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.     

A combined random effect and fixed effect forecast for panel data models

When some of the regressors in a panel data model are correlated with the random individual effects, the random effect (RE) estimator becomes inconsistent while the fixed effect (FE) estimator is consistent. Depending on the various degree of such correlation, we can combine the RE estimator and FE estimator to form a combined estimator which can be better than each of the FE and RE estimators. In this paper, we are interested in whether the combined estimator may be used to form a combined forecast to improve upon the RE forecast (forecast made using the RE estimator) and the FE forecast (forecast using the FE estimator) in out-of-sample forecasting. Our simulation experiment shows that the combined forecast does dominate the FE forecast for all degrees of endogeneity in terms of mean squared forecast errors (MSFE), demonstrating that the theoretical results of the risk dominance for the in-sample estimation carry over to the out-of-sample forecasting. It also shows that the combined forecast can reduce MSFE relative to the RE forecast for moderate to large degrees of endogeneity and for large degrees of heterogeneity in individual effects.     

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.     

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.     

Forecasting (aggregate) demand for US commercial air travel

We analyze whether it is better to forecast air travel demand using aggregate data at (say) a national level, or to aggregate the forecasts derived for individual airports using airport-specific data. We compare the US Federal Aviation Administration’s (FAA) practice of predicting the total number of passengers using macroeconomic variables with an equivalently specified AIM (aggregating individual markets) approach. The AIM approach outperforms the aggregate forecasting approach in terms of its out-of-sample air travel demand predictions for different forecast horizons. Variants of AIM, where we restrict the coefficient estimates of some explanatory variables to be the same across individual airports, generally dominate both the aggregate and AIM approaches. The superior out-of-sample performances of these so-called quasi-AIM approaches depend on the trade-off between heterogeneity and estimation uncertainty. We argue that the quasi-AIM approaches exploit the heterogeneity across individual airports efficiently, without suffering from as much estimation uncertainty as the AIM approach.     

Are professional forecasters overconfident?

Do professional forecasters have an accurate sense of the uncertainties surrounding their own forecasts? This paper examines forecaster overconfidence by comparing ex ante, surveyed forecaster uncertainty with ex post, realised uncertainty based on the dispersion of an individual’s forecast errors. Unlike the literature that focuses on consensus forecasts, our focus is at the level of the individual forecaster. Using microdata from the three major surveys of professional forecasters (Euro Area, US and UK), we examine real GDP growth forecasts over the period 1999–2015. Our findings show that overconfidence dominates among individual forecasters, particularly for longer forecast horizons, and that individual forecasters appear to have little understanding of their own uncertainty.     

The Measurement and Behavior of Uncertainty: Evidence from the ECB Survey of Professional Forecasters

We examine matched point and density forecasts of output growth, inflation and unemployment from the ECB Survey of Professional Forecasters. We construct measures of uncertainty from individual histograms, and find that the measures display countercyclical behavior and have increased across all forecast horizons since 2007. We also derive measures of forecast dispersion and forecast accuracy, and find that they are not reliable proxies for uncertainty. There is, however, evidence of a meaningful co‐movement between uncertainty and aggregate point predictions for output growth and unemployment. These results are robust to changes in the composition of the survey respondents over time. Copyright © 2015 John Wiley & Sons, Ltd.     

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.     

An information-theoretic approach for forecasting interval-valued SP500 daily returns

We develop an iterative and efficient information-theoretic estimator for forecasting interval-valued data, and use our estimator to forecast the SP500 returns up to five days ahead using moving windows. Our forecasts are based on 13 years of data. We show that our estimator is superior to its competitors under all of the common criteria that are used to evaluate forecasts of interval data. Our approach differs from other methods that are used to forecast interval data in two major ways. First, rather than applying the more traditional methods that use only certain moments of the intervals in the estimation process, our estimator uses the complete sample information. Second, our method simultaneously selects the model (or models) and infers the model’s parameters. It is an iterative approach that imposes minimal structure and statistical assumptions.     

Accounting for the Political Uncertainty Factor

We build our analysis upon previous work by Bloom et al. (Measuring the Effect of Political Uncertainty. Working Paper, Stanford University, 2012) and Baker et al. (Political Uncertainty: A New Indicator. CentrePiece 2012; 16 (3): 21–23), who estimate the dynamic effects of a shock to a newly constructed surrogate measure of political uncertainty (PU) on the US economy. Comparable to their results we demonstrate that a shock to PU has pervasive effects on the dynamic evolution of the US economy. Using an estimated structural dynamic factor model we find that more globally integrated markets exhibit significantly more pronounced responses than other measures of real economic activity. Impulse responses reveal a small but statistically significant ‘flight‐to‐safety’ effect, depressing government bond yields across the entire term structure following a shock to PU. Forecast error variance decompositions are predominantly composed of supply, demand, and PU shocks over all horizons, with PU shocks contributing less and supply shocks contributing more to forecast errors at longer horizons. Technology shocks, by contrast, are found to affect forecast accuracy closer to impact with quickly decaying contributions over extended forecast horizons. Copyright © 2015 John Wiley & Sons, Ltd.     

Quantile forecast optimal combination to enhance safety stock estimation

The safety stock calculation requires a measure of the forecast error uncertainty. Such errors are usually assumed to be Gaussian iid (independently and identically distributed). However, deviations from iid lead to a deterioration in the performance of the supply chain. Recent research has shown that, contrary to theoretical approaches, empirical techniques that do not rely on the aforementioned assumptions can enhance the calculation of safety stocks. In particular, GARCH models cope with time-varying heterocedastic forecast error, and kernel density estimation does not need to rely on a determined distribution. However, if the forecast errors are time-varying heterocedastic and do not follow a determined distribution, the previous approaches are inadequate. We overcome this by proposing an optimal combination of the empirical methods that minimizes the asymmetric piecewise linear loss function, also known as the tick loss. The results show that combining quantile forecasts yields safety stocks with a lower cost. The methodology is illustrated with simulations and real data experiments for different lead times.     

Does the Capitalization of Development Costs Improve Analyst Forecast Accuracy? Evidence from the UK

It has been documented that investments in Research and Development (R&D) are associated with increased errors and inaccuracy in earnings forecasts made by financial analysts. These deficiencies have been generally attributed to information complexity and the uncertainty of the future benefits of R&D. This paper examines whether the capitalization of development costs can reduce analyst uncertainty about the future economic outcome of R&D investments, provide outsiders with a better matching of future R&D‐related revenues and costs, and therefore promote accuracy in analyst forecasts. UK data is used, because accounting rules in the United Kingdom permitted firms to conditionally capitalize development costs even before the introduction of the International Financial Reporting Standards. The choice to expense R&D rather than conditionally capitalize development costs is found to relate positively to signed analyst forecast errors. This finding is robust to controlling for the influence of other factors that may affect errors, as well as for the influence of R&D investments on forecast errors. The decision to capitalize versus expense is not observed to have a significant influence on analyst forecast revisions. The findings are interpreted as evidence that the choice to capitalize as opposed to expense may help to reduce deficiencies in analyst forecasts; hence, is informative for users of financial statements. Increased informativeness is expected to have repercussions for the effectiveness with which analysts produce earnings forecasts, and, as a result, market efficiency.     

Forecasting China's foreign exchange reserves using dynamic model averaging: The roles of macroeconomic fundamentals,financial stress and economic uncertainty

We develop models for examining possible predictors of growth of China's foreign exchange reserves that embrace Chinese and global trade, financial and risk (uncertainty) factors. Specifically, by comparing with other alternative models, we show that the dynamic model averaging (DMA) and dynamic model selection (DMS) models outperform not only linear models (such as random walk, recursive OLS-AR(1) models, recursive OLS with all predictive variables models) but also the Bayesian model averaging (BMA) model for examining possible predictors of growth of those reserves. The DMS is the best overall across all forecast horizons. While some predictors matter more than others over the forecast horizons, there are few that stand the test of time. The US–China interest rate differential has a superior predictive power among the 13 predictors considered, followed by the nominal effective exchange rate and the interest rate spread for most of the forecast horizons. The relative predictive prowess of the oil and copper prices alternates, depending on the commodity cycles. Policy implications are also provided.     

Content horizons for univariate time-series forecasts

This paper investigates the maximum horizon at which conditioning information can be shown to have value for univariate time series forecasts. In particular, we consider the problem of determining the horizon beyond which forecasts from univariate time series models of stationary processes add nothing to the forecast implicit in the unconditional mean. We refer to this as the content horizon for forecasts, and provide a formal definition of the corresponding forecast content function at horizons s=1,… S. This function depends upon parameter estimation uncertainty as well as on autocorrelation structure of the process. We show that for autoregressive processes it is possible to give an asymptotic expression for the forecast content function, and show by simulation that the expression gives a good approximation even at modest sample sizes. The results are applied to the growth rate of GDP and to inflation, using US and Canadian data.     

Averaging estimators for autoregressions with a near unit root

This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple graphical comparisons. Our results strongly caution against pre-testing. Strong evidence supports averaging based on Mallows weights. In particular, our Mallows averaging method has uniformly and substantially smaller risk than the conventional unconstrained estimator, and this holds for autoregressive roots far from unity. Our averaging estimator is a new approach to forecast combination.     

Estimation methods for male labor supply functions How to take account of nonlinear taxes

Nonlinear taxes create econometric difficulties when estimating labor supply functions. One estimation method that tackles these problems accounts for the complete form of the budget constraint and uses the maximum likelihood method to estimate parameters. Another method linearizes budget constraints and uses instrumental variables techniques. Using Monte Carlo simulations I investigate the small-sample properties of these estimation methods and how they are affected by measurement errors in independent variables. No estimator is uniquely best. Hence, in actual estimation the choice of estimator should depend on the sample size and type of measurement errors in the data. Complementing actual estimates with a Monte Carlo study of the estimator used, given the type of measurement errors that characterize the data, would often help interpreting the estimates. This paper shows how such a study can be performed.     

Population forecasting theory,methods and assessments of accuracy. The magnitude of error due to different vital processes in population forecasts

The accuracy of population forecasts depends in part upon the method chosen for forecasting the vital rates of fertility, mortality, and migration. Methods for handling the stochastic propagation of error calculations in demographic forecasting are hard to do precisely. This paper discusses this obstacle in stochastic cohort-component population forecasts. The uncertainty of forecasts is due to uncertain estimates of the jump-off population and to errors in the forecasts of the vital rates. Empirically based of each source are presented and propagated through a simplified analytical model of population growth that allows assessment of the role of each component in the total error. Numerical estimates based on the errors of an actual vector ARIMA forecast of the US female population. These results broadly agree with those of the analytical model. This work especially uncertainty in the fertility forecasts to be so much higher than that in the other sources that the latter can be ignored in the propagation of error calculations for those cohorts that are born after the jump-off year of the forecast. A methodology is therefore presented which far simplifies the propagation of error calculations. It is noted, however, that the uncertainty of the jump-off population, migration, and mortality in the propagation of error for those alive at the jump-off time of the forecast must still be considered.     

Dimensionality reduction in forecasting with temporal hierarchies

Combining forecasts from multiple temporal aggregation levels exploits information differences and mitigates model uncertainty, while reconciliation ensures a unified prediction that supports aligned decisions at different horizons. It can be challenging to estimate the full cross-covariance matrix for a temporal hierarchy, which can easily be of very large dimension, yet it is difficult to know a priori which part of the error structure is most important. To address these issues, we propose to use eigendecomposition for dimensionality reduction when reconciling forecasts to extract as much information as possible from the error structure given the data available. We evaluate the proposed estimator in a simulation study and demonstrate its usefulness through applications to short-term electricity load and financial volatility forecasting. We find that accuracy can be improved uniformly across all aggregation levels, as the estimator achieves state-of-the-art accuracy while being applicable to hierarchies of all sizes.     

The effect of investors’ confidence on monetary policy transmission mechanism: A Multivariate GARCH approach

This paper investigates the financial stability’s effect on the monetary policy transmission mechanisms. The correlations between investors’ confidence in the markets, money growth and economic growth are analyzed along with the correlations within their volatilities. Specifically, the heteroskedasticity of the errors is exploited in a Multivariate GARCH framework to obtain endogenously estimated measures of uncertainty. By a two-step estimator, the indirect interplay of money growth and financial markets is highlighted at different time horizons. The results contrast previous literature supportive of the “Great Moderation” as causing the recent financial crisis. Effectively, by accounting for the breaks in volatility series due to structural shifts in monetary policy, a low period of macroeconomic volatility is found not to drive directly low financial stability.