The accuracy of extrapolation methods; an automatic box–jenkins package sift

Hill and Woodworth (1980) proposed an algorithm suitable for identifying Box–Jenkins models automatically without reliance on the investigator. This paper first reviews the method. It is then used on the 111 series analysed by Anderson in the Makridakis forecasting competition. The results show that the automatic method of Hill and Woodworth is comparable in terms of accuracy to the full Box–Jenkins identification procedure.     

The role of time series analysis in the evaluation of econometric models

This paper compares the properties of a structural model—the London Business School model of the U.K. economy—with a time series model. Information provided by this type of comparison is a useful diagnostic tool for detecting types of model misspecification. This is a more meaningful way of proceeding rather than attempting to establish the superiority of one type of model over another. In lieu of a better structural model, the effects of inappropriate dynamic specification can be reduced by combining the forecasts of both the structural and time series models. For many variables considered here these provide more accurate forecasts than each of the model types alone.     

An evaluation of bayesian forecasting

‘Bayesian forecasting’ is a time series method of forecasting which (in the United Kingdom) has become synonymous with the state space formulation of Harrison and Stevens (1976). The approach is distinct from other time series methods in that it envisages changes in model structure. A disjoint class of models is chosen to encompass the changes. Each data point is retrospectively evaluated (using Bayes theorem) to judge which of the models held. Forecasts are then derived conditional on an assumed model holding true. The final forecasts are weighted sums of these conditional forecasts. Few empirical evaluations have been carried out. This paper reports a large scale comparison of time series forecasting methods including the Bayesian. The approach is two fold: a simulation study to examine parameter sensitivity and an empirical study which contrasts Bayesian with other time series methods.     

Forecasting the economic recession in the U.K. 1979-1982: A comparison of model-based ex ante Forecasts

This paper compares the forecasts of recession and recovery made by five non-government U.K. teams modelling the economy (Cambridge Econometrics, the London Business School, the National Institute of Economic and Social Research, the Cambridge Economic Policy Group and the Liverpool Research Group). The paper concentrates on annual ex ante projections as published over the period 1978-1982, i.e. forecasts made, before the event, of the onset, length, depth and character of the economic recession in the U.K. which began in 1979. The comparison is in terms of year by year changes in production, unemployment, prices and other variables. It concludes that no group was systematically better or worse than other groups (confirming U.S. experience) and that the groups tended to perform better in their chosen areas of specialization, e.g. medium-term groups did better at forecasting the medium-term outcome.     

Exponential smoothing: The state of the art

This paper is a critical review of exponential smoothing since the original work by Brown and Holt in the 1950s. Exponential smoothing is based on a pragmatic approach to forecasting which is shared in this review. The aim is to develop state-of-the-art guidelines for application of the exponential smoothing methodology. The first part of the paper discusses the class of relatively simple models which rely on the Holt-Winters procedure for seasonal adjustment of the data. Next, we review general exponential smoothing (GES), which uses Fourier functions of time to model seasonality. The research is reviewed according to the following questions. What are the useful properties of these models? What parameters should be used? How should the models be initialized? After the review of model-building, we turn to problems in the maintenance of forecasting systems based on exponential smoothing. Topics in the maintenance area include the use of quality control models to detect bias in the forecast errors, adaptive parameters to improve the response to structural changes in the time series, and two-stage forecasting, whereby we use a model of the errors or some other model of the data to improve our initial forecasts. Some of the major conclusions: the parameter ranges and starting values typically used in practice are arbitrary and may detract from accuracy. The empirical evidence favours Holt's model for trends over that of Brown. A linear trend should be damped at long horizons. The empirical evidence favours the Holt-Winters approach to seasonal data over GES. It is difficult to justify GES in standard form–the equivalent ARIMA model is simpler and more efficient. The cumulative sum of the errors appears to be the most practical forecast monitoring device. There is no evidence that adaptive parameters improve forecast accuracy. In fact, the reverse may be true.     

Short-term forecasting of industrial production by means of quick indicators

This paper reports results on building transfer function models with linear combinations of quick indicators as inputs for very short-term prediction of the monthly time series of the volume of industrial production in Finland. The number of input variables in the transfer function models is reduced in two alternative ways: by replacing the original indicators by their two first principal components and by omitting certain indicators. The prediction accuracy of the transfer function models is checked outside the sample and found superior to that of corresponding ARIMA models. Neither of the two ways of reducing the number of input variables leads to consistently more accurate forecasts than the other. It is also found that the prediction accuracy of the transfer function models compares rather favourably with the preliminary values of the volume of industrial production published by the Central Statistical Office during the periods of rapid growth.     

Discount weighted estimation

The parsimonious method of exponentially weighted regression (EWR) is attractive but limited in application because it depends upon just one discount factor. This paper generalizes the EWR approach to a method called discount weighted estimation (DWE) which allowed distinct model components to have different associated discount factors. The method includes EWR as a special case. The general non-limiting recurrence relationships will be useful in practice, especially when practitioners wish to specify prior information, to intervene with subjective judgement and to derive estimates and forecasts sequentially based upon limited data. Two theorems extend the important EWR limiting results of Dobbie and McKenzie to DWE. The latter permits the derivation of a large class of known processs for which DWE is optimal. The method is illustrated by two applications, one of which uses the famous international airline passenger data. This allows a comparision with the ICI MULDO system which uses a particular two discount factor forecasting method. A companion paper extends the discount methods to Bayesian forecasting, Kalman filtering and state space modelling.     

Efficient use of information in the formation of subjective industry forecasts

The paper considers the use of information by a panel of expert industry forecasters, focusing on their information-processing biases. The panel forecasts construction output by sector up to three years ahead. It is found that the biases observed in laboratory experiments, particularly ‘anchoring’, are observable. The expectations are formed by adjusting the previous forecast to take new information into account. By analysing forecast errors it is concluded that the panel overweight recently released information and do not understand the dynamics of the industry. However, their forecasts, both short and long term, are better than an alternative econometric model, and combining the two sources of forecasts leads to a deterioration in forecast accuracy. The expert forecasts can be ‘de-biased’, and this leads to the conclusion that it is better to optimally process information sources than to combine (optimally) alternative forecasts.     

The chatfield-prothero case study: Another look

The Chatfield-Prothero case study in time series, ‘Sales of a company X’, is analysed from a perspective different to that of the authors. More accurate forecasting performance for these data is obtained by adopting the following two tactics: (1) shifting from a problem in transformation of the original series to one of seasonality adjustment; (2) assuming a mixed seasonality type model in contrast to employing a multiplicative assumption.     

The M-competition with a fully automatic box–jenkins procedure

CAPRI is a fully automatic and quick procedure for forecasting. It is based on the Box–Jenkins methodology and needs no a priori knowledge about the time series. The 1001 series of the Makridakis competition have been analysed with this program and its accuracy measured in comparison with other methods. CAPRI is recommended for short term forecasting horizons in cases where the user does not want to interfere with the modelling process.     

A unified view of statistical forecasting procedures

A large number of statistical forecasting procedures for univariate time series have been proposed in the literature. These range from simple methods, such as the exponentially weighted moving average, to more complex procedures such as Box–Jenkins ARIMA modelling and Harrison–Stevens Bayesian forecasting. This paper sets out to show the relationship between these various procedures by adopting a framework in which a time series model is viewed in terms of trend, seasonal and irregular components. The framework is then extended to cover models with explanatory variables. From the technical point of view the Kalman filter plays an important role in allowing an integrated treatment of these topics.     

An interpretation of the non-symmetric responding logistic model in terms of price and experience effects

This paper presents an alternative derivation and a generalization of the non-symmetric responding logistic model of Easingwood, Mahajan and Muller (1981) based upon a combination of experience curve and price elasticity effects.     

General exponential smoothing and the equivalent arma process

Although the basic principles of exponential smoothing and discounted least squares are easily understood, the full power of the technique is only rarely exploited. The reason for this failure lies in the complexity of the standard procedures. Often they require fairly complex mathematical models and use a variety of cumbersome algebraic manipulations. An alternative formulation for exponential smoothing is presented. It simplifies these procedures and allows an easier use of the full range of models. This new formulation is obtained by considering the relationship between general exponential smoothing (GES) and the well-known ARMA process of Box and Jenkins. The three commonest seasonal models have only recently been considered for GES systems. They are discussed in some detail here. The computational requirements of the GES and equivalent ARMA procedures are reviewed and some recommendations for their application are made. The initialization of GES forecasting systems and the important problem of model selection is also discussed. A brief illustrative example is given.     

Using the bootstrap to evaluate forecasting equations

The bootstrap, like the jack-knife, is a technique for estimating standard errors. The idea is to use Monte Carlo simulation, based on a non-parametric estimate of the underlying error distribution. The bootstrap will be applied to an econometric equation describing the demand for energy by industry, to determine multi-period forecasting error and choose among competing specifications. The delta method for estimating forecast errors turns out to be too optimistic by a factor of 2.     

The use of growth curves in forecasting market development—a review and appraisal

The growth curves suitable for forecasting market development are identified and described. The underlying theoretical basis, if any, for their use is examined, and published examples of their applications are given. Doubt is cast on the value of long-term forecasts derived from growth curves applied to markets for consumables. The problems of choice between competing curves are demonstrated by means of some examples. The requirements that a growth curve should meet in order to be an appropriate forecasting tool are identified and illustrated. Many of the published examples of growth curve use are shown to be vulnerable to criticism under one or more of these criteria.     

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.     

Political forecasting as a management tool

Political forces in developing countries permeate and significantly shape the business environment. Yet the political information used by managers is usually general, subjective and superficial. Managers lack an appropriate analytical framework for systematically examining political factors and forecasting their impact on the firm. This paper attempts to present such a framework. The framework focuses on the impact of political forces on development strategies, public policies and policy instruments. It then discusses how the analysis of these factors can be made managerially relevant by integrating them with firm specific characteristics and corporate strategy. This approach departs from many of the traditional political forecasting techniques which only concentrate on macro-level factors and indicators.     

Worlds in the Everett interpretation

This is a discussion of how we can understand the world-view given to us by the Everett interpretation of quantum mechanics, and in particular the rôle played by the concept of ‘world’. The view presented is that we are entitled to use ‘many-worlds’ terminology even if the theory does not specify the worlds in the formalism; this is defended by means of an extensive analogy with the concept of an ‘instant’ or moment of time in relativity, with the lack of a preferred foliation of spacetime being compared with the lack of a preferred basis in quantum theory. Implications for identity of worlds over time, and for relativistic quantum mechanics, are discussed.     

Ethnographic analogy,the comparative method,and archaeological special pleading

Ethnographic analogy, the use of comparative data from anthropology to inform reconstructions of past human societies, has a troubled history. Archaeologists often express concern about, or outright reject, the practice—and sometimes do so in problematically general terms. This is odd, as (or so I argue) the use of comparative data in archaeology is the same pattern of reasoning as the ‘comparative method’ in biology, which is a well-developed and robust set of inferences which play a central role in discovering the biological past. In pointing out this continuity, I argue that there is no ‘special pleading’ on the part of archaeologists in this regard: biologists must overcome analogous epistemic difficulties in their use of comparative data. I then go on to emphasize the local, empirically tractable ways in which particular ethnographic analogies may be licensed.     

Forecasting market potential and market penetration of residential water heater load control programs

This paper presents a model which estimates market potential and forecasts market penetration for one demand-side management (DSM) programwater heater load controlin the service territory of Virginia Power Corporation, a large electric utility in the south-eastern United States. Water heater load control is a voluntary program where customers are paid a monthly incentive to allow the utility to shut off power to their electric water heaters during periods of peak demand. Reducing the level of peak demand through DSM programs is one way for utilities to avoid building new power plants. The current total energy (or demand) impact due to a load control program is the sum of the changes in energy (or demand) for all program participants. The projected energy and demand impact due to a load control program is the average change per participant multiplied by the number of participants or adopters of the program. While it is reasonably straightforward to measure the energy savings resulting from shutting off power to a water heater, the more difficult task for planning purposes is forecasting the number of customers who will actually join the program (i.e. the market penetration) for a given incentive. The customer decision process is divided into three stages: eligibility, awareness, and adoption. The responsiveness of market penetration to changes in advertising and incentive amounts is demonstrated. In addition, the impact of changing advertising and incentive amounts on the percentage of aware customers who adopt the program and on that of eligible customers who become aware of the program is estimated. This model can be used by utility planners and managers to forecast the market penetration of both new and existing load control programs. In addition, it can be employed to estimate the impact of various promotion and marketing schemes on both market potential and market penetration.