Are Analysts' Loss Functions Asymmetric?

Despite displaying a statistically significant optimism bias, analysts' earnings forecasts are an important input to investors’ valuation models. Understanding the possible reasons for any bias is important if information is to be extracted from earnings forecasts and used optimally by investors. Extant research into the shape of analysts' loss functions explains optimism bias as resulting from analysts minimizing the mean absolute forecast error under symmetric, linear loss functions. When the distribution of earnings outcomes is skewed, optimalforecasts can appear biased. In contrast, research into analysts' economic incentives suggests that positive and negative earnings forecast errors made by analysts are not penalized or rewarded symmetrically, suggesting that asymmetric loss functions are an appropriate characterization. To reconcile these findings, we exploit results from economic theory relating to the Linex loss function to discriminate between the symmetric linear loss and the asymmetric loss explanations of analyst forecast bias. Under asymmetric loss functions optimal forecasts will appear biased even if earnings outcomes are symmetric. Our empirical results support the asymmetric loss function explanation. Further analysis also reveals that forecast bias varies systematically across firm characteristics that capture systematic variation in the earnings forecast error distribution. Copyright © 2011 John Wiley & Sons, Ltd.     

Combining multivariate volatility forecasts using weighted losses

The ability to improve out-of-sample forecasting performance by combining forecasts is well established in the literature. This paper advances this literature in the area of multivariate volatility forecasts by developing two combination weighting schemes that exploit volatility persistence to emphasise certain losses within the combination estimation period. A comprehensive empirical analysis of the out-of-sample forecast performance across varying dimensions, loss functions, sub-samples and forecast horizons show that new approaches significantly outperform their counterparts in terms of statistical accuracy. Within the financial applications considered, significant benefits from combination forecasts relative to the individual candidate models are observed. Although the more sophisticated combination approaches consistently rank higher relative to the equally weighted approach, their performance is statistically indistinguishable given the relatively low power of these loss functions. Finally, within the applications, further analysis highlights how combination forecasts dramatically reduce the variability in the parameter of interest, namely the portfolio weight or beta.     

Correcting the January optimism effect

Each month, various professional forecasters give forecasts for next year's real gross domestic product (GDP) growth and unemployment. January is a special month, when the forecast horizon moves to the following calendar year. Instead of deleting the January data when analyzing forecast updates, I propose a periodic version of a test regression for weak-form efficiency. An application of this periodic model for many forecasts across a range of countries shows that in January GDP forecast updates are positive, whereas the forecast updates for unemployment are negative. I document that this January optimism about the new calendar year is detrimental to forecast accuracy. To empirically analyze Okun's law, I also propose a periodic test regression, and its application provides more support for this law.     

Evaluating the predictive accuracy of volatility models

Standard statistical loss functions, such as mean‐squared error, are commonly used for evaluating financial volatility forecasts. In this paper, an alternative evaluation framework, based on probability scoring rules that can be more closely tailored to a forecast user's decision problem, is proposed. According to the decision at hand, the user specifies the economic events to be forecast, the scoring rule with which to evaluate these probability forecasts, and the subsets of the forecasts of particular interest. The volatility forecasts from a model are then transformed into probability forecasts of the relevant events and evaluated using the selected scoring rule and calibration tests. An empirical example using exchange rate data illustrates the framework and confirms that the choice of loss function directly affects the forecast evaluation results. Copyright © 2001 John Wiley & Sons, Ltd.     

Forecasting the conditional covariance matrix of a portfolio under long‐run temporal dependence

Long‐range persistence in volatility is widely modelled and forecast in terms of the so‐called fractional integrated models. These models are mostly applied in the univariate framework, since the extension to the multivariate context of assets portfolios, while relevant, is not straightforward. We discuss and apply a procedure which is able to forecast the multivariate volatility of a portfolio including assets with long memory. The main advantage of this model is that it is feasible enough to be applied on large‐scale portfolios, solving the problem of dealing with extremely complex likelihood functions which typically arises in this context. An application of this procedure to a portfolio of five daily exchange rate series shows that the out‐of‐sample forecasts for the multivariate volatility are improved under several loss functions when the long‐range dependence property of the portfolio assets is explicitly accounted for. Copyright © 2006 John Wiley & Sons, Ltd.     

Estimating private information usage amongst analysts: evidence from UK earnings forecasts

This paper introduces a methodology for estimating the likelihood of private information usage amongst earnings analysts. This is achieved by assuming that one group of analysts generate forecasts based on the underlying dynamics of earnings, while all other analysts are assumed to issue forecasts based on the prevailing consensus forecast. Given this behavioural dichotomy, we are able to derive (and estimate) a structural econometric model of forecast behaviour, which has implications regarding the determinants of analysts' private information endowments and forecast accuracy over the forecast horizon. Copyright © 2010 John Wiley & Sons, Ltd.     

Mincer–Zarnowitz quantile and expectile regressions for forecast evaluations under aysmmetric loss functions

Forecasts are pervasive in all areas of applications in business and daily life. Hence evaluating the accuracy of a forecast is important for both the generators and consumers of forecasts. There are two aspects in forecast evaluation: (a) measuring the accuracy of past forecasts using some summary statistics, and (b) testing the optimality properties of the forecasts through some diagnostic tests. On measuring the accuracy of a past forecast, this paper illustrates that the summary statistics used should match the loss function that was used to generate the forecast. If there is strong evidence that an asymmetric loss function has been used in the generation of a forecast, then a summary statistic that corresponds to that asymmetric loss function should be used in assessing the accuracy of the forecast instead of the popular root mean square error or mean absolute error. On testing the optimality of the forecasts, it is demonstrated how the quantile regressions set in the prediction–realization framework of Mincer and Zarnowitz (in J. Mincer (Ed.), Economic Forecasts and Expectations: Analysis of Forecasting Behavior and Performance (pp. 14–20), 1969) can be used to recover the unknown parameter that controls the potentially asymmetric loss function used in generating the past forecasts. Finally, the prediction–realization framework is applied to the Federal Reserve's economic growth forecast and forecast sharing in a PC manufacturing supply chain. It is found that the Federal Reserve values overprediction approximately 1.5 times more costly than underprediction. It is also found that the PC manufacturer weighs positive forecast errors (under forecasts) about four times as costly as negative forecast errors (over forecasts).     

A test of the joint efficiency of macroeconomic forecasts using multivariate random forests

We contribute to recent research on the joint evaluation of the properties of macroeconomic forecasts in a multivariate setting. The specific property of forecasts that we are interested in is their joint efficiency. We study the joint efficiency of forecasts by means of multivariate random forests, which we use to model the links between forecast errors and predictor variables in a forecaster's information set. We then use permutation tests to study whether the Mahalanobis distance between the predicted forecast errors for the growth and inflation forecasts of four leading German economic research institutes and actual forecast errors is significantly smaller than under the null hypothesis of forecast efficiency. We reject joint efficiency in several cases, but also document heterogeneity across research institutes with regard to the joint efficiency of their forecasts.     

Forecasting Errors,Directional Accuracy and Profitability of Currency Trading: The Case of EUR/USD Exchange Rate

We provide a comprehensive study of out‐of‐sample forecasts for the EUR/USD exchange rate based on multivariate macroeconomic models and forecast combinations. We use profit maximization measures based on directional accuracy and trading strategies in addition to standard loss minimization measures. When comparing predictive accuracy and profit measures, data snooping bias free tests are used. The results indicate that forecast combinations, in particular those based on principal components of forecasts, help to improve over benchmark trading strategies, although the excess return per unit of deviation is limited. Copyright © 2016 John Wiley & Sons, Ltd.     

Forecasting in long horizons using smoothed direct forecast

This paper constructs a forecast method that obtains long‐horizon forecasts with improved performance through modification of the direct forecast approach. Direct forecasts are more robust to model misspecification compared to iterated forecasts, which makes them preferable in long horizons. However, direct forecast estimates tend to have jagged shapes across horizons. Our forecast method aims to “smooth out” erratic estimates across horizons while maintaining the robust aspect of direct forecasts through ridge regression, which is a restricted regression on the first differences of regression coefficients. The forecasts are compared to the conventional iterated and direct forecasts in two empirical applications: real oil prices and US macroeconomic series. In both applications, our method shows improvement over direct forecasts.     

The use of encompassing tests for forecast combinations

This paper proposes an algorithm that uses forecast encompassing tests for combining forecasts when there are a large number of forecasts that might enter the combination. The algorithm excludes a forecast from the combination if it is encompassed by another forecast. To assess the usefulness of this approach, an extensive empirical analysis is undertaken using a US macroeconomic dataset. The results are encouraging; the algorithm forecasts outperform benchmark model forecasts, in a mean square error (MSE) sense, in a majority of cases. The paper also compares the empirical performance of different approaches to forecast combination, and provides a rule‐of‐thumb cut‐off point for the thick‐modeling approach. Copyright © 2009 John Wiley & Sons, Ltd.     

Forecasting for business planning: A case study of IBM product sales

This is a case study of a closely managed product. Its purpose is to determine whether time-series methods can be appropriate for business planning. By appropriate, we mean two things: whether these methods can model and estimate the special events or features that are often present in sales data; and whether they can forecast accurately enough one, two and four quarters ahead to be useful for business planning. We use two time-series methods, Box-Jenkins modeling and Holt-Winters adaptive forecasting, to obtain forecasts of shipments of a closely managed product. We show how Box-Jenkins transfer-function models can account for the special events in the data. We develop criteria for choosing a final model which differ from the usual methods and are specifically directed towards maximizing the accuracy of next-quarter, next-half-year and next-full-year forecasts. We find that the best Box-Jenkins models give forecasts which are clearly better than those obtained from Holt-Winters forecast functions, and are also better than the judgmental forecasts of IBM's own planners. In conclusion, we judge that Box-Jenkins models can be appropriate for business planning, in particular for determining at the end of the year baseline business-as-usual annual and monthly forecasts for the next year, and in mid-year for resetting the remaining monthly forecasts.     

Exchange rate forecasting and the performance of currency portfolios

We examine the potential gains of using exchange rate forecast models and forecast combination methods in the management of currency portfolios for three exchange rates: the euro versus the US dollar, the British pound, and the Japanese yen. We use a battery of econometric specifications to evaluate whether optimal currency portfolios implied by trading strategies based on exchange rate forecasts outperform single currencies and the equally weighted portfolio. We assess the differences in profitability of optimal currency portfolios for different types of investor preferences, two trading strategies, mean squared error‐based composite forecasts, and different forecast horizons. Our results indicate that there are clear benefits of integrating exchange rate forecasts from state‐of‐the‐art econometric models in currency portfolios. These benefits vary across investor preferences and prediction horizons but are rather similar across trading strategies.     

Forecasting the 10‐year US Treasury rate

This study compares the performance of two forecasting models of the 10‐year Treasury rate: a random walk (RW) model and an augmented‐autoregressive (A‐A) model which utilizes the information in the expected inflation rate. For 1993–2008, the RW and A‐A forecasts (with different lead times and forecast horizons) are generally unbiased and accurately predict directional change under symmetric loss. However, the A‐A forecasts outperform the RW, suggesting that the expected inflation rate (as a leading indicator) helps improve forecast accuracy. This finding is important since bond market efficiency implies that the RW forecasts are optimal and cannot be improved. Copyright © 2009 John Wiley & Sons, Ltd.     

The Effects of Disaggregation on Forecasting Nonstationary Time Series

This paper focuses on the effects of disaggregation on forecast accuracy for nonstationary time series using dynamic factor models. We compare the forecasts obtained directly from the aggregated series based on its univariate model with the aggregation of the forecasts obtained for each component of the aggregate. Within this framework (first obtain the forecasts for the component series and then aggregate the forecasts), we try two different approaches: (i) generate forecasts from the multivariate dynamic factor model and (ii) generate the forecasts from univariate models for each component of the aggregate. In this regard, we provide analytical conditions for the equality of forecasts. The results are applied to quarterly gross domestic product (GDP) data of several European countries of the euro area and to their aggregated GDP. This will be compared to the prediction obtained directly from modeling and forecasting the aggregate GDP of these European countries. In particular, we would like to check whether long‐run relationships between the levels of the components are useful for improving the forecasting accuracy of the aggregate growth rate. We will make forecasts at the country level and then pool them to obtain the forecast of the aggregate. The empirical analysis suggests that forecasts built by aggregating the country‐specific models are more accurate than forecasts constructed using the aggregated data. Copyright © 2014 John Wiley & Sons, Ltd.     

A Multiplicative Error Model with Heterogeneous Components for Forecasting Realized Volatility

To forecast realized volatility, this paper introduces a multiplicative error model that incorporates heterogeneous components: weekly and monthly realized volatility measures. While the model captures the long‐memory property, estimation simply proceeds using quasi‐maximum likelihood estimation. This paper investigates its forecasting ability using the realized kernels of 34 different assets provided by the Oxford‐Man Institute's Realized Library. The model outperforms benchmark models such as ARFIMA, HAR, Log‐HAR and HEAVY‐RM in within‐sample fitting and out‐of‐sample (1‐, 10‐ and 22‐step) forecasts. It performed best in both pointwise and cumulative comparisons of multi‐step‐ahead forecasts, regardless of loss function (QLIKE or MSE). Copyright © 2015 John Wiley & Sons, Ltd.     

Evaluating the Rationality of Fixed-event Forecasts

A test of forecast rationality based on the weak efficiency of fixed-event forecasts was proposed by Nordhaus (1987). This paper considers the scope for pooling fixed-event forecasts across ‘events’, to deliver more powerful tests of the weak-efficiency hypothesis, when only a small number of fixed-event forecasts are available. In an empirical illustration we demonstrate the usefulness of this approach. We also suggest an interpretation of the rejection of the null hypothesis of weak efficiency in favour of negative autocorrelation in series of revisions to fixed-event forecasts. The relationship between weak efficiency and rationality when loss functions are asymmetric and prediction error variances are time-varying is also considered.© 1997 John Wiley & Sons, Ltd.     

Forecasting the duration of short‐term deflation episodes

The paper proposes a simulation‐based approach to multistep probabilistic forecasting, applied for predicting the probability and duration of negative inflation. The essence of this approach is in counting runs simulated from a multivariate distribution representing the probabilistic forecasts, which enters the negative inflation regime. The marginal distributions of forecasts are estimated using the series of past forecast errors, and the joint distribution is obtained by a multivariate copula approach. This technique is applied for estimating the probability of negative inflation in China and its expected duration, with the marginal distributions computed by fitting weighted skew‐normal and two‐piece normal distributions to autoregressive moving average ex post forecast errors and using the multivariate Student t copula.     

Testing for unreliable estimators and insignificant forecasts in combined forecasts

The reliability and precision of the weights used in combining individual forecasts, irrespective of the method of combination, is important in evaluating a combined forecast. The objective of this study is not to suggest the ‘best’ method of combining individual forecasts, but rather to propose exploratory procedures, that make use of all available sample information contained in the covariance matrix of individual forecast errors, to (1) detect if the weights used in combining forecasts are ‘reliable’ (and ‘stable’ if it is known that the covariance matrix of forecast errors is stationary over time) and (2) test for ‘insignificant’ individual forecasts used in forming a combined forecast. We present empirical applications using two-year sales and individual forecast data provided by a major consumer durables manufacturer to illustrate the feasibility of our proposed procedures.     

Combination of Forecasts across Estimation Windows: An Application to Air Travel Demand

This paper applies combining forecasts of air travel demand generated from the same model but over different estimation windows. The combination approach used resorts to Pesaran and Pick (Journal of Business Economics and Statistics 2011; 29 : 307–318), but the empirical application is extended in several ways. The forecasts are based on a seasonal Box–Jenkins model (SARIMA), which is adequate to forecast monthly air travel demand with distinct seasonal patterns at the largest German airport: Frankfurt am Main. Furthermore, forecasts with forecast horizons from 1 to 12 months ahead, which are based on different average estimation windows, expanding windows and single rolling windows, are compared with baseline forecasts based on an expanding window of the observations after a structural break. The forecast exercise shows that the average window forecasts mostly outperform the alternative single window forecasts. Copyright © 2016 John Wiley & Sons, Ltd.