As we have noted, it is common to use fairly small values for α in exponential smoothing systems in order to filter out random variations in demand. When actual demand rates increase or decrease gradually, such forecasting systems can track the changes rather well. If demand changes suddenly, however, a forecasting system that uses a small value for α will lag substantially behind the actual change. Thus, adaptive response systems have been proposed.

The basic idea of adaptive smoothing systems is to monitor the forecast error and, based on preset rules, to react to large errors by increasing the value of α. The value of α in the Trigg and Leach (1967) model is set equal to the absolute value of a tracking signal.

Tracking signal = Smoothed forecast error/Smoothed absolute forecast error

The smoothing of error is accomplished by using an equation similar to Equation 2. If the error is small, α will be small. If, due to a sudden shift in demand, the error is large, then the tracking signal will be large. Thus, if a step error would result. The large error signals that α should increase in order to give greater weight to current demand. The forecast would then reflect the change in actual demand. When actual demand stabilizes at the new level, adaptive systems would reset the value of α to a lower level that filters out random variations effectively. A number of approaches to adaptive response systems have been proposed, see, for example, Chow (1965), Trigg and Leach (1967) and Roberts and Reed (1969).

Adaptive models may be useful for new products for which little historical data are available; the adaptive models should correct and stabilize themselves quickly. If demand shows rapid shifts and little randomness, then adaptive methods may perform well. Such a demand pattern will, however, be uncommon in production inventory situations. Limitations of adaptive methods rest in the greater amounts of historical data, and computer time they require in comparison to the simpler models.

Causal or Explanatory Methods:

When we have enough historical data and experience, it may be possible to relate forecasts to factors in the economy that cause the trends, seasonal fluctuations. Thus, if we can measure these causal factors and can determine their relationships to the product or service of interest, we can compute forecasts of considerable accuracy.

The factors used in causal models are of several types: disposable income new marriages, housing starts, inventories, and cost of living indices as well as predictions of dynamic factors and/or disturbances, such as strikes, actions of competitors, and sales promotion campaigns. The causal forecasting model expresses mathematical relationships between the causal factors and the demand for the item being forecast. There are two general types of causal models: regression analysis and econometric methods.

Regression Analysis:

Forecasting based on regression methods establishes a forecasting function called a regression equation. The regression equation expresses the series to be forecast in terms of other series that presumably control or cause sales to increase or decrease.

The rationale can be general or specific. For example, in furniture sales we might postulate that sales are related to disposable personal income: if disposable personal income is up, sales will increase, and if people have less money to spend, sales will decrease. Establishing the empirical relationship is accomplished through the regression equation. To consider additional factors, we might postulate that furniture sales are controlled to some extent by the number of new marriages and the number of new housing starts. These are both specific indicators of possible demand for furniture.

To summarize, the central idea in regression analysis is to identify variables that influence the variable to be forecasted and establish the relationship between them so that the known values of the independent variables can be used to estimate the unknown or forecasted value of the dependent variable.

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