Towards a taxonomy of forecast error measures a factor-comparative investigation of forecast error dimensions

This study explores the nature of information conveyed by 14 error measures drawn from the literature, using real-life forecasting data from 691 individual product items over six quarterly periods. Principal components analysis is used to derive factor solutions that are subsequently compared for two forecasting methods, a version of Holt's exponential smoothing, and the random walk model (Naive 1). The results reveal four underlying forecast error dimensions that are stable across the two factor solutions. The potentially confounding influence of sales volume on the derived error dimensions is also explored via correlation analysis.     

Evidence for the selection of forecasting methods

Reid (1972) was among the first to argue that the relative accuracy of forecasting methods changes according to the properties of the time series. Comparative analyses of forecasting performance such as the M‐Competition tend to support this argument. The issue addressed here is the usefulness of statistics summarizing the data available in a time series in predicting the relative accuracy of different forecasting methods. Nine forecasting methods are described and the literature suggesting summary statistics for choice of forecasting method is summarized. Based on this literature and further argument a set of these statistics is proposed for the analysis. These statistics are used as explanatory variables in predicting the relative performance of the nine methods using a set of simulated time series with known properties. These results are evaluated on observed data sets, the M‐Competition data and Fildes Telecommunications data. The general conclusion is that the summary statistics can be used to select a good forecasting method (or set of methods) but not necessarily the best. Copyright © 2000 John Wiley & Sons, Ltd.     

The accuracy of extrapolation (time series) methods: Results of a forecasting competition

In the last few decades many methods have become available for forecasting. As always, when alternatives exist, choices need to be made so that an appropriate forecasting method can be selected and used for the specific situation being considered. This paper reports the results of a forecasting competition that provides information to facilitate such choice. Seven experts in each of the 24 methods forecasted up to 1001 series for six up to eighteen time horizons. The results of the competition are presented in this paper whose purpose is to provide empirical evidence about differences found to exist among the various extrapolative (time series) methods used in the competition.     

Time-series forecasting of the German unemployment rate

The purpose of the paper is to investigate the accuracy of forecasts derived from univariate and multivariate time-series models. An iterative method to adjust for impact assessment in univariate ARIMA models is discussed and illustrated for the German unemployment rate. Finally, we also examine the pros and cons of the impact assessment model in comparison with VAR models.     

An exploration of some practical issues in the use of quantitative forecasting models

Extrapolative forecasting models have been available for many years and as most organizations have the need to regularly develop forecasts one might anticipate the widespread use of these models. The evidence in Australia indicates that computer based forecasting systems are not being widely used and in fact a number of established systems have been discarded, with the issue of forecast accuracy often being mentioned as a problem area. Two experiments are carried out to examine this issue by comparing judgemental and quantitative forecasts. Other problem areas mentioned as contributing to the abandonment of forecasting systems include the difficulty of manually reviewing the computer forecasts and the effort required to carefully massage the forecast database to remove extraordinary events.     

The importance of the forecast

Careful forecasts, as accurate as possible, are central to the successful implementation of policy. There are fundamental reasons why policy makers cannot ‘play by ear’, adjusting policy quickly to each unexpected deviation in economic outcomes. Specific incidents are described where economic policy went awry because of faulty forecasts. The policy process is described in detail to show precisely where the forecast enters. Forecasting as a validation tool for establishing credibility in policy formation is analysed and discussed. Some estimated measure of forecast accuracy is presented, together with commentary on the necessary degrees of precision for successful implementation of policy.     

The impact of forecasting methodology on the accuracy of national population forecasts: evidence from the Netherlands and Czechoslovakia

"This study considers the accuracy of national population forecasts of the Netherlands and the Czechoslovak Socialist Republic.... We look at the demographic components employed in each forecast, the procedure to extrapolate fertility and the level at which assumptions for each component are formulated. Errors in total population size, fertility, mortality and foreign migration, and age structure are considered. We discuss trends in errors and methodology since 1950 and compare the situations in the two countries. The findings suggest that methodology has only a very limited impact on the accuracy of national population forecasts."     

A comparison of adaptive structural forecasting methods for electricity sales

This paper presents the results of a study to determine whether new forecasting technologies might be of use to electric utilities for sales forecasting up to 3 years into the future. The methods considered included ordinary least squares on dynamic structural models, autocorrelated error models, adaptive variance and adaptive parameter models. Overall, the more adaptive models performed best, but most of the methods proved vastly superior to simple least squares models which do not take dynamics into account.     

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.     

A forecasting comparison of classical and Bayesian methods for modelling logistic diffusion

A Bayesian procedure for forecasting S‐shaped growth is introduced and compared to classical methods of estimation and prediction using three variants of the logistic functional form and annual times series of the diffusion of music compact discs in twelve countries. The Bayesian procedure was found not only to improve forecast accuracy, using the medians of the predictive densities as point forecasts, but also to produce intervals with a width and asymmetry more in accord with the outcomes than intervals from the classical alternative. While the analysis in this paper focuses on logistic growth, the problem is set up so that the methods are transportable to other characterizations of the growth process. Copyright © 2001 John Wiley & Sons, Ltd.     

A comparison of approximate Bayesian forecasting methods for non‐Gaussian time series

We present the results on the comparison of efficiency of approximate Bayesian methods for the analysis and forecasting of non‐Gaussian dynamic processes. A numerical algorithm based on MCMC methods has been developed to carry out the Bayesian analysis of non‐linear time series. Although the MCMC‐based approach is not fast, it allows us to study the efficiency, in predicting future observations, of approximate propagation procedures that, being algebraic, have the practical advantage of being very quick. Copyright © 2000 John Wiley & Sons, Ltd.     

The role of jumps in the agricultural futures market on forecasting stock market volatility: New evidence

In this study, we explore the effect of cojumps within the agricultural futures market, and cojumps between the agricultural futures market and the stock market, on stock volatility forecasting. Also, we take into account large and small components of cojumps. We have several noteworthy findings. First, large jumps may lead to more substantial fluctuations and are more powerful than small jumps. The effect of cojumps and their decompositions on future volatility are mixed. Second, a model including large and small cojumps between the agricultural futures market and the stock market can achieve a higher forecasting accuracy, implying that large and small cojumps contain more useful predictive information than cojumps themselves. Third, our conclusions are robust based on various robustness tests such as the realized kernel, expanding forecasts, different forecasting windows, different jump tests, and different threshold values.     

Google Trends and the forecasting performance of exchange rate models

In this paper, we use Google Trends data for exchange rate forecasting in the context of a broad literature review that ties the exchange rate movements with macroeconomic fundamentals. The sample covers 11 OECD countries’ exchange rates for the period from January 2004 to June 2014. In out‐of‐sample forecasting of monthly returns on exchange rates, our findings indicate that the Google Trends search query data do a better job than the structural models in predicting the true direction of changes in nominal exchange rates. We also observed that Google Trends‐based forecasts are better at picking up the direction of the changes in the monthly nominal exchange rates after the Great Recession era (2008–2009). Based on the Clark and West inference procedure of equal predictive accuracy testing, we found that the relative performance of Google Trends‐based exchange rate predictions against the null of a random walk model is no worse than the purchasing power parity model. On the other hand, although the monetary model fundamentals could beat the random walk null only in one out of 11 currency pairs, with Google Trends predictors we found evidence of better performance for five currency pairs. We believe that these findings necessitate further research in this area to investigate the extravalue one can get from Google search query data.     

Local to unity,long‐horizon forecasting thresholds for model selection in the AR(1)

This article introduces a novel framework for analysing long‐horizon forecasting of the near non‐stationary AR(1) model. Using the local to unity specification of the autoregressive parameter, I derive the asymptotic distributions of long‐horizon forecast errors both for the unrestricted AR(1), estimated using an ordinary least squares (OLS) regression, and for the random walk (RW). I then identify functions, relating local to unity ‘drift’ to forecast horizon, such that OLS and RW forecasts share the same expected square error. OLS forecasts are preferred on one side of these ‘forecasting thresholds’, while RW forecasts are preferred on the other. In addition to explaining the relative performance of forecasts from these two models, these thresholds prove useful in developing model selection criteria that help a forecaster reduce error. Copyright © 2004 John Wiley & Sons, Ltd.     

Effect of regressor forecast error on the variance of regression forecasts

It is well understood that the standard formulation for the variance of a regression‐model forecast produces interval estimates that are too narrow, principally because it ignores regressor forecast error. While the theoretical problem has been addressed, there has not been an adequate explanation of the effect of regressor forecast error, and the empirical literature has supplied a disparate variety of bits and pieces of evidence. Most business‐forecasting software programs continue to supply only the standard formulation. This paper extends existing analysis to derive and evaluate large‐sample approximations for the forecast error variance in a single‐equation regression model. We show how these approximations substantially clarify the expected effects of regressor forecast error. We then present a case study, which (a) demonstrates how rolling out‐of‐sample evaluations can be applied to obtain empirical estimates of the forecast error variance, (b) shows that these estimates are consistent with our large‐sample approximations and (c) illustrates, for ‘typical’ data, how seriously the standard formulation can understate the forecast error variance. Copyright © 2000 John Wiley & Sons, Ltd.     

基于企业声誉的行业协会功能研究

经过30年的改革开放,行业协会成为我国政府退出或转变其行业控制权的一种制度选择。本文在文献研究的基础上,提出行业协会功能的实现,可以促进企业声誉的形成与维护。一方面,行业协会可以为企业提供交流平台,使得声誉信息可以在企业之间低成本、快速地流通;另一方面,通过行业协会专业、灵活的仲裁功能,抑制企业的机会主义倾向。     

The importance of interest rates for forecasting the exchange rate

This study compares the forecasting performance of a structural exchange rate model that combines the purchasing power parity condition with the interest rate differential in the long run, with some alternative exchange rate models. The analysis is applied to the Norwegian exchange rate. The long‐run equilibrium relationship is embedded in a parsimonious representation for the exchange rate. The structural exchange rate representation is stable over the sample and outperforms a random walk in an out‐of‐sample forecasting exercise at one to four horizons. Ignoring the interest rate differential in the long run, however, the structural model no longer outperforms a random walk. Copyright © 2006 John Wiley _ Sons, Ltd.     

基于隶属度比较的描述逻辑SHOIQ模糊扩展

语义Web模糊知识的表示和应用经常需要涉及多个模糊隶属度值及其比较的复杂模糊知识描述,但现有的描述逻辑模糊扩展缺乏描述和使用这类复杂模糊知识的能力.文中提出新的描述逻辑SHOIQ模糊扩展SHOIQFC语言.SHOIQFC不仅具有模糊描述逻辑FSHOIQ的全部表达能力,还支持涉及多隶属度值及其比较的复杂模糊知识的表示与推理,拓展了描述逻辑模糊扩展的应用范围.证明了SHOIQFC知识库一致性问题的可判定性并给出Tableau推理算法,为实现语义Web复杂模糊知识的表示与推理提供理论基础.     

A comparison of models for forecasting the discovery of hydrocarbon deposits

There are many geologic resource assessment techniques available that can be used to estimate the hydrocarbon potential of frontier basins. The techniques do not, however, produce discovery rate forecasts, which are critical to government and industry planners. Various methods of predicting the discovery rate in frontier basins are reviewed and appraised within the context of the drilling history of Canada's Scotian Shelf. The reviewed models include a mean historical discovery rate technique, the exponential decline model, a logistic curve technique and a class of models based on a sampling without replacement approach to prediction. Models are found to perform best over the longer forecast horizons, with those models based on the sampling without replacement technique tending to perform best.     

Computing the variance of the forecast error for the holt-winters seasonal models

This paper presents expressions for the variance of the forecast error for arbitrary lead times for both the additive and multiplicative Holt-Winters seasonal forecasting models. It is shown that even when the smoothing constants are chosen to have values between zero and one, when the period is greater than four, the variance may not be finite for some values of the smoothing constants. In addition, the regions where the variance becomes infinite are almost the same for both models. These results are of importance for practitioners, who may choose values for the smoothing constants arbitrarily, or by searching on the unit cube for values which minimize the sum of the squared errors when fitting the model to a data set. It is also shown that the variance of the forecast error for the multiplicative model is nonstationary and periodic.