID period. The estimates we obtain yield very large increases in macroeconomic and financial uncertainty over the course of the COVID-19 period. These increases have contributed to the downturn in economic and financial conditions, but with both models, the contributions of uncertainty are small compared to the overall movements in many macroeconomic and financial indicators. That implies that the downturn is driven more by other dimensions of the COVID crisis than shocks to aggregate uncertainty (as measured by our method).
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Working Paper
09.22.2020 |
WP 20-27
We derive a Bayesian prior from a no-arbitrage affine term structure model and use it to estimate the coefficients of a vector autoregression of a panel of government bond yields, specifying a common time-varying volatility for the disturbances. Results based on US data show that this method improves the precision of both point and density forecasts of the term structure of government bond yields, compared to a fully fledged term structure model with time-varying volatility and to a no-change random walk forecast. Further analysis reveals that the approach might work better than an exact term structure model because it relaxes the requirements that yields obey a strict factor structure and that the factors follow a Markov process. Instead, the cross-equation no-arbitrage restrictions on the factor loadings play a marginal role in producing forecasting gains.
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Working Paper
09.22.2020 |
WP 20-02R
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and it has relied on quantile regression methods to estimate tail risks. Although much of this work discusses asymmetries in conditional predictive distributions, the analysis often focuses on evidence of downside risk varying more than upside risk. We note that this pattern in risk estimates over time could obtain with conditional distributions that are symmetric but subject to simultaneous shifts in conditional means (down) and variances (up). Building on that insight, we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification with a common factor in volatility that enters the VAR’s conditional mean. Even though the one-step-ahead conditional predictive distributions from the conventional stochastic volatility specification are symmetric, the model estimates yield more time variation in downside risk as compared to upside risk. Results from the model that includes a volatility factor in the conditional mean and thereby allows for asymmetries in conditional distributions are very similar. Our paper also extends the recent literature by formally evaluating the accuracy of tail risk forecasts and assessing the performance of Bayesian quantile regression, as well as our Bayesian VARs, in this context. Overall, the BVAR models perform comparably to quantile regression for estimating and forecasting tail risks, complementing BVARs’ established performance for forecasting and structural analysis.
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Working Paper
09.22.2020 |
WP 20-13R2
This paper focuses on nowcasts of tail risk to GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, as well as classical and Bayesian quantile regressions) and also different methods for data reduction (either forecasts from models that incorporate data reduction or the combination of forecasts from smaller models). Our results show that, within some limits, more information helps the accuracy of nowcasts of tail risk to GDP growth. Accuracy typically improves as time moves forward within a quarter, making additional data available, with monthly data more important to accuracy than weekly data. Accuracy also typically improves with the use of financial indicators in addition to a base set of macroeconomic indicators. The better-performing models or methods include the Bayesian regression model with stochastic volatility, Bayesian quantile regression, some approaches to data reduction that make use of factors, and forecast averaging. In contrast, simple quantile regression performs relatively poorly.
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Working Paper
06.30.2020 |
WP 20-13R
This paper focuses on nowcasts of tail risk to GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, classical and Bayesian quantile regressions, quantile MIDAS regressions) and also different methods for data reduction (either forecasts from models that incorporate data reduction or the combination of forecasts from smaller models). Our results show that, within some limits, more information helps the accuracy of nowcasts of tail risk to GDP growth. Accuracy typically improves as time moves forward within a quarter, making additional data available, with monthly data more important to accuracy than weekly data. Accuracy also typically improves with the use of financial indicators in addition to a base set of macroeconomic indicators. The better-performing models or methods include the Bayesian regression model with stochastic volatility, Bayesian quantile regression, some approaches to data reduction that make use of factors, and forecast averaging. In contrast, simple quantile regression and quantile MIDAS regression perform relatively poorly.
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Working Paper
05.11.2020 |
WP 20-13
This paper focuses on tail risk nowcasts of economic activity, measured by GDP growth, with a potentially wide array of monthly and weekly information. We consider different models (Bayesian mixed frequency regressions with stochastic volatility, classical and Bayesian quantile regressions, quantile MIDAS regressions) and also different methods for data reduction (either the combination of forecasts from smaller models or forecasts from models that incorporate data reduction). The results show that classical and MIDAS quantile regressions perform very well in-sample but not out-of-sample, where the Bayesian mixed frequency and quantile regressions are generally clearly superior. Such a ranking of methods appears to be driven by substantial variability over time in the recursively estimated parameters in classical quantile regressions, while the use of priors in the Bayesian approaches reduces sampling variability and its effects on forecast accuracy. From an economic point of view, we find that the weekly information flow is quite useful in improving tail nowcasts of economic activity, with initial claims for unemployment insurance, stock prices, a term spread, a credit spread, and the Chicago Fed’s index of financial conditions emerging as particularly relevant indicators. Additional weekly indicators of economic activity do not improve historical forecast accuracy but do not harm it much, either.
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Working Paper
01.16.2020 |
WP 20-02
A rapidly growing body of research has examined tail risks in macroeconomic outcomes. Most of this work has focused on the risks of significant declines in GDP, and has relied on quantile regression methods to estimate tail risks. In this paper we examine the ability of Bayesian VARs with stochastic volatility to capture tail risks in macroeconomic forecast distributions and outcomes. We consider both a conventional stochastic volatility specification and a specification featuring a common volatility factor that is a function of past financial conditions. Even though the conditional predictive distributions from the VAR models are symmetric, our estimated models featuring time-varying volatility yield more time variation in downside risk as compared to upside risk—a feature highlighted in other work that has advocated for quantile regression methods or focused on asymmetric conditional distributions. Overall, the BVAR models perform comparably to quantile regression for estimating tail risks, with, in addition, some gains in standard point and density forecasts.
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Working Paper
09.05.2019 |
WP 18-03R
This paper uses a large vector autoregression to measure international macroeconomic uncertainty and its effects on major economies. We provide evidence of significant commonality in macroeconomic volatility, with one common factor driving strong comovement across economies and variables. We measure uncertainty and its effects with a large model in which the error volatilities feature a factor structure containing time-varying global components and idiosyncratic components. Global uncertainty contemporaneously affects both the levels and volatilities of the included variables. Our new estimates of international macroeconomic uncertainty indicate that surprise increases in uncertainty reduce output and stock prices, adversely affect labor market conditions, and in some economies lead to an easing of monetary policy.
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Working Paper
05.08.2018 |
WP 17-15R
We estimate uncertainty measures for point forecasts obtained from survey data, pooling information embedded in observed forecast errors for different forecast horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. We apply our method to forecasts for various macroeconomic variables from the Survey of Professional Forecasters. Compared to constant variance approaches, our stochastic volatility model improves the accuracy of uncertainty measures for survey forecasts. Our method can also be applied to other surveys like the Blue Chip Consensus, or the Federal Open Market Committee’s Summary of Economic Projections.
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Working Paper
03.29.2018 |
WP 18-05
We show that macroeconomic uncertainty can be considered as exogenous when assessing its effects on the U.S. economy. Instead, financial uncertainty can at least in part arise as an endogenous response to some macroeconomic developments, and overlooking this channel leads to distortions in the estimated effects of financial uncertainty shocks on the economy. We obtain these empirical findings with an econometric model that simultaneously allows for contemporaneous effects of both uncertainty shocks on economic variables and of economic shocks on uncertainty. While the traditional econometric approaches do not allow us to simultaneously identify both of these transmission channels, we achieve identification by exploiting the heteroskedasticity of macroeconomic data. Methodologically, we develop a structural VAR with time-varying volatility in which one of the variables (the uncertainty measure) impacts both the mean and the variance of the other variables. We provide conditional posterior distributions for this model, which is a substantial extension of the popular leverage model of Jacquier, Polson, and Rossi (2004), and provide an MCMC algorithm for estimation.
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Working Paper
03.02.2018 |
WP 18-03
This paper uses a large vector autoregression (VAR) to measure international macroeconomic uncertainty and its effects on major economies, using two datasets, one with GDP growth rates for 19 industrialized countries and the other with a larger set of macroeconomic indicators for the U.S., euro area, and U.K. Using basic factor model diagnostics, we first provide evidence of significant commonality in international macroeconomic volatility, with one common factor accounting for strong comovement across economies and variables. We then turn to measuring uncertainty and its effects with a large VAR in which the error volatilities evolve over time according to a factor structure. The volatility of each variable in the system reflects time-varying common (global) components and idiosyncratic components. In this model, global uncertainty is allowed to contemporaneously affect the macroeconomies of the included nations—both the levels and volatilities of the included variables. In this setup, uncertainty and its effects are estimated in a single step within the same model. Our estimates yield new measures of international macroeconomic uncertainty, and indicate that uncertainty shocks (surprise increases) lower GDP and many of its components, adversely affect labor market conditions, lower stock prices, and in some economies lead to an easing of monetary policy.
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Working Paper
09.01.2017 |
WP 17-15
We develop uncertainty measures for point forecasts from surveys such as the Survey of Professional Forecasters, Blue Chip, or the Federal Open Market Committee’s Summary of Economic Projections. At a given point of time, these surveys provide forecasts for macroeconomic variables at multiple horizons. To track time-varying uncertainty in the associated forecast errors, we derive a multiple-horizon specification of stochastic volatility. Compared to constant-variance approaches, our stochastic-volatility model improves the accuracy of uncertainty measures for survey forecasts.
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Working Paper
05.09.2017 |
WP 16-22R
We propose a new model for measuring uncertainty and its effects on the economy, based on a large vector autoregression with stochastic volatility driven by common factors representing macroeconomic and financial uncertainty.
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Working Paper
10.14.2016 |
WP 16-22
We propose a new framework for measuring uncertainty and its effects on the economy, based on a large VAR model with errors whose stochastic volatility is driven by two common unobservable factors, representing aggregate macroeconomic and financial uncertainty. The uncertainty measures can also influence the levels of the variables so that, contrary to most existing measures, ours reflect changes in both the conditional mean and volatility of the variables, and their impact on the economy can be assessed within the same framework.
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Working Paper
06.30.2016 |
WP 16-17
In this paper we propose a new Bayesian estimation procedure for (possibly very large) VARs featuring time varying volatilities and general priors.
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Working Paper
10.19.2015 |
WP 15-20
This paper adds to the growing literature which uses survey-based long-run forecasts of inflation to estimate trend inflation.
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Working Paper
04.20.2015 |
WP 14-11R
Small or medium-scale VARs are commonly used in applied macroeconomics for forecasting and evaluating the shock transmission mechanism. We conduct a similar analysis but focus on the effects of the recent crisis.
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Working Paper
04.08.2015 |
WP 14-13R
Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments.
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Working Paper
12.29.2014 |
WP 14-39
This paper shows entropic tilting to be a flexible and powerful tool for combining medium-term forecasts from BVARs with short-term forecasts from other sources (nowcasts from either surveys or other models).
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Working Paper
09.29.2014 |
WP 14-13
Many forecasts are conditional in nature. For example, a number of central banks routinely report forecasts conditional on particular paths of policy instruments.
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Working Paper
09.08.2014 |
WP 14-11
Small or medium-scale VARs are commonly used in applied macroeconomics for forecasting and evaluating the shock transmission mechanism. We conduct a similar analysis but focus on the effects of the recent crisis.
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Working Paper
11.14.2012 |
WP 12-27
This paper develops a method for producing current-quarter forecasts of GDP growth with a (possibly large) range of available within-the-quarter monthly observations of economic indicators ...
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Working Paper
09.20.2012 |
WP 12-18
This paper compares alternative models of time-varying macroeconomic volatility on the basis of the accuracy of point and density forecasts of macroeconomic variables.
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Working Paper
03.14.2012 |
WP 12-06
The estimation of large vector autoregressions with stochastic volatility using standard methods is computationally very demanding.
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Working Paper
12.29.2011 |
WP 11-34
This paper uses Bayesian methods to assess alternative models of trend inflation.
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Working Paper
09.07.2011 |
WP 11-21
This paper examines the asymptotic and finite-sample properties of tests of equal forecast accuracy when the models being compared are overlapping in the sense of Vuong (1989).
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Working Paper
09.04.2011 |
WP 11-20
This paper surveys recent developments in the evaluation of point forecasts.
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Working Paper
05.03.2011 |
WP 11-12
In this paper we examine how the forecasting performance of Bayesian VARs is affected by a number of specification choices.
