Perceived Inflation Persistence

This article constructs and estimates a measure called perceived inflation persistence that can be used to determine if professional forecasters’ inflation forecasts indicate there has been a change in inflation persistence. This measure is built via the implied autocorrelation function that follows from the estimates obtained using a forecaster-specific state-space model. Findings indicate that U.S. perceived inflation persistence has changed since the mid-1990s with more consensus among forecasters at lower levels of persistence. When compared to the autocorrelation function for actual inflation, forecasters typically react less to shocks to inflation than the actual inflation data would suggest.     

To Aggregate,Pool, or Neither

It is well known that, even if all forecasters are rational, unbiasedness tests using consensus forecasts are inconsistent because forecasters have private information. However, if all forecasters face a common realization, pooled estimators are also inconsistent. In contrast, we show that when predictions and realizations are integrated and cointegrated, microhomogeneity ensures that consensus and pooled estimators are consistent. Therefore, contrary to claims in the literature, in the absence of microhomogeneity, pooling is not a solution to the aggregation problem. We reject microhomogeneity for a number of forecasts from the Survey of Professional Forecasters. Therefore, for these variables unbiasedness can only be tested at the individual level.     

Combining Economic Forecasts

A method for combining forecasts may or may not account for dependence and differing precision among forecasts. In this article we test a variety of such methods in the context of combining forecasts of GNP from four major econometric models. The methods include one in which forecasting errors are jointly normally distributed and several variants of this model as well as some simpler procedures and a Bayesian approach with a prior distribution based on exchangeability of forecasters. The results indicate that a simple average, the normal model with an independence assumption, and the Bayesian model perform better than the other approaches that are studied here.     

Comparing Possibly Misspecified Forecasts

Abstract

Recent work has emphasized the importance of evaluating estimates of a statistical functional (such as a conditional mean, quantile, or distribution) using a loss function that is consistent for the functional of interest, of which there is an infinite number. If forecasters all use correctly specified models free from estimation error, and if the information sets of competing forecasters are nested, then the ranking induced by a single consistent loss function is sufficient for the ranking by any consistent loss function. This article shows, via analytical results and realistic simulation-based analyses, that the presence of misspecified models, parameter estimation error, or nonnested information sets, leads generally to sensitivity to the choice of (consistent) loss function. Thus, rather than merely specifying the target functional, which narrows the set of relevant loss functions only to the class of loss functions consistent for that functional, forecast consumers or survey designers should specify the single specific loss function that will be used to evaluate forecasts. An application to survey forecasts of U.S. inflation illustrates the results.     

An Exponential Inequality for Strictly Stationary and Negatively Associated Random Variables

Beanplot is a graphical method for visualizing univariate distributions. Density forecasts have an important role to play in many applications. Although graphical methods are widely used for illustrating distributions, suitable graphical methods to help for the purposes of analysis and comparison of density forecasters do not exist. This article explains how density forecasts and related observed densities are visualized parallel using beanplots in different groups of data. The visualization method is illustrated with industrial and simulated data. The functionality extends the plotting function of R package beanplot and the developed functions are made available for R programming language.     

Uncertainty,information, and disagreement of economic forecasters

ABSTRACT

An information framework is proposed for studying uncertainty and disagreement of economic forecasters. This framework builds upon the mixture model of combining density forecasts through a systematic application of the information theory. The framework encompasses the measures used in the literature and leads to their generalizations. The focal measure is the Jensen–Shannon divergence of the mixture which admits Kullback–Leibler and mutual information representations. Illustrations include exploring the dynamics of the individual and aggregate uncertainty about the US inflation rate using the survey of professional forecasters (SPF). We show that the normalized entropy index corrects some of the distortions caused by changes of the design of the SPF over time. Bayesian hierarchical models are used to examine the association of the inflation uncertainty with the anticipated inflation and the dispersion of point forecasts. Implementation of the information framework based on the variance and Dirichlet model for capturing uncertainty about the probability distribution of the economic variable are briefly discussed.     

Combination forecasting for directional accuracy: An application to survey interest rate forecasts

Using published interest rates forecasts issued by professional economists, two combination forecasts designed to improve the directional accuracy of interest rate forecasting are constructed. The first combination forecast takes a weighted average of the individual forecasters' predictions. The more successful the forecaster was in past forecasts at predicting the direction of change in interest rates, the greater is the weight given to his/her current forecast. The second combination forecast is simply the forecast issued by the forecaster who had the greatest success rate at predicting the direction of change in interest rates in previous forecasts. In cases where two or more forecasters tie for best historic directional accuracy track record, the arithmetic mean of these forecasters is used. The study finds that neither combination forecasting method performs better than coin-flipping at predicting the direction of change in interest rates. Nor does either method beat the simple arithmetic mean of the predictions of all the forecasters surveyed at predicting the direction of change in interest rates.     

Forecasting the industrial production using alternative factor models and business survey data

This paper compares the forecasting performance of three alternative factor models based on business survey data for the industrial production in Italy. The first model uses static principal component analysis, while the other two apply dynamic principal component analysis in frequency domain and subspace algorithms for state-space representation, respectively. Once the factors are extracted from the business survey data, then they are included into a single equation to predict the industrial production index. The forecast results show that the three factor models have a better performance than that of a simple autoregressive benchmark model regardless of the specification and estimation methods. Furthermore, the state-space model yields superior forecasts amongst the factor models.     

Scenarios, Uncertainty and Conditional Forecasts of the World Population

Current official population forecasts differ little from those that Whelpton made 50 years ago either in the cohort–component methodology used or in the arguments used to motivate the assumptions. However, Whelpton produced some of the most erroneous forecasts of this century. This suggests that current forecasters should ensure that they give users an assessment of the uncertainty of their forecasts. We show how simple statistical methods can be combined with expert judgment to arrive at an overall predictive distribution for the future population. We apply the methods to a world population forecast that was made in 1994. Accepting that point forecast, we find that the probability is only about 2% that the world population in the year 2030 will be less than the low scenario of 8317 million. The probability that the world population will exceed the high scenario of 10 736 million is about 13%. Similarly, the probability is only about 51% that the high–low interval of a recent United Nations (UN) forecast will contain the true population in the year 2025. Even if we consider the UN high–low intervals as conditional on the possible future policies of its member states, they appear to have a relatively small probability of encompassing the future population.     

Forecast Uncertainty—Ex Ante and Ex Post: U.S. Inflation and Output Growth

Survey respondents who make point predictions and histogram forecasts of macro-variables reveal both how uncertain they believe the future to be, ex ante, as well as their ex post performance. Macroeconomic forecasters tend to be overconfident at horizons of a year or more, but overestimate (i.e., are underconfident regarding) the uncertainty surrounding their predictions at short horizons. Ex ante uncertainty remains at a high level compared to the ex post measure as the forecast horizon shortens. There is little evidence of a link between individuals’ ex post forecast accuracy and their ex ante subjective assessments.     

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.     

Calibration and refinement for classification trees

The calibration of forecasts for a sequence of events has an extensive literature. Since calibration does not ensure ‘good’ forecasts, the notion of refinement was introduced to provide a structure into which methods for comparing well-calibrated forecasters could be embedded.In this paper we apply these two concepts, calibration and refinement, to tree-structured statistical probability prediction systems by viewing predictions in terms of the expected value of a response variable given the values of a set of explanatory variables. When all of the variables are categorical, we show that, under suitable conditions, branching at the terminal node of a tree by adding another explanatory variable yields a tree with more refined predictions.     

The Promise of Prediction Contests

This article examines the prediction contest as a vehicle for aggregating the opinions of a crowd of experts. After proposing a general definition distinguishing prediction contests from other mechanisms for harnessing the wisdom of crowds, we focus on point-forecasting contests—contests in which forecasters submit point forecasts with a prize going to the entry closest to the quantity of interest. We first illustrate the incentive for forecasters to submit reports that exaggerate in the direction of their private information. Whereas this exaggeration raises a forecaster's mean squared error, it increases his or her chances of winning the contest. And in contrast to conventional wisdom, this nontruthful reporting usually improves the accuracy of the resulting crowd forecast. The source of this improvement is that exaggeration shifts weight away from public information (information known to all forecasters) and by so doing helps alleviate public knowledge bias. In the context of a simple theoretical model of overlapping information and forecaster behaviors, we present closed-form expressions for the mean squared error of the crowd forecasts which will help identify the situations in which point forecasting contests will be most useful.     

Forecasting cohort fertility rates by using an exponential function

"Population forecasts based on cross sectional data do not allow for the variations in cohort fertility. In this paper methods are developed to fit cohort fertility rates by an exponential function. Out of a number of selected functions the Weibull-function shows the best fit. For predicting cohort fertility pattern the parameter values can be derived from the forecasts of a small number of demographic statistics." (summary in ENG)     

Understanding exponential smoothing via kernel regression

Exponential smoothing is the most common model-free means of forecasting a future realization of a time series. It requires the specification of a smoothing factor which is usually chosen from the data to minimize the average squared residual of previous one-step-ahead forecasts. In this paper we show that exponential smoothing can be put into a nonparametric regression framework and gain some interesting insights into its performance through this interpretation. We also use theoretical developments from the kernel regression field to derive, for the first time, asymptotic properties of exponential smoothing forecasters.     

On prediction of population and subpopulation characteristics for future periods

The estimation or prediction of population characteristics based on the sample information is the key issue in survey sampling. If the sample sizes in subpopulations (domains) are large enough, similar methods as used for the whole population can be used to estimate or to predict subpopulations characteristics as well. To estimate or to predict characteristics of domains with small or even zero sample sizes, small area estimation methods “borrowing strength” from other subpopulations or time periods are widely used. We extend this problem and study methods of prediction of future population and subpopulations’ characteristics based on the longitudinal data.     

Forecasting electricity consumption with extra-model information provided by consumers

SUMMARY Univariate time series models make efficient use of available historical records of electricity consumption for short-term forecasting. However, the information (expectations) provided by electricity consumers in an energy-saving survey, even though qualitative, was considered to be particularly important, because the consumers' perception of the future may take into account the changing economic conditions. Our approach to forecasting electricity consumption combines historical data with expectations of the consumers in an optimal manner, using the technique of restricted forecasts. The same technique can be applied in some other forecasting situations in which additional information-besides the historical record of a variable-is available in the form of expectations.     

Predicting Early Data Revisions to U.S. GDP and the Effects of Releases on Equity Markets

The effects of data uncertainty on real-time decision-making can be reduced by predicting data revisions to U.S. GDP growth. We show that survey forecasts efficiently predict the revision implicit in the second estimate of GDP growth, but that forecasting models incorporating monthly economic indicators and daily equity returns provide superior forecasts of the data revision implied by the release of the third estimate. We use forecasting models to measure the impact of surprises in GDP announcements on equity markets, and to analyze the effects of anticipated future revisions on announcement-day returns. We show that the publication of better than expected third-release GDP figures provides a boost to equity markets, and if future upward revisions are expected, the effects are enhanced during recessions.     

Macroeconomic Uncertainty Through the Lens of Professional Forecasters

ABSTRACT

We analyze the evolution of macroeconomic uncertainty in the United States, based on the forecast errors of consensus survey forecasts of various economic indicators. Comprehensive information contained in the survey forecasts enables us to capture a real-time measure of uncertainty surrounding subjective forecasts in a simple framework. We jointly model and estimate macroeconomic (common) and indicator-specific uncertainties of four indicators, using a factor stochastic volatility model. Our macroeconomic uncertainty estimates have three major spikes has three major spikes aligned with the 1973–1975, 1980, and 2007–2009 recessions, while other recessions were characterized by increases in indicator-specific uncertainties. We also show that the selection of data vintages affects the estimates and relative size of jumps in estimated uncertainty series. Finally, our macroeconomic uncertainty has a persistent negative impact on real economic activity, rather than producing “wait-and-see” dynamics.     

Bayesian Procrustes analysis with applications to hydrology

In this paper, we introduce Procrustes analysis in a Bayesian framework, by treating the classic Procrustes regression equation from a Bayesian perspective, while modeling shapes in two dimensions. The Bayesian approach allows us to compute point estimates and credible sets for the full Procrustes fit parameters. The methods are illustrated through an application to radar data from short-term weather forecasts (nowcasts), a very important problem in hydrology and meteorology.