Asymmetric loss in the Greenbook and the Survey of Professional Forecasters

This paper examines the forecast rationality of the Greenbook and the Survey of Professional Forecasters (SPF) under asymmetric loss functions, using the method proposed by Elliott, Komunjer, and Timmermann (2005) with a rolling window strategy. Over rolling periods, the degree and direction of the asymmetry in forecast loss functions are time-varying. While rationality under symmetric loss is often rejected, forecast rationality under asymmetric loss fails to be rejected over nearly all rolling periods. Besides, real output growth is consistently under-predicted in the 1990s, and the inflation rate is consistently over-predicted in the 1980s and 1990s. In general, inflation forecasts, especially for long horizons, exhibit greater levels of loss asymmetry in magnitude and frequency. The loss asymmetry of real output growth forecasts is more pronounced when the last revised vintage data are used than when the real-time vintage is used. All of these results hold for both the Greenbook and SPF forecasts. The results are also similar with the use of different sets of instrumental variables for estimating the asymmetric loss and testing for forecast rationality.     

Quantiles as optimal point forecasts

Loss functions play a central role in the theory and practice of forecasting. If the loss function is quadratic, the mean of the predictive distribution is the unique optimal point predictor. If the loss is symmetric piecewise linear, any median is an optimal point forecast. Quantiles arise as optimal point forecasts under a general class of economically relevant loss functions, which nests the asymmetric piecewise linear loss, and which we refer to as generalized piecewise linear (GPL). The level of the quantile depends on a generic asymmetry parameter which reflects the possibly distinct costs of underprediction and overprediction. Conversely, a loss function for which quantiles are optimal point forecasts is necessarily GPL. We review characterizations of this type in the work of Thomson, Saerens and Komunjer, and relate to proper scoring rules, incentive-compatible compensation schemes and quantile regression. In the empirical part of the paper, the relevance of decision theoretic guidance in the transition from a predictive distribution to a point forecast is illustrated using the Bank of England’s density forecasts of United Kingdom inflation rates, and probabilistic predictions of wind energy resources in the Pacific Northwest.     

Asymmetric loss functions and the rationality of expected stock returns

We combine the innovative approaches of Elliott, Komunjer, and Timmermann (2005) and Patton and Timmermann (2007) with a block bootstrap to analyze whether asymmetric loss functions can rationalize the S&P 500 return expectations of individual forecasters from the Livingston Surveys. Although the rationality of these forecasts has often been rejected, earlier studies have relied on the assumption that positive and negative forecast errors of identical magnitudes are equally important to forecasters. Allowing for homogenous asymmetric loss, our evidence still strongly rejects forecast rationality. However, if we allow for variation in asymmetric loss functions across forecasters, not only do we find significant differences in preferences, but also we can often no longer reject forecast rationality. Our conclusions raise serious doubts about the homogeneous expectations assumption often made in asset pricing, portfolio construction and corporate finance models.     

The asymmetry of judgemental confidence intervals in time series forecasting

In forecasting a time series, one may be asked to communicate the likely distribution of the future actual value, often expressed as a confidence interval. Whilst the accuracy (calibration) of these intervals has dominated most studies to date, this paper is concerned with other possible characteristics of the intervals. It reports a study in which the prevalence and determinants of the symmetry of judgemental confidence intervals in time series forecasting was examined. Most prior work has assumed that this interval is symmetrically placed around the forecast. However, this study shows that people generally estimate asymmetric confidence intervals where the forecast is not the midpoint of the estimated interval. Many of these intervals are grossly asymmetric. Results indicate that the placement of the forecast in relation to the last actual value of a time series is a major determinant of the direction and size of the asymmetry.     

Volatility forecasting in the Bitcoin market: A new proposed measure based on the VS-ACARR approach

This paper proposes a new volatility-spillover-asymmetric conditional autoregressive range (VS-ACARR) approach that takes into account the intraday information, the volatility spillover from crude oil as well as the volatility asymmetry (leverage effect) to model/forecast Bitcoin volatility (price range). An empirical application to Bitcoin and crude oil (WTI) price ranges shows the existence of strong volatility spillover from crude oil to the Bitcoin market and a weak leverage effect in the Bitcoin market. The VS-ACARR model yields higher forecasting accuracy than the GARCH, CARR, and VS-CARR models regarding out-of-sample forecast performance, suggesting that accounting for the volatility spillover and asymmetry can significantly improve the forecasting accuracy of Bitcoin volatility. The superior forecast performance of the VS-ACARR model is robust to alternative out-of-sample forecast windows. Our findings highlight the importance of accommodating intraday information, spillover from crude oil, and volatility asymmetry in forecasting Bitcoin volatility.     

A new approach for detecting shifts in forecast accuracy

Forecasts play a critical role at inflation-targeting central banks, such as the Bank of England. Breaks in the forecast performance of a model can potentially incur important policy costs. However, commonly-used statistical procedures implicitly place a lot of weight on type I errors (or false positives), which results in a relatively low power of the tests to identify forecast breakdowns in small samples. We develop a procedure which aims to capture the policy cost of missing a break. We use data-based rules to find the test size that optimally trades off the costs associated with false positives with those that can result from a break going undetected for too long. In so doing, we also explicitly study forecast errors as a multivariate system. The covariance between forecast errors for different series, although often overlooked in the forecasting literature, not only enables us to consider testing in a multivariate setting, but also increases the test power. As a result, we can tailor our choice of the critical values for each series not only to the in-sample properties of each series, but also to the way in which the series of forecast errors covary.     

The Effect of Leasing versus Buying on Entry Deterrence

Models of entry deterrence typically require that incumbents possess a cost advantage as a prerequisite for deterring entry. Potential entrants possess a cost advantage over incumbents, however, if input costs fall over time. This paper models the behavior of an incumbent and a potential entrant when the input cost falls over time and the firms have the option of buying or leasing the input. The model shows that if the future cost savings from new technology exceed the marginal transaction costs of leasing the current equipment, then leasing increases the incumbent's ability to deter entry. Copyright © 2011 John Wiley & Sons, Ltd.     

Nonparametric and semiparametric regressions subject to monotonicity constraints: Estimation and forecasting

This paper considers nonparametric and semiparametric regression models subject to monotonicity constraint. We use bagging as an alternative approach to Hall and Huang (2001). Asymptotic properties of our proposed estimators and forecasts are established. Monte Carlo simulation is conducted to show their finite sample performance. An application to predicting equity premium is taken for illustration. We introduce a new forecasting evaluation criterion based on the second order stochastic dominance in the size of forecast errors and compare models over different sizes of forecast errors. Imposing monotonicity constraint can mitigate the chance of making large size forecast errors.     

Are GDP forecasts optimal? Evidence on European countries

We assess the accuracy of real GDP growth forecasts released by governments and international organizations for European countries in the years 1999–2017. We implement three testing procedures characterized by different assumptions on the forecasters’ loss functions. First, we test forecast rationality within the traditional approach based on a quadratic loss function (Mincer and Zarnowitz, 1969). Second, following Elliott, Timmermann and Komunjer (2005), we test rationality by allowing for a flexible loss function where the shape parameter driving the extent of asymmetry is unknown and estimated from the empirical distribution of forecast errors. Lastly, we implement the tests proposed by Patton and Timmermann (2007a) that hold regardless of the functional form of the loss function. We conclude that governmental forecasts are biased and not rational under a symmetric and quadratic loss function, but they are optimal under more general assumptions on the loss function. We also find that the preferences of forecasters change with the forecasting horizon: when moving from one- to two-year-ahead forecasts, the optimistic bias increases and the parameter of asymmetry in the loss function significantly increases.     

Static and dynamic models for multivariate distribution forecasts: Proper scoring rule tests of factor-quantile versus multivariate GARCH models

Many static and dynamic models exist to forecast Value-at-Risk and other quantile-related metrics used in financial risk management. Industry practice favours simpler, static models such as historical simulation or its variants. Most academic research focuses on dynamic models in the GARCH family. While numerous studies examine the accuracy of multivariate models for forecasting risk metrics, there is little research on accurately predicting the entire multivariate distribution. However, this is an essential element of asset pricing or portfolio optimization problems having non-analytic solutions. We approach this highly complex problem using various proper multivariate scoring rules to evaluate forecasts of eight-dimensional multivariate distributions: exchange rates, interest rates and commodity futures. This way, we test the performance of static models, namely, empirical distribution functions and a new factor-quantile model with commonly used dynamic models in the asymmetric multivariate GARCH class.     

SEARCH AND VACANCY COSTS IN THE TOKYO HOUSING MARKET: ATTEMPT TO MEASURE SOCIAL COSTS OF IMPERFECT INFORMATION

The social cost of imperfect information, in terms of buyers' search costs and sellers' opportunity costs of vacancy, is estimated in the real estate market of resale condominiums in central Tokyo by using a new, comprehensive dataset of resale condominium transactions. The results suggest a substantial social cost. Specifically, if housing information were perfectly available and marketing time were null, sellers would get benefits of 22.59% of imputed net rents of their property. In addition, buyers would save 1,042,000 yen spent on search activities for one transaction, if information were perfect. This is equivalent to 13.2% of buyers' average annual income.     

Leasing versus purchasing: Direct evidence on a corporation’s motivations for leasing and consequences of leasing

This paper provides new evidence on the possible sources of lessee equity value changes when leasing contracts are announced. We show that lessee common equity value increases significantly in sale and leasebacks and insignificantly in direct leases. We find support, in sale and leasebacks, for the tax-savings hypothesis and for the savings in bankruptcy costs hypothesis. We also find support for the hypothesis that leasing reduces the external financing costs related to adverse selection that arise in markets with asymmetric information. Finally, we show that lessees gain less in direct leases when they lease assets with salvage values that are sensitive to use.     

Forecasting Errors: the Track Record

This Briefing Paper is the last of a series of three about forecasting. In this one we examine our forecasting record; it complements the February paper in which we analysed the properties of our forecasting model in terms of the error bands attached to the central forecast.
There are many ways of measuring forecasting errors, and in the first part of this Briefing Paper we describe briefing how we have tackled the problem. (A more detailed analysis can be found in the Appendix.) In Part II we report and comment upon the errors in our forecasts of annual growth rates and show how our forecasting performance has improved over the years. In Part III we focus on quarterly forecasts up to 8 quarters ahead, and compare our forecasting errors with measurement errors in the oficial statistics; with the estimation errors built into our forecast equations; and with the stochastic model errors we reported last February. A brief summary of the main conclusions is given below.     

What determines forecasters’ forecasting errors?

This paper contributes to the growing body of literature in macroeconomics and finance on expectation formation and information processing by analyzing the relationship between expectation formation at the individual level and the prediction of macroeconomic aggregates. Using information from business tendency surveys, we present a new approach of analyzing forecasters’ qualitative forecasting errors. Based on a quantal response approach with misclassification, we define forecasters’ qualitative mispredictions in terms of deviations from the qualitative rational expectation forecast, and relate them to the individual and macro factors that are driving these mispredictions. Our approach permits a detailed analysis of individual forecasting decisions, allowing for the introduction of individual and economy-wide determinants that affect the individual forecasting error process.     

Asymmetric Price Adjustments in Airlines

This paper uses a unique daily time series data set to investigate the asymmetric response of airline prices to capacity costs driven by demand fluctuations. We use a Markov regime‐switching model with time‐varying transition probabilities to capture the time variation in the response. The results show strong evidence of asymmetric price adjustments: positive cost shifts have a large positive effect, whereas negative cost shifts have no effect. The asymmetry is also explained by summer travel but not by the size of cost shifts. The findings show the importance of consumer heterogeneity and capacity constraints as a source of asymmetric responses. Copyright © 2012 John Wiley & Sons, Ltd.     

Forecasting automobile insurance paid claim costs using econometric and ARIMA models

Automobile insurance companies in the United States currently utilize simple exponential trend models to forecast paid claim costs, an important variable in ratemaking. This paper tests the performance of econometric and ARIMA models, as well as the current insurance industry method, in forecasting two paid claim cost series. The experiments encompass eight forecast periods ranging from 1974 through early 1983. The results indicate that automobile insurers could significantly improve their forecasts of property damage liability claim costs by adopting econometric models. For bodily injury liability claim costs, the accuracy of the econometric and insurance industry methods is approximately the same, and both outperform the ARIMA models. Overall, a net gain in accuracy could be achieved by adopting econometric models.     

Commodity futures prices: More evidence on forecast power,risk premia and the theory of storage

In this paper, we examine the temporal stability of the evidence for two commodity futures pricing theories. We investigate whether the forecast power of commodity futures can be attributed to the extent to which they exhibit seasonality and we also consider whether there are time varying parameters or structural breaks in these pricing relationships. Compared to previous studies, we find stronger evidence of seasonality in the basis, which supports the theory of storage. The power of the basis to forecast subsequent price changes is also strengthened, while results on the presence of a risk premium are inconclusive. In addition, we show that the forecasting power of commodity futures cannot be attributed to the extent to which they exhibit seasonality. We find that in most cases where structural breaks occur, only changes in the intercepts and not the slopes are detected, illustrating that the forecast power of the basis is stable over different economic environments.     

Performance evaluation of the LDR and the PSH with forecast errors

Despite its ability to produce optimal solutions, the Linear Decision Rule (LDR) has not had a significant impact in the business environment. The Production Switching Heuristic (PSH), which has shown promising results when compared with the LDR, has experienced some business application because of its practicability and flexibility. During aggregate production planning, forecast errors are almost unavoidable, but the sensitivity of these models to such errors has not been thoroughly tested. Insufficient attention has been paid to truly understand the cost effects of forecast errors and other important interactions. The study investigates these issues by analyzing the results of 740 simulated problems.Using the famous “paint factory” cost data, the sensitivity of the LDR and the PSH are examined under various experimental conditions. The factors controlled at different levels are: forecast error mean, forecast error standard deviation, demand pattern, demand variability, and cost coefficients. The results show that 1) the PSH is generally less sensitive than the LDR to forecast errors, 2) both forecast error mean and standard deviation effectively measure the severity of forecast errors, and 3) underforecasts cause less cost penalty than overforecasts.The outcome of the study has helpful managerial implications for aggregate planning related decisionmaking. It suggests that the use of the PSH could result in potential cost savings even if significant forecast errors are envisioned as long as the period-to-period demand variability is not substantially high. Also, BIAS warrants more attention than MSE in evaluating the extent of forecast errors and their eventual cost impact on aggregate production planning.     

Technical change,inflation and pricing decisions

The paper discusses long-term managerial cost pricing, thus taking into account both operating and capital costs of new plant. This approach is relevant to the public industries, oligopoly and can also be the basis for competitive pricing. The model integrates pricing and investment decisions, and incorporates, among other factors, expected future technical change and inflation. The treatment is illustrated in relation to a range of industries with very different rates of technical advance. It also discusses the reasons for the frequent failure for full potential gains from such advances to be realized and hence for sluggish economic growth.     

DIRECT MULTI-STEP ESTIMATION AND FORECASTING

Abstract.  This paper surveys the literature on multi-step forecasting when the model or the estimation method focuses directly on the link between the forecast origin and the horizon of interest. Among diverse contributions, we show how the current consensual concepts have emerged. We present an exhaustive overview of the existing results, including a conclusive review of the circumstances favourable to direct multi-step forecasting, namely different forms of non-stationarity and appropriate model design. We also provide a unifying framework which allows us to analyse the sources of forecast errors and hence of accuracy improvements from direct over iterated multi-step forecasting.