The use of non-time series information in sales forecasting: A case study

The contribution of product and industry knowledge to the accuracy of sales forecasting was investigated by examining the company forecasts of a leading manufacturer and marketer of consumable products. The company forecasts of 18 products produced by a meeting of marketing, sales, and production personnel were compared with those generated by the same company personnel when denied specific product knowledge and with the forecasts of selected judgemental and statistical time series methods. Results indicated that product knowledge contributed significantly to forecast accuracy and that the forecast accuracy of company personnel who possessed industry forecasting knowledge (but not product knowledge) was not significantly different from the time series based methods. Furthermore, the company forecasts were more accurate than averages of the judgemental and statistical time series forecasts. These results point to the importance of specific product information to forecast accuracy and accordingly call into question the continuing strong emphasis on improving extrapolation techniques without consideration of the inclusion of non-time series knowledge.     

Judgemental revision of sales forecasts: The relative performance of judgementally revised versus non-revised forecasts

The judgemental revision of sales forecasts is an issue which is receiving increasing attention in the forecasting literature. This paper compares the performance of forecasts after revision by managers with that of the forecasts which were accepted by them without revision. The data set consists of sales forecasting data from an industrial company, spanning six quarterly periods and relating to some 900 individual products. The findings show that, in general, the improvements made by managers bring the forecast errors of revised forecasts more into line with non-revised forecasts, but the change is often marginal, and the best result is equivalence between revised and non-revised forecasts.     

Judgemental revision of sales forecasts: A longitudinal eetension

When quantitative models are used for short-term multi-item sales forecasts it is possible that the managers who use such forecasts may disagree with at least some of the estimates obtained, and wish to change them so that they become more consistent with their own (subjective) evaluation of the marketplace. This study reports on an analysis of the effectiveness of judgemental revision of sales forecasts over six quarterly forecasting periods. The results give general support for the practice of forecast manipulation as a means of improving forecasting accuracy. It is also observed that the effectiveness of revision activity varies across different time periods.     

Decision trees for forecasting

Recent years have seen an increasing cross-fertilization between the fields of decision analysis and forecasting. Decision-analytic models often require forecasts as inputs, and aspects of the Bayesian decision-theoretic framework underlying decision analysis have proved useful to forecasting, particularly in contexts where subjective judgemental inputs are required. This paper describes the use of decision tree analysis for forecasting and illustrates its use for corporate divisional forecasting and planning. A specialized decision-analytic technique, acts as events, is also described and illustrated to forecast a new product's earnings. Conclusions are drawn about the applicability of decision analysis for forecasting.     

Forecasting with an econometric model: The issue of judgemental adjustment

The paper outlines the current state of forecasting with an econometric model. After briefly distinguishing econometric techniques from other statistical approaches and arguing the advantages of this approach the paper concentrates on the issue of judgemental adjustments to models for forecasting purposes. Two types of adjustment are distinguished and the conditions under which each is justified are stated. Guidance in the use of adjustment is offered through a review of considerations in an actual forecasting situation.     

Going Up–Going Down: How Good Are People at Forecasting Trends and Changes in Trends?

Prior studies of judgemental time-series forecasting have found that people have problems with downward-sloping series. This laboratory-based study presents a controlled experiment of series direction and it investigates the problems of changing trends. Results confirm that people have significant difficulties in dealing with downward-sloping series and that behaviour is consistent with a general tendency to anticipate that downward series will reverse themselves. There is a significantly less tendency to do so for upward series. Results are discussed in terms of systematic and unsystematic error.© 1997 John Wiley & Sons, Ltd.     

Political manoeuvrings as sources of measurement errors in forecasts

We test the extent to which political manoeuvrings can be the sources of measurement errors in forecasts. Our objective is to examine the forecast error based on a simple model in which we attempt to explain deviations between the March budget forecast and the November forecast, and deviations between the outcome and the March budget forecast in the UK. The analysis is based on forecasts made by the general government. We use the forecasts of the variables as alternatives to the outcomes. We also test for political spins in the GDP forecast updates and the GDP forecast errors. We find evidence of partisan and electoral effects in forecast updates and forecast errors. Copyright © 2005 John Wiley & Sons, Ltd.     

The role of judgement in macroeconomic forecasting

This paper examines the rationale for, and influence of, judgemental adjustments in macroeconomic forecasting, using two particular forecasts for the UK economy recently published by the National Institute of Economic and Social Research and the London Business School. It is found that in some cases such adjustments have a major effect on the forecasts and can also explain some of the differences in the two rival forecasts. However the number of adjustments for which this is true is not great. An implication of these findings is that, if these forecasts can be regarded as typical, then macroeconomic forecasters should be urged to give a reasonable account of the role of judgemental adjustments in their forecasts, particularly since the amount of information which would be required is not likely to be excessive.     

The consistency,coherence and calibration of holistic,decomposed and recomposed judgemental probability forecasts

In this paper we make an empirical investigation of the relationship between the consistency, coherence and validity of probability judgements in a real-world forecasting context. Our results indicate that these measures of the adequacy of an individual's probability assessments are not closely related as we anticipated. Twenty-nine of our thirty-six subjects were better calibrated in point probabilities than in odds and our subjects were, in general more coherent using point probabilities than odds forecasts. Contrary to our expectations we found very little difference in forecasting response and performance between simple and compound holistic forecasts. This result is evidence against the ‘divide-and-conquer’ rationale underlying most applications of normative decision theory. In addition, our recompositions of marginal and conditional assessments into compound forecasts were no better calibrated or resolved than their holistic counterparts. These findings convey two implications for forecasting. First, untrained judgemental forecasters should use point probabilities in preference to odds. Second, judgemental forecasts of complex compound probabilities may be as well assessed holistically as they are using methods of decomposition and recomposition. In addition, our study provides a paradigm for further studies of the relationship between consistency, coherence and validity in judgemental probability forecasting.     

The multi‐chain Markov switching model

In many real phenomena the behaviour of a certain variable, subject to different regimes, depends on the state of other variables or the same variable observed in other subjects, so the knowledge of the state of the latter could be important to forecast the state of the former. In this paper a particular multivariate Markov switching model is developed to represent this case. The transition probabilities of this model are characterized by the dependence on the regime of the other variables. The estimation of the transition probabilities provides useful information for the researcher to forecast the regime of the variables analysed. Theoretical background and an application are shown. Copyright © 2005 John Wiley & Sons, Ltd.     

Beyond heuristics and biases: A contingency model of judgemental forecasting

The conflicting viewpoints about the quality of judgemental forecasts are examined and a model is proposed that attempts to resolve the conflict. The model sees forecasts as contingent upon the repertory of forecasting strategies that the forecaster brings to the forecasting task, the strategy that he or she selects as a function of the characteristics of the task, and the rigour with which he or she applies the strategy as a function of the motivating characteristics of the environment in which the task is encountered. The implications of differences in subjects' and experimenters' assumptions about which strategies are appropriate in experimental studies are examined, as are the implications of the differences between the motivating aspects of experimental and applied settings on both performance and on the generatizability of the results of experiments to applied judgemental forecasting.     

Forecasting euro area variables with German pre‐EMU data

It is investigated whether euro area variables can be forecast better based on synthetic time series for the pre‐euro period or by using just data from Germany for the pre‐euro period. Our forecast comparison is based on quarterly data for the period 1970Q1–2003Q4 for 10 macroeconomic variables. The years 2000–2003 are used as forecasting period. A range of different univariate forecasting methods is applied. Some of them are based on linear autoregressive models and we also use some nonlinear or time‐varying coefficient models. It turns out that most variables which have a similar level for Germany and the euro area such as prices can be better predicted based on German data, while aggregated European data are preferable for forecasting variables which need considerable adjustments in their levels when joining German and European Monetary Union (EMU) data. These results suggest that for variables which have a similar level for Germany and the euro area it may be reasonable to consider the German pre‐EMU data for studying economic problems in the euro area. Copyright © 2008 John Wiley & Sons, Ltd.     

Choosing the Number of Conditioning Events in Judgemental Forecasting

One method for judgemental forecasting involves the use of decomposition; i.e. estimating the conditional means of an unknown quantity of interest for a finite number of conditioning events, and weighting these estimated conditional means by the estimated marginal probabilities of the corresponding conditioning events. In this paper we investigate how the level of decomposition (i.e. the number of conditioning events) affects the precision of the resulting forecast. Previous analyses assume that key parameters (the informativeness of the decomposition, and the precision of estimation for the conditional means and the marginal probabilities) remain constant as the number of conditioning events increases. However, this assumption is unreasonable, and for some parameters mathematically impossible; the values of these parameters are likely to change significantly even for small numbers of conditioning events. Therefore, we introduce models for how these key parameters may depend on the level of decomposition. We then investigate the implications of these models for the precision of the resulting forecast. In particular, we identify cases in which decomposition is never desirable, always desirable, or desirable only near the optimal number of conditioning events. This second case was not observed previously. We focus throughout on the situation likely to be of greatest interest in practice; namely, the behaviour of decomposition for relatively small numbers of conditioning events.© 1997 John Wiley & Sons, Ltd.     

Effects of difficulty on judgemental probability forecasting of control response efficacy

A judgemental control task was framed as a problem of medical decision making. The control parameter of a recursive system (i.e. a patient) was initially set so that output (i.e. a diagnostic index) fell outside a designated criterion range (corresponding to health). Subjects were told to bring the system's output into the designated range by resetting this control parameter (by specifying the dose of a drug). After each of these control responses, they made a probabilistic forecast that it would have the desired effect. It was found that these forecasts were more overconfident when the control task was more difficult but that the reason for this varied. When difficulty was manipulated across subjects, there was little evidence that lower control performance was associated with any lowering of the probabilistic forecasts. When difficulty was manipulated within subjects, they did lower their forecasts for more difficult task variants but did so insufficiently. In fact, relations between probabilistic forecasts of control response efficacy and proportion of those responses that were actually effective was linear with a slope of 0.44.     

Long‐run forecasting in multicointegrated systems

We extend the analysis of Christoffersen and Diebold (1998) on long‐run forecasting in cointegrated systems to multicointegrated systems. For the forecast evaluation we consider several loss functions, each of which has a particular interpretation in the context of stock‐flow models where multicointegration typically occurs. A loss function based on a standard mean square forecast error (MSFE) criterion focuses on the forecast errors of the flow variables alone. Likewise, a loss function based on the triangular representation of cointegrated systems (suggested by Christoffersen and Diebold) considers forecast errors associated with changes in both stock (modelled through the cointegrating restrictions) and flow variables. We suggest a new loss function based on the triangular representation of multicointegrated systems which further penalizes deviations from the long‐run relationship between the levels of stock and flow variables as well as changes in the flow variables. Among other things, we show that if one is concerned with all possible long‐run relations between stock and flow variables, this new loss function entails high and increasing forecasting gains compared to both the standard MSFE criterion and Christoffersen and Diebold's criterion. This paper demonstrates the importance of carefully selecting loss functions in forecast evaluation of models involving stock and flow variables. Copyright © 2004 John Wiley & Sons, Ltd.     

Judgement in learning‐curve forecasting: a laboratory study

This study investigates whether human judgement can be of value to users of industrial learning curves, either alone or in conjunction with statistical models. In a laboratory setting, it compares the forecast accuracy of a statistical model and judgemental forecasts, contingent on three factors: the amount of data available prior to forecasting, the forecasting horizon, and the availability of a decision aid (projections from a fitted learning curve). The results indicate that human judgement was better than the curve forecasts overall. Despite their lack of field experience with learning curve use, 52 of the 79 subjects outperformed the curve on the set of 120 forecasts, based on mean absolute percentage error. Human performance was statistically superior to the model when few data points were available and when forecasting further into the future. These results indicate substantial potential for human judgement to improve predictive accuracy in the industrial learning‐curve context. Copyright © 1999 John Wiley & Sons, Ltd.     

Volatility forecasting for stock market incorporating macroeconomic variables based on GARCH-MIDAS and deep learning models

Empirical experiments have shown that macroeconomic variables can affect the volatility of stock market. However, the frequencies of macroeconomic variables are low and different from the stock market volatility, and few literature considers the low-frequency macroeconomic variables as input indicators for deep learning models. In this paper, we forecast the stock market volatility incorporating low-frequency macroeconomic variables based on a hybrid model integrating the deep learning method with generalized autoregressive conditional heteroskedasticity and mixed data sampling (GARCH-MIDAS) model to process the mixing frequency data. This paper firstly takes macroeconomic variables as exogenous variables then uses the GARCH-MIDAS model to deal with the problem of different frequencies between the macroeconomic variables and stock market volatility and to forecast the short-term volatility and finally takes the predicted short-term volatility as the input indicator into machine learning and deep learning models to forecast the realized volatility of stock market. It is found that adding macroeconomic variables can significantly improve the forecasting ability in the comparison of the forecasting effects of the same model before and after adding the macroeconomic variables. Additionally, in the comparison of the forecasting effects among different models, it is also found that the forecasting effect of the deep learning model is the best, the machine learning model is worse, and the traditional econometric model is the worst.     

Adjusting Judgemental Extrapolations using Theil's Method and Discounted Weighted Regression

Theil's method can be applied to judgemental forecasts to remove systematic errors. However, under conditions of change the method can reduce the accuracy of forecasts by correcting for biases that no longer apply. In these circumstances, it may be worth applying an adaptive correction model which attaches a greater weight to more recent observations. This paper reports on the application of Theil's original method and a discounted weighted regression form of Theil's method (DWR) to the judgemental extrapolations made by 100 subjects in an experiment. Extrapolations were made for both stationary and non-stationary and low- and high-noise series. The results suggest DWR can lead to significant improvements in accuracy where the underlying time-series signal becomes more discernible over time or where the signal is subject to change. Theil's method appears to be most effective when a series has a high level of noise. However, while Theil's corrections seriously reduced the accuracy of judgemental extrapolations for some series the DWR method performed well under a wide range of conditions and never significantly degraded the original forecasts. © 1997 by John Wiley & Sons, Ltd.     

Subjective confidence in forecasts

Forecasts have little value to decision makers unless it is known how much confidence to place in them. Those expressions of confidence have, in turn, little value unless forecasters are able to assess the limits of their own knowledge accurately Previous research has shown very robust patterns in the judgements of individuals who have not received special training in confidence assessment: Knowledge generally increases as confidence increases. However, it increases too swiftly, with a doubling of confidence being associated with perhaps a 50 per cent increase in knowledge. With all but the easiest of tasks, people tend to be overconfident regarding how much they know These results have typically been derived from studies of judgements of general knowledge. The present study found that they also pertained to confidence in forecasts. Indeed, the confidence-knowledge curves observed here were strikingly similar to those observed previously. The only deviation was the discovery that a substantial minority of judges never expressed complete confidence in any of their forecasts. These individuals also proved to be better assessors of the extent of their own knowledge Apparently confidence in forecasts is determined by processes similar to those that determine confidence in general knowledge. Decision makers can use forecasters assessments in a relative sense, in order to predict when they are more and less likely to be correct. However, they should be hesitant to take confidence assessments literally. Someone is more likely to be right when he or she is ‘certain’than when he or she is ‘fairly confident’; but there is no guarantee that the certain forecast will come true.     

Forecast covariances in the linear multiregression dynamic model

The linear multiregression dynamic model (LMDM) is a Bayesian dynamic model which preserves any conditional independence and causal structure across a multivariate time series. The conditional independence structure is used to model the multivariate series by separate (conditional) univariate dynamic linear models, where each series has contemporaneous variables as regressors in its model. Calculating the forecast covariance matrix (which is required for calculating forecast variances in the LMDM) is not always straightforward in its current formulation. In this paper we introduce a simple algebraic form for calculating LMDM forecast covariances. Calculation of the covariance between model regression components can also be useful and we shall present a simple algebraic method for calculating these component covariances. In the LMDM formulation, certain pairs of series are constrained to have zero forecast covariance. We shall also introduce a possible method to relax this restriction. Copyright © 2008 John Wiley & Sons, Ltd.