Combining Judgmental and Statistical Forecasts: An Application to Earnings Forecasts

This study investigated the accuracy of combinations of statistical and judgmental forecasts of annual accounting earnings. Combined forecasts were generated as equally weighted (i.e., simple averages) and unequally weighted combinations of individual forecasts from time-series models of quarterly and annual earnings (statistical forecasts) and security analysts' forecasts of quarterly and annual earnings (judgmental forecasts). The effect of the number of individual forecasts combined on the accuracy of the combined forecasts was also examined. The empirical results indicated that, on the average, combined forecasts were more accurate than individual forecasts. The results also indicated that although analysts' forecasts are based on a wider information set, the accuracy of their forecasts could be improved by combining them with forecasts generated from statistical models. Even if the best individual forecast could be identified in advance, gains in accuracy could be achieved by using combinations of two other forecasting methods. Several of the combined forecasts were superior to the most accurate individual forecast. Forecasts combined by using unequal weights derived from a regression model proved more accurate than equally weighted combinations. Forecasting accuracy improved and the variability of accuracy across different combinations decreased as the number of forecasts in the combination increased.     

Some Empirical Findings on Short-Term Forecasting: Technique Complexity and Combinations

The purpose of this research is to determine if prior findings that favor simple forecasting techniques and technique combinations hold true in a short-term forecasting environment, where demand data can be quite volatile. Twenty-two time series of daily data from a real business setting are used to test one-period ahead forecasts, the epitome of short-term forecasting. The time series vary systematically as to data volatility and forecast difficulty. Forecast accuracy is measured in terms of both mean absolute percentage error (MAPE) and mean percentage error (MPE).     

Combining Forecasts: Multiple Regression versus a Bayesian Approach*

Simple linear combinations of forecasts have consistently been found to be more accurate than individual forecasts. Several recent studies have found that combination forecasts derived by constrained or unconstrained multiple regression are more accurate than a simple average of individual forecasts. This study uses macroeconomic data to compare the accuracy of combination forecasts derived by a Bayesian methodology with the accuracy of composite forecasts derived by multiple regression. Using the forecasts of four macroeconomic variables from five well-known econometric models, the study finds that the Bayesian combination procedure produces more accurate composite forecasts than does the regression combination procedure, based on a version of Theil's U² statistic.     

The Value of Weather Information for E‐Commerce Operations

To be efficient, logistics operations in e‐commerce require warehousing and transportation resources to be aligned with sales. Customer orders must be fulfilled with short lead times to ensure high customer satisfaction, and the costly under‐utilization of workers must be avoided. To approach this ideal, forecasting order quantities with high accuracy is essential. Many drivers of online sales, including seasonality, special promotions and public holidays, are well known, and they have been frequently incorporated into forecasting approaches. However, the impact of weather on e‐commerce operations has not been rigorously analyzed. In this study, we integrate weather data into the sales forecasting of the largest European online fashion retailer. We find that sunshine, temperature, and rain have a significant impact on daily sales, particularly in the summer, on weekends, and on days with extreme weather. Using weather forecasts, we have significantly improved sales forecast accuracy. We find that including weather data in the sales forecast model can lead to fewer sales forecast errors, reducing them by, on average, 8.6% to 12.2% and up to 50.6% on summer weekends. In turn, the improvement in sales forecast accuracy has a measurable impact on logistics and warehousing operations. We quantify the value of incorporating weather forecasts in the planning process for the order fulfillment center workforce and show how their incorporation can be leveraged to reduce costs and increase performance. With a perfect information planning scenario, excess costs can be reduced by 11.6% compared with the cost reduction attainable with a baseline model that ignores weather information in workforce planning.     

Tests of Conditional Predictive Ability

We propose a framework for out‐of‐sample predictive ability testing and forecast selection designed for use in the realistic situation in which the forecasting model is possibly misspecified, due to unmodeled dynamics, unmodeled heterogeneity, incorrect functional form, or any combination of these. Relative to the existing literature (Diebold and Mariano (1995) and West (1996)), we introduce two main innovations: (i) We derive our tests in an environment where the finite sample properties of the estimators on which the forecasts may depend are preserved asymptotically. (ii) We accommodate conditional evaluation objectives (can we predict which forecast will be more accurate at a future date?), which nest unconditional objectives (which forecast was more accurate on average?), that have been the sole focus of previous literature. As a result of (i), our tests have several advantages: they capture the effect of estimation uncertainty on relative forecast performance, they can handle forecasts based on both nested and nonnested models, they allow the forecasts to be produced by general estimation methods, and they are easy to compute. Although both unconditional and conditional approaches are informative, conditioning can help fine‐tune the forecast selection to current economic conditions. To this end, we propose a two‐step decision rule that uses current information to select the best forecast for the future date of interest. We illustrate the usefulness of our approach by comparing forecasts from leading parameter‐reduction methods for macroeconomic forecasting using a large number of predictors.     

Impact of Bias Magnification on Supply Chain Costs: The Mitigating Role of Forecast Sharing

The impact of forecast error magnification on supply chain cost has been well documented. Unlike past studies that measure forecast error in terms of forecast standard deviation, our study extends research to consider the impact of forecast bias, and the complex interaction between these variables. Simulating a two‐stage supply chain using realistic cost data we test the impact of bias magnification comparing two scenarios: one with forecast sharing between retailer and supplier, and one without. We then corroborate findings via survey data. Results show magnification of forecast bias to have a considerably greater impact on supply chain cost than magnification of forecast standard deviation. Particularly damaging is high bias in the presence of high forecast standard deviation. Forecast sharing is found to mitigate the impact of forecast error, however, primarily at higher levels of forecast standard deviation. At low levels of forecast standard deviation the benefits are not significant suggesting that engaging in such mitigation strategies may be less effective when there is little opportunity for improvement in accuracy. Furthermore, forecast sharing is found to be much less effective against high levels of bias. This is an important finding as managers often deliberately bias their forecasts and underscores the importance of exercising caution even with forecast sharing, particularly for forecasts that have inherently large errors. The findings provide a deeper understanding of the impact of forecast errors, suggest limitations of forecast sharing, and offer implications for research and practice alike.     

The futility of forecasting

Long-range forecasting is an integral part of planning, but relying on its accuracy may be a mistake. The landscape is strewn with often wildly inaccurate forecasts. This article studies performances of some forecasts, analyses factors contributing to forecast error, and suggests ways in which management may deal with the uncertainty resulting from faulty forecasting performances.     

Neural Network Earnings per Share Forecasting Models: A Comparative Analysis of Alternative Methods

In this paper, we present a comparative analysis of the forecasting accuracy of univariate and multivariate linear models that incorporate fundamental accounting variables (i.e., inventory, accounts receivable, and so on) with the forecast accuracy of neural network models. Unique to this study is the focus of our comparison on the multivariate models to examine whether the neural network models incorporating the fundamental accounting variables can generate more accurate forecasts of future earnings than the models assuming a linear combination of these same variables. We investigate four types of models: univariate‐linear, multivariate‐linear, univariate‐neural network, and multivariate‐neural network using a sample of 283 firms spanning 41 industries. This study shows that the application of the neural network approach incorporating fundamental accounting variables results in forecasts that are more accurate than linear forecasting models. The results also reveal limitations of the forecasting capacity of investors in the security market when compared to neural network models.     

Influence of user participation on DSS use and decision accuracy

The paper reports a study of the impact on user satisfaction and forecast accuracy of user involvement in the design of a forecasting decision support system (FDSS). Two versions of an FDSS were tested via a laboratory study. Version 1, allowed the user control over all aspects of the system including the “look” of various screen elements and, most importantly, the model to be used could be selected (and tested) from a number of alternative forecasting models provided within the FDSS. In contrast, Version 2 did not allow the user to modify the “look” of the screen, and also provided no opportunity for model selection: this feature was carried out optimally by the FDSS. The user was told the advantage of optimal model selection. Both versions finished by asking the user to either accept the forecast (displayed as a point on the time-series graph) or to modify it via the mouse if unhappy with it. Results showed a much greater satisfaction with the forecasts provided by Version 1, confirming the importance of user involvement. Users of Version 1, in about half the cases, selected poor models with high forecast error. Where a model close to optimal was selected, the accuracy of Version 1 users greatly outperformed low involvement Version 2 users. Overall, however, the accuracy of the final forecasts for users of Version 1 was slightly inferior to that of users of Version 2. Measurements of ease of use and usefulness showed no real differences between the two versions.     

Aligning supply chain collaboration using Analytic Hierarchy Process

The significance of collaboration among supply chain members has been sufficiently stressed in the recent literature as a powerful tool for increasing accuracy of demand forecasts and for consequent cost reductions. Since it has been recognized that naïve forecasting is no longer cost efficient, Supply Chain (SC) members have found it very important to exchange relevant information that will help improve accuracy of demand forecasting. This information differs widely in terms of their characteristics. For example, some information (e.g. historic sales data) that is cheap to exchange may not contribute to a great increase in forecast accuracy. Similarly, some information may not be very reliable (e.g. demand forecast by individual SC members). In general, there is a trade-off in the kind of information required and the kind of information exchanged. This study analyses these trade-offs using an Analytic Hierarchy Process (AHP) model. The model is then implemented based on case studies conducted in two manufacturing firms. The AHP model ranks available information in terms of their contributions to improve forecast accuracy, and can provide vital clues to SC partners for preparing exchangeable data. From the case studies using AHP model, it was proved that using the preferred SC data, the firms could enhance forecasts accuracy. This in turn can help the firms to make decisions on SC collaborative arrangements for information exchange.     

Modeling External Risks in Project Management

To ascertain the viability of a project, undertake resource allocation, take part in bidding processes, and other related decisions, modern project management requires forecasting techniques for cost, duration, and performance of a project, not only under normal circumstances, but also under external events that might abruptly change the status quo. We provide a Bayesian framework that provides a global forecast of a project's performance. We aim at predicting the probabilities and impacts of a set of potential scenarios caused by combinations of disruptive events, and using this information to deal with project management issues. To introduce the methodology, we focus on a project's cost, but the ideas equally apply to project duration or performance forecasting. We illustrate our approach with an example based on a real case study involving estimation of the uncertainty in project cost while bidding for a contract.     

Mechanisms to Induce Buyer Forecasting: Do Suppliers Always Benefit from Better Forecasting?

In this study, we consider a supplier's contract offerings to a buyer who may obtain improved forecasts for her demand over time. We investigate how the supplier can take advantage of the buyer's better forecasts and what kind of contracts he should offer to the buyer in order to maximize his profits. We model a natural forecast evolution where the buyer can obtain a more accurate forecast closer to the selling season. We assume there is information asymmetry between the buyer and the supplier at all times in that the buyer understands her demand better than the supplier. Three types of contracts that the supplier can offer are considered: (1) one where a contract is offered before the buyer has a chance to obtain improved forecasts, (2) one where a contract is offered after the buyer has obtained improved forecasts, and (3) a contingent (dynamic) contract which offers an initial contract to the buyer before she obtains improved forecasts, followed by a later contract (contingent on the initial contract) offered after improved forecasts have been obtained. We consider two scenarios: (1) where the supplier is certain that the buyer can obtain more accurate forecasts over time, and (2) where the supplier is uncertain about the buyer's forecasting capability (or forecasting cost). In the first scenario, we show that among the three types of contracts, the contingent contract is always the most profitable for the supplier. Furthermore, using the contingent contract, the supplier always benefits from higher accuracy of the buyer's demand forecasts. In the second scenario, we explicitly model the supplier's level of certainty about the buyer's capability of obtaining better forecasts, and explore how the supplier can design contracts to induce the buyer to obtain better forecasts when she is capable.     

AN EVALUATION OF FORECAST ERROR IN MASTER PRODUCTION SCHEDULING FOR MATERIAL REQUIREMENTS PLANNING SYSTEMS.

Typical forecast-error measures such as mean squared error, mean absolute deviation and bias generally are accepted indicators of forecasting performance. However, the eventual cost impact of forecast errors on system performance and the degree to which cost consequences are explained by typical error measures have not been studied thoroughly. The present paper demonstrates that these typical error measures often are not good predictors of cost consequences in material requirements planning (MRP) settings. MRP systems rely directly on the master production schedule (MPS) to specify gross requirements. These MRP environments receive forecast errors indirectly when the errors create inaccuracies in the MPS. Our study results suggest that within MRP environments the predictive capabilities of forecast-error measures are contingent on the lot-sizing rule and the product components structure When forecast errors and MRP system costs are coanalyzed, bias emerges as having reasonable predictive ability. In further investigations of bias, loss functions are evaluated to explain the MRP cost consequences of forecast errors. Estimating the loss functions of forecast errors through regression analysis demonstrates the superiority of loss functions as measures over typical forecast error measures in the MPS.     

Quantifying costs of forecast errors: A case study of the warehouse environment

Our study evaluates the impact of forecast errors on organizational cost by simulating a labor-intensive warehouse environment using realistic cost data from a case study. Unlike past studies that measure forecast error in terms of forecast standard deviation, our study also considers the impact of forecast bias, and the complex interaction between these variables. Two cases of organizational cost curves are considered, with differing and asymmetric structures. Results find forecast bias to have a considerably greater impact on organizational cost than forecast standard deviation. Particularly damaging is a high bias in the presence of high forecast standard deviation. Although biasing the forecast in the least costly direction is shown to yield lower costs, sensitivity analysis shows that increasing bias beyond the optimum point rapidly increases costs. ‘Overshooting’ the optimal amount of bias appears to be more damaging than not biasing the forecast at all. Given that managers often deliberately bias their forecasts, this finding underscores the importance of having a good understanding of organizational cost structures before arbitrarily introducing bias. This finding also suggests that managers should exercise caution when introducing bias, particularly for forecasts that inherently have large errors. These findings have important implications for organizational decision making beyond the simulated warehouse, as high forecast errors are endemic to many labor-intensive organizations.     

The Dynamic Newsvendor Model with Correlated Demand

The classic newsvendor model was developed under the assumption that period‐to‐period demand is independent over time. In real‐life applications, the notion of independent demand is often challenged. In this article, we examine the newsvendor model in the presence of correlated demands. Specifically under a stationary AR(1) demand, we study the performance of the traditional newsvendor implementation versus a dynamic forecast‐based implementation. We demonstrate theoretically that implementing a minimum mean square error (MSE) forecast model will always have improved performance relative to the traditional implementation in terms of cost savings. In light of the widespread usage of all‐purpose models like the moving‐average method and exponential smoothing method, we compare the performance of these popular alternative forecasting methods against both the MSE‐optimal implementation and the traditional newsvendor implementation. If only alternative forecasting methods are being considered, we find that under certain conditions it is best to ignore the correlation and opt out of forecasting and to simply implement the traditional newsvendor model.      

A diagnostic analysis of the impact of forecast errors on production planning via MRP system nervousness

Abstract. The purpose of this paper is to examine the impact of forecast errors on the performance of a multi-product, multilevel production planning system via MRP system nervousness. The accuracy of forecasting methods was at one time a major concern of production scheduling and inventory control. However, with the advent of material requirements planning (MRP) systems, the significance of selecting an accurate forecasting method has diminished. Inaccurate forecast results are taken as a fact of life in production planning. Instead of attempting to develop an accurate forecasting method, efforts have been devoted towards providing an appropriate buffering method ai the master production schedule level or on the shop floor level to counteract fluctuations in demand. MRP is capable of rescheduling planned orders as well as open orders to restore the priority integrity after the disruptive changes of forecast errors occur. Nevertheless, excessive rescheduling may lead to a problem, generally referred to as system nervousness. This study investigates this problem by means of a computer simulation model. The results show that the presence of forecasi     

COST INCREASES DUE TO DEMAND UNCERTAINTY IN MRP LOT SIZING

This paper analyzes the cost increases due to demand uncertainty in single-level MRP lot sizing on a rolling horizon. It is shown that forecast errors have a tremendous effect on the cost effectiveness of lot-sizing techniques even when these forecast errors are small. Moreover, the cost differences between different techniques become rather insignificant in the presence of forecast errors. Since most industrial firms face demand uncertainty to some extent, our findings may have important managerial implications. Various simulation experiments give insight into both the nature and the magnitude of the cost increases for different heuristics. Analytical results are developed for the constant-demand case with random noise and forecasting by exponential smoothing. It is also shown how optimal buffers can be obtained by use of a simple model. Although the analysis in this paper is restricted to simplified cases, the results merit further consideration and study. This paper is one of the first to inject forecast errors into MRP lot-sizing research. As such it attempts to deal with one of the major objections against the practical relevance of previous research in this area.     

Sales forecasting— using a combination of approaches

The authors of this article argue that when market researchers and managers are faced with two or more forecasts of the same event, the typical approach is to attempt to determine which is better (or best). The superior forecasting technique is then accepted and the rest are discarded. However, in today's uncertain markets such a procedure is generally inferior to combining different forecasting approaches. Not only will the composite forecast usually have a lower average error but significant information will be generated from the diverse forecasting sources, providing management with valuable insights and diagnostics.     

INDIVIDUAL ITEM FORECASTING MODEL EVALUATION*

A computer simulation experiment was conducted to evaluate and compare seven individual item forecasting models across five different demand patterns. Results indicate the best model varies depending upon the demand pattern, the time period forecast, the noise level of the demand pattern, and to a lesser extent the measure of forecast error. Across all demand patterns, exponential double smoothing was best for the long run forecast and at least second best for the short run regardless of noise level in the demand patterns. Analysis of models within a demand pattern yielded, in most cases, several models as ranking equally well. The adaptive model developed here did not perform as well as some other models. For example, it ranked no better than third on a step function demand pattern.     

ON THE IMPLICATIONS OF SPECIFICATION UNCERTAINTY IN FORECASTING*

Forecasters typically select a statistical forecasting model from among a set of alternative models. Subsequently, forecasts are generated with the chosen model and reported to management (forecast consumers) as if specification uncertainty did not exist (i.e., as if the chosen model were the “true” model of the forecast variable). In this note, a well-known Bayesian model-comparison procedure is used to illustrate some of the ambiguities and distortions of forecasts that do not reflect specification uncertainty. It is shown that a single selected forecasting model (however chosen) will generally misstate measures of forecast risk and lead to point and interval forecasts that are misplaced from a decision-theoretic point of view.