Judgemental revision of sales forecasts: Effectiveness of forecast selection

When managers make revisions to sales forecasts initially generated by a rational quantitative model it is important that the particular forecasts selected for adjustment are those which would benefit most from the adjustment process (i.e. realize high errors). This study reports an empirical investigation on this issue, spanning six quarterly forecasting periods and incorporating forecasting data on over 850 products. The results show that the errors of the forecasts chosen for revision are, in general, higher than those which were not chosen. In addition, it is shown that managesrs tend to revise forecasts which are initially low, hence possibily introducing some degree of bias into the overall forecasts.     

Nonlinear identification of judgmental forecasts effects at SKU level

Prediction of demand is a key component within supply chain management. Improved accuracy in forecasts directly affects all levels of the supply chain, reducing stock costs and increasing customer satisfaction. In many application areas, demand prediction relies on statistical software which provides an initial forecast subsequently modified by the expert's judgment. This paper outlines a new methodology based on state‐dependent parameter (SDP) estimation techniques to identify the nonlinear behaviour of such managerial adjustments. This non‐parametric SDP estimate is used as a guideline to propose a nonlinear model that corrects the bias introduced by the managerial adjustments. One‐step‐ahead forecasts of stock‐keeping unit sales sampled monthly from a manufacturing company are utilized to test the proposed methodology. The results indicate that adjustments introduce a nonlinear pattern, undermining accuracy. This understanding can be used to enhance the design of the forecasting support system in order to help forecasters towards more efficient judgmental adjustments. Copyright © 2010 John Wiley & Sons, Ltd.     

Henderson‐Trending of Macroeconomic Variables and Forecasting Accuracy

Using a structural time‐series model, the forecasting accuracy of a wide range of macroeconomic variables is investigated. Specifically of importance is whether the Henderson moving‐average procedure distorts the underlying time‐series properties of the data for forecasting purposes. Given the weight of attention in the literature to the seasonal adjustment process used by various statistical agencies, this study hopes to address the dearth of literature on ‘trending’ procedures. Forecasts using both the trended and untrended series are generated. The forecasts are then made comparable by ‘detrending’ the trended forecasts, and comparing both series to the realised values. Forecasting accuracy is measured by a suite of common methods, and a test of significance of difference is applied to the respective root mean square errors. It is found that the Henderson procedure does not lead to deterioration in forecasting accuracy in Australian macroeconomic variables on most occasions, though the conclusions are very different between the one‐step‐ahead and multi‐step‐ahead forecasts. Copyright © 2011 John Wiley & Sons, Ltd.     

Estimating the strength of expert judgement: The case of US mortality forecasts

The use of expert judgement is an important part of demographic forecasting. However, because judgement enters into the forecasting process in an informal way, it has been very difficult to assess its role relative to the analysis of past data. The use of targets in demographic forecasts permits us to embed the subjective forecasting process into a simple time-series regression model, in which expert judgement is incorporated via mixed estimation. The strength of expert judgement is denned, and estimated using the official forecasts of cause-specific mortality in the United States. We show that the weight given to judgement varies in an improbable manner by age. Overall, the weight given to judgement appears too high. An alternative approach to combining expert judgement and past data is suggested.     

Do forecasts produced by organizations reflect anchoring and adjustment?

In attempting to improve forecasting, many facets of the forecasting process may be addressed including techniques, psychological factors, and organizational factors. This research examines whether a robust psychological bias (anchoring and adjustment) can be observed in a set of organizationally-produced forecasts. Rather than a simple consistent bias, biases were found to vary across organizations and items being forecast. Such bias patterns suggest that organizational factors may be important in determining the biases found in organizationally-produced forecasts.     

A comparative evaluation of objective and subjective weather forecasts in the united states

This paper is concerned primarily with the evaluation and comparison of objective and subjective weather forecasts. Operational forecasts of three weather elements are considered: (1) probability forecasts of precipitation occurrence, (2) categorical (i.e. non-probabilistic) forecasts of maximum and minimum temperatures and (3) categorical forecasts of cloud amount. The objective forecasts are prepared by numerical-statistical procedures, whereas the subjective forecasts are based on the judgements of individual forecasters. In formulating the latter, the forecasters consult information from a variety of sources, including the objective forecasts themselves. The precipitation probability forecasts are found to be both reliable and skilful, and evaluation of the temperature/cloud amount forecasts reveals that they are quite accurate/skilful. Comparison of the objective and subjective forecasts of precipitation occurrence indicates that the latter are generally more skilful than the former for shorter lead times (e.g. 12–24 hours), whereas the two types of forecasts are of approximately equal skill for longer lead times (e.g. 36–48 hours). Similar results are obtained for the maximum and minimum temperature forecasts. Objective cloud amount forecasts are more skilful than subjective cloud amount forecasts for all lead times. Examination of trends in performance over the last decade reveals that both types of forecasts for all three elements increased in skill (or accuracy) over the period, with improvements in objective forecasts equalling or exceeding improvements in subjective forecasts. The role and impact of the objective forecasts in the subjective weather forecasting process are discussed in some detail. The need to conduct controlled experiments and other studies of this process, with particular reference to the assimilation of information from different sources, is emphasized. Important characteristics of the forecasting system in meteorology are identified, and they are used to describe similarities and differences between weather forecasting and forecasting in other fields. Acquisition of some of these characteristics may be beneficial to other forecasting systems.     

Forecasting nonlinear time series with feed‐forward neural networks: a case study of Canadian lynx data

The forecasting capabilities of feed‐forward neural network (FFNN) models are compared to those of other competing time series models by carrying out forecasting experiments. As demonstrated by the detailed forecasting results for the Canadian lynx data set, FFNN models perform very well, especially when the series contains nonlinear and non‐Gaussian characteristics. To compare the forecasting accuracy of a FFNN model with an alternative model, Pitman's test is employed to ascertain if one model forecasts significantly better than another when generating one‐step‐ahead forecasts. Moreover, the residual‐fit spread plot is utilized in a novel fashion in this paper to compare visually out‐of‐sample forecasts of two alternative forecasting models. Finally, forecasting findings on the lynx data are used to explain under what conditions one would expect FFNN models to furnish reliable and accurate forecasts. Copyright © 2005 John Wiley & Sons, Ltd.     

Sales forecasting using multi-equation transfer function models

The purpose of this study is first, to demonstrate how multivariate forecasting models can be effectively used to generate high performance forecasts for typical business applications. Second, this study compares the forecasts generated by a simultaneous transfer function model (STF) model and a white noise regression model with that of a univariate ARIMA model. The accuracy of these forecasting models is judged using their residual variances and forecasting errors in a post-sample period. It is found that ignoring the residual serial correlation can greatly degrade the forecasting performance of a multi-variable model, and in some situations, cause a multi-variable model to perform inferior to a univariate ARIMA model. This paper also demonstrates how a forecaster can use an STF model to compute both the multi-step ahead forecasts and their variances easily.     

Requirements for effective use of graphical methods in interactive forecasting

The construction of forecasts using interactive data analysis systems is greatly aided by the availability of graphical procedures. Data exploration, model identification and estimation, and interpretation of final forecasts are made considerably easier by the visual relay of information. This article discusses some recent developments in time series graphics designed to assist in the forecasting process. A discussion of requirerients for effective use of graphics in interactive forecasting is included as illustrated through an application of the Box-Jenkins methodology. Illustrations are included from the STATGRAPHICS system, a prototype implementation in APL.     

Short-run macroeconomic forecasting: The OECD performance

Forecasts for the seven major industrial countries, Canada, France, Germany, Italy, Japan, the United Kingdom and the United States, are published on a regular basis in the OECD's Economic Outlook. This paper analyses the accuracy of the OECD annual forecasts of output and price changes and of the current balance in the balance of payments. As a reference basis, the forecasts are compared with those generated by a naive model, a random walk process. The measures of forecasting accuracy used are the mean-absolute error, the root-mean-square error, the median-absolute error, and Theil's inequality coefficient. The OECD forecasts of real GNP changes are significantly superior to those generated by the random walk process; however, the OECD price and current balance forecasts are not significantly more accurate than those obtained from the naive model. The OECD's forecasting performance has neither improved nor deteriorated over time.     

Can cointegration‐based forecasting outperform univariate models? An application to Asian exchange rates

Conventional wisdom holds that restrictions on low‐frequency dynamics among cointegrated variables should provide more accurate short‐ to medium‐term forecasts than univariate techniques that contain no such information; even though, on standard accuracy measures, the information may not improve long‐term forecasting. But inconclusive empirical evidence is complicated by confusion about an appropriate accuracy criterion and the role of integration and cointegration in forecasting accuracy. We evaluate the short‐ and medium‐term forecasting accuracy of univariate Box–Jenkins type ARIMA techniques that imply only integration against multivariate cointegration models that contain both integration and cointegration for a system of five cointegrated Asian exchange rate time series. We use a rolling‐window technique to make multiple out of sample forecasts from one to forty steps ahead. Relative forecasting accuracy for individual exchange rates appears to be sensitive to the behaviour of the exchange rate series and the forecast horizon length. Over short horizons, ARIMA model forecasts are more accurate for series with moving‐average terms of order >1. ECMs perform better over medium‐term time horizons for series with no moving average terms. The results suggest a need to distinguish between ‘sequential’ and ‘synchronous’ forecasting ability in such comparisons. Copyright © 2002 John Wiley & Sons, Ltd.     

A Dynamic Factor Approach to Mortality Modeling

Longevity risk has become one of the major risks facing the insurance and pensions markets globally. The trade in longevity risk is underpinned by accurate forecasting of mortality rates. Using techniques from macroeconomic forecasting we propose a dynamic factor model of mortality that fits and forecasts age‐specific mortality rates parsimoniously. We compare the forecasting quality of this model against the Lee–Carter model and its variants. Our results show the dynamic factor model generally provides superior forecasts when applied to international mortality data. We also show that existing multifactorial models have superior fit but their forecasting performance worsens as more factors are added. The dynamic factor approach used here can potentially be further improved upon by applying an appropriate stopping rule for the number of static and dynamic factors. Copyright © 2013 John Wiley & Sons, Ltd.     

Merging monthly and quarterly forecasts: Experience with mqem

Forecasts from quarterly econometric models are typically revised on a monthly basis to reflect the information in current economic data. The revision process usually involves setting targets for the quarterly values of endogenous variables for which monthly observations are available and then altering the intercept terms in the quarterly forecasting model to achieve the target values. A formal statistical approach to the use of monthly data to update quarterly forecasts is described and the procedure is applied to the Michigan Quarterly Econometric Model of the US Economy. The procedure is evaluated in terms of both ex post and ex ante forecasting performance. The ex ante results for 1986 and 1987 indicate that the method is quite promising. With a few notable exceptions, the formal procedure produces forecasts of GNP growth that are very close to the published ex ante forecasts.     

Comparing the DSGE model with the factor model: an out‐of‐sample forecasting experiment

In this paper, we put dynamic stochastic general equilibrium DSGE forecasts in competition with factor forecasts. We focus on these two models since they represent nicely the two opposing forecasting philosophies. The DSGE model on the one hand has a strong theoretical economic background; the factor model on the other hand is mainly data‐driven. We show that incorporating a large information set using factor analysis can indeed improve the short‐horizon predictive ability, as claimed by many researchers. The micro‐founded DSGE model can provide reasonable forecasts for US inflation, especially with growing forecast horizons. To a certain extent, our results are consistent with the prevailing view that simple time series models should be used in short‐horizon forecasting and structural models should be used in long‐horizon forecasting. Our paper compares both state‐of‐the‐art data‐driven and theory‐based modelling in a rigorous manner. Copyright © 2008 John Wiley & Sons, Ltd.     

Forecasting time series with outliers

Time-series data are often contaminated with outliers due to the influence of unusual and non-repetitive events. Forecast accuracy in such situations is reduced due to (1) a carry-over effect of the outlier on the point forecast and (2) a bias in the estimates of model parameters. Hillmer (1984) and Ledolter (1989) studied the effect of additive outliers on forecasts. It was found that forecast intervals are quite sensitive to additive outliers, but that point forecasts are largely unaffected unless the outlier occurs near the forecast origin. In such a situation the carry-over effect of the outlier can be quite substantial. In this study, we investigate the issues of forecasting when outliers occur near or at the forecast origin. We propose a strategy which first estimates the model parameters and outlier effects using the procedure of Chen and Liu (1993) to reduce the bias in the parameter estimates, and then uses a lower critical value to detect outliers near the forecast origin in the forecasting stage. One aspect of this study is on the carry-over effects of outliers on forecasts. Four types of outliers are considered: innovational outlier, additive outlier, temporary change, and level shift. The effects due to a misidentification of an outlier type are examined. The performance of the outlier detection procedure is studied for cases where outliers are near the end of the series. In such cases, we demonstrate that statistical procedures may not be able to effectively determine the outlier types due to insufficient information. Some strategies are recommended to reduce potential difficulties caused by incorrectly detected outlier types. These findings may serve as a justification for forecasting in conjunction with judgment. Two real examples are employed to illustrate the issues discussed.     

On the Predictive Content of Autoregression Residuals: A Semiparametric,Copula‐Based Approach to Time Series Prediction

This paper proposes an adjustment of linear autoregressive conditional mean forecasts that exploits the predictive content of uncorrelated model residuals. The adjustment is motivated by non‐Gaussian characteristics of model residuals, and implemented in a semiparametric fashion by means of conditional moments of simulated bivariate distributions. A pseudo ex ante forecasting comparison is conducted for a set of 494 macroeconomic time series recently collected by Dees et al. (Journal of Applied Econometrics 2007; 22: 1–38). In total, 10,374 time series realizations are contrasted against competing short‐, medium‐ and longer‐term purely autoregressive and adjusted predictors. With regard to all forecast horizons, the adjusted predictions consistently outperform conditionally Gaussian forecasts according to cross‐sectional mean group evaluation of absolute forecast errors and directional accuracy. Copyright © 2012 John Wiley & Sons, Ltd.     

Forecasting temporally aggregated vector ARMA processes

If interest centres on forecasting a temporally aggregated multiple time series and the generation process of the disaggregate series is a known vector ARMA (autoregressive moving average) process then forecasting the disaggregate series and temporally aggregating the forecasts is at least as efficient, under a mean squared error measure, as forecasting the aggregated series directly. Necessary and sufficient conditions for equality of the two forecasts are given. In practice the data generation process is usually unknown and has to be determined from the available data. Using asymptotic theory it is shown that also in this case aggregated forecasts from the disaggregate process will usually be superior to forecasts obtained from the aggregated process.     

The importance of time‐varying volatility and country interactions in forecasting economic activity

This paper examines the relative importance of allowing for time‐varying volatility and country interactions in a forecast model of economic activity. Allowing for these issues is done by augmenting autoregressive models of growth with cross‐country weighted averages of growth and the generalized autoregressive conditional heteroskedasticity framework. The forecasts are evaluated using statistical criteria through point and density forecasts, and an economic criterion based on forecasting recessions. The results show that, compared to an autoregressive model, both components improve forecast ability in terms of point and density forecasts, especially one‐period‐ahead forecasts, but that the forecast ability is not stable over time. The random walk model, however, still dominates in terms of forecasting recessions.     

Model‐based forecast adjustment: With an illustration to inflation

This paper introduces the idea of adjusting forecasts from a linear time series model where the adjustment relies on the assumption that this linear model is an approximation of a nonlinear time series model. This way of creating forecasts could be convenient when inference for a nonlinear model is impossible, complicated or unreliable in small samples. The size of the forecast adjustment can be based on the estimation results for the linear model and on other data properties such as the first few moments or autocorrelations. An illustration is given for a first‐order diagonal bilinear time series model, which in certain properties can be approximated by a linear ARMA(1, 1) model. For this case, the forecast adjustment is easy to derive, which is convenient as the particular bilinear model is indeed cumbersome to analyze in practice. An application to a range of inflation series for low‐income countries shows that such adjustment can lead to some improved forecasts, although the gain is small for this particular bilinear time series model.     

Hierarchical bayes forecasts of multinomial dirichlet data applied to coupon redemptions

This paper considers forecasting count data from a multinomial Dirichlet distribution. The forecasting procedure implements hierarchical Bayes methods in order to develop a prior distribution for a new series of data. The methodology is applied to the redemption of cents-off promotional coupons. In a forecasting experiment, early forecasts of new series are similar to those from pooling all redemptions from previous coupon promotions. However, the hierarchical Bayes model provides realistic estimates of forecasting errors, while those for the pooled forecasts are consistently optimistic. As the current series evolves, the hierarchical Bayes forecasts adapt more rapidly and are more accurate than pooled forecasts.