Showing papers by "Steven C. Wheelwright published in 1973"

Forecasting Methods for Management

Abstract: Part 1 The role and importance of forecasting in management: forecasting and management - an introduction the need for, and role of, forecasting what can and cannot be predicted. Part 2 quantitative forecasting methods - introduction to quantitative forecasting methods smoothing methods decomposition methods for time-series forecasting autoregressive/moving average (ARMA) methods simple regression methods multiple regression econometric modeling. Part 3 Forecasting challenges: explaining the past versus predicting the future judgmental approaches to forecasting biases and limitations in judgmental methods monitoring approaches selecting appropriate and quantitative methods integrating judgmental and quantitative methods technological and environmental forecasting. Part 4 Forecasting applications: the use of forecasting in business organizations forecasting the short term forecasting the medium term forecasting the long term support tools for quanti

An Examination of the Use of Adaptive Filtering in Forecasting

Abstract: Adaptive filtering is a technique for preparing short- to medium-term forecasts based on the weighting of historical observations, in a similar way to moving average and exponential smoothing. However, adaptive filtering, as it has been developed in electrical engineering, attempts to distinguish a signal pattern from random noise, rather than simply smoothing the noise of past data. This paper reviews the technique of adaptive filtering and investigates its applications and limitations for the forecasting practitioner. This is done by looking at the performance of adaptive filtering in forecasting a number of time series and by comparing it with other forecasting techniques.

Foregasting with adaptive filtering

Abstract: — During the past decade Régression Analysis has gained wide acceptance as a method for preparing medium and long range forecasts for time series. However/for a shortterm forecasting situation or when the number of observations is small, régression analysis is costly and of ten impractical. Exponential smoothing is the forecasting method most of ten used in these latter situations, but it has some major shortcomings ioo. Rather than trying to distinguish some underlying pattern from the noise (randomness) includedin observed data, exponential smoothing simpfy « smooths » the extreme values in preparing a forecast, which in many cases is not completely suitable. Thus there are a number of medium range forecasting situations and cases for which not much data is available where neither régression analysis nor exponential smoothing methods are appropriate. This paper briefly examines the gênerai class of forecasting methods that are based on a weighting of past observations and then présents the theoretical and practical aspects of adaptive filtering, a method for determining an appropriate set ofweights. Adaptive Filtering* a technique prevlously developed in télécommunications engineering, is attractive in many forecasting situations involving time series because it does discriminate between noise and an underlying pattern, it is conceptually appealing and easy to apply, it can be used with a relatively small amount of data, and the accuracy and reliability of its forecasts compare very favorably with other techniques. Some Existing Techniques for Forecasting There are numerous situations which arise in the opération of a business that require the development of a forecast for a time series. One of the most common of these involves the area of production scheduling and inventory control. In order to control out-of-stock costs and keep inventory costs within reason, firms must forecast demand for individual products and groups of products and then use those forecasts in making production décisions. Similarly, in the areas of finance, budgeting and marketing, forecasts must be prepared for working capital, cash flow, prices and other time series. While most of these situations involve short or medium term forecasts, firms also are faced with requirements for longer term projections in areas such as capacity utilization, capital requirements, and market growth. (1) Harvard Business School, Boston, Massachusetts. (2) INSEAD, Fontainebleau, France. Revue Française d* Automatique, Informatique et Recherche Opérationnelle n° mars 1973, V-l. 32 S. WHEELWRIGHT ET S. MAKRIDAKIS In order to meet these forecasting requirements, a number of methods have been developed for managers. These have been adopted to varying degrees, based largely on the manager's évaluation of their accuracy, their cost, and his ability to understand what they actually do (*). The majority of these methods are based on the idea that past observations contain information about some underlying pattern of the time series. The purpose of the forecasting method is then to distinguish that pattern from any noise (randomness) that also may be contained in past observations and then to use that pattern to predict future values in the series. A gênerai class of widely used forecasting methods that attempts to deal with both causes of fluctuations in a time series is that of smoothing. Spécifie techniques of this type assume that the extreme values in a series represent the randomness and thus by « smoothing » these extrêmes, the basic pattern can be identified. The two methods of this type that are used most often are moving averages and exponential smoothing. The technique of moving averages consists of taking the n most recent observations of a time series, finding the average of those values, and using that average as a forecast for the next value in the series. That is (), Jf+l = [ * * + **-l + . . +*,-(„-!)] where st +1 = the moving average forecast for period t + 1 based on the previous n observations n = the number of observations included in the average x% = the observed value in period i (i = 1, 2,... t). This approach to short term forecasting is referred to as moving averages because n is held constant and for each new forecast, t is incremented by 1 and the average is recomputed by dropping the oldest observation and picking up a new observation. The value of n détermines how much ofthe fluctuations in observed values is carried into the smoothed value, st+i : a larger value of n giving a more smoothed forecast than a smaller value of n. A major drawback of moving averages is that it assigns equal weight to each of the past n observations and no weight to observations before that. It can often be argued that the most recent observations in a series contain more information than the older values. Following this line of reasoning, many managers have adopted the technique of exponential smoothing which gives decreasing importance (smaller weights) to older observations. (1) As has become evident during the past few years, the ease with which a manager can understand a forecasting method is a major factor in determining its use in practice. (2) The notation used throughout this paper is that lower case letters represent scalar quantities and upper case letters represent vectors. The only exception to this is that q> is used to represent a single cross corrélation, $(x, d) is used to represent a vector, and [o(x, x)] is used to represent a matrix of these coefficients. Finally, where the range of values for a summation index is not given, it is from t — n + 1 to t. Revue Française d'Automatique* Informatique et Recherche Opérationnelle FORECASTING WITH ADAFITVE FILTERING 33 Exponential smoothing can be described mathematieally as st+t = oexf + (l —'a)st where st+ x = the exponentially smoothed value to be used as a forecast for period t + 1 a =s the smoothing constant (0 ^ a ^ 1) Xi = the observed value in period i (i — 1,2,... f). This gênerai équation can be expanded by replacing st with its computed value. Carrying out this expansion gives st+t = axt + a(l —