A Note on the Paper: An Examination of the Use of Adaptive Filtering in Forecasting

Journal of the Operational Research Society -     

A Note on Forecasting with Adaptive Filtering

Adaptive filtering has been suggested as a short-term-forecasting technique that is superior to other time series analysis methods. This note discusses several aspects of adaptive filtering and indicates its equivalence to an autoregressive process. The performance of adaptive filtering and two other forecasting techniques are compared for a particular time series.     

Adaptive Filtering: An Integrated Autoregressive/Moving Average Filter for Time Series Forecasting

Journal of the Operational Research Society - This paper extends the applicability of a heuristic filtering technique, adaptive filtering, by dealing with a number of practical considerations in...     

Adaptive Filtering: An Empirical Evaluation

This paper compares the Makridakis and Wheelwright adaptive filtering forecast technique with the recursive least squares procedure, which assumes constant coefficients. A simulation study is performed to examine its relative forecast accuracy under several models of time-varying coefficients. It is shown that the choice of the learning constant in adaptive filtering is quite critical, and that only in cases with substantial coefficient variability will adaptive filtering lead to forecast improvements.     

Forecasting Using Growth Curves—An Adaptive Approach

Growth curves such as the logistic and Gompertz are widely used for forecasting market development. The approach proposed is specifically designed for forecasting, rather than fitting available data—the usual approach with non-linear least squares regression. Two innovations form the foundation for this approach. The growth curves are reformulated from a time basis to an observation basis. This ensures that the available observations and the forecasts form a monotonic series; this is not necessarily true for least squares extrapolations of growth curves. An extension of the Kalman filter, an approach already used with linear forecasting models, is applied to the estimation of the growth curve coefficients. This allows the coefficients the flexibility to change over time if the market environment changes. The extended Kalman filter also proves the information for the generation of confidence intervals about the forecasts. Alternative forecasting approaches, least squares and an adaptive Bass model, suggested by Bretschneider and Mahajan, are used to produce comparative forecasts for a number of different data sets. The approach using the extended Kalman filter is shown to be more robust and almost always more accurate than the alternatives.     

On Adaptive Filtering

The adaptive filtering technique has recently been proposed as a method for short-to medium-term forecasting. The present note demonstrates some of the shortcomings implicit in the theory and gives illustrative examples.     

Adaptive Filtering Revisited

This paper shows that the adaptive filtering and forecasting techniques proposed by Makridakis and Wheelwright can be viewed as approximations to a more precise filtering method in which the Kalman filter is applied to a dynamic autoregressive model which is a special case of the models of Harrison and Stevens. The correct "learning" or "training factors" are shown to be data-dependent matrices rather than scalar constants.     

Choice of Regularization Parameter in Adaptive Filtering Problems

Computational Mathematics and Mathematical Physics - The paper proposes a new method for choosing a regularization parameter when solving an integral equation of convolution type in problems of...     

Adaptive Holt—Winters Forecasting

The Holt-Winters method has been found to be a simple, robust and accurate method of forecasting seasonal series, but Trigg-and-Leach extensions have not proved successful. This note shows the reasons for this, and develops a Holt-Winters method which is adaptive in the Trigg-and-Leach sense. Numerical tests suggest that it may be superior to non-adaptive Holt-Winters.     

Adaptive Filtering: A Critical Assessment

A forecasting procedure called adaptive filtering (AF) is reexamined. The theoretical foundations of the method have been questioned by several authors, and further difficulties are discussed here. In addition, the Box-Jenkins airline data are reanalysed and, contrary to the claims of Makridakis and Wheelwright, it is shown that AF does not compare favourably with other forecasting methods. In view of the theoretical and practical difficulties, the routine use of AF in business forecasting is not recommended.     

Adaptive Filtering: Once More with Gusto

Adaptive filtering, when used as a forecasting method, proposes to be able to distinguish a "signal pattern" of a time series instead of just smoothing out the random noise introduced by the data. Adaptive filtering is claimed by its creators to "...always do as well if not better than either moving averages, exponential smoothing,...". In order to see whether this claim could be substantiated, the author has taken the approach of a casual user of forecasting methods and has sought to determine whether adaptive filtering is useful, or not, as a forecasting method. The method was used to compute forecasts for ten sets of data on monthly insurance payments in a Finnish insurance company, and the experience gained from this work is compared with criticisms of the method expressed by a number of writers. It is shown that the method performs quite well for practical purposes, despite the fact that it has some major theoretical shortcomings.     

Adaptive Sales Forecasting with Many Stockouts

The firm distributing products periodically may set distribution quantities so that a high percentage (60-90%) of all periods are stockouts but in this environment must still attempt to forecast demand. This paper presents a fast, low storage, forecasting methodology which systematically adjusts for stockouts and presents simulation results which illustrate the usefulness of the procedure.     

Optimal Stopping Time Formulation of Adaptive Image Filtering

This paper presents an approach to image filtering based on an optimal stopping time problem for the evolution equation describing the filtering kernel. This approach allows us to obtain easily an adaptivity of the filter with respect to the noise level. Well-posedness of the problem and convergence of fully discrete approximations are proved and numerical examples are presented and discussed. Accepted 25 October 2000. Online publication 9 April 2001.     

An Application of Forecasting in the Alcoholic Drinks Industry

The sales of cider in the U.K. experienced an upsurge in demand during the good summer of 1975 and the record drought of 1976. Conventional linear growth seasonal forecasting systems are unable to isolate out the effects of this exceptional weather and would produce a high forecast for the (average/poor) year of 1977. Furthermore at the end of 1976 the Government imposed an Excise Duty which depressed demand still further. A model capable of isolating and measuring these (and other) effects was required and this was achieved within the framework of the Dynamic Linear Model proposed by Harrison and Stevens¹ usually referred to as the Bayesian methods.The model finally included growth and seasonality plus the effect of exceptional weather together with price, inflation and the transfer effects of price changes. The forecasts have been very satisfactory and enable future alternative pricing strategies to be investigated.     

Adaptive Filtering: a Theoretical and Simulation Study of the Convergence of the Parameter Estimates

The existence of bias in the final parameter estimates using adaptive filtering is demonstrated theoretically. For observations generated by an autoregressive model of order one, an approximate theoretical expression for the bias is derived which is valid for long series of observations. The validity of the expression is investigated by simulation and comparing the theoretical bias with the simulated bias at the end of one major iteration. By carrying out a number of major iterations, it is shown that the bias reaches a stable value which is a function of the learning constant. The magnitude of the stable bias may be made as small as desired by taking smaller values for the learning constant. However, as the learning constant decreases, the number of major iterations required to achieve stability increases. By means of simulation experiments, the existence of bias in the final parameter estimates is demonstrated for shorter series of observations generated by an AR(1) model, and for long series of observations generated by an AR(2) model. Again the bias appears to increase with the magnitude of the learning constant. It is argued that the presence of this bias need not be a drawback in the practical application of the method since, by systematic reduction of the training constant between major iterations, the bias may also be reduced, while reasonably rapid convergence can still be maintained.     

The Use of Models for Environmental Forecasting and Corporate Planning

This paper presents briefly, the forecasting and planning activities which have evolved over the years in Esso Petroleum Company. It describes three computer models developed in the Corporate Planning Department for these activities an econometric model for short-term environmental forecasting and economic analysis; a horizon year optimization model for long-range corporate objectives setting; and a multi-time period simulation model for financial forecasting and planning both in short and long term. The structure, use and limitations of each of the models are discussed.