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Another approach, sometimes called “regression without models” [Farlow, 1984] does not assume a class of models. 8 exemplify this approach [Worbos, 1975]. There are sensitive assumptions behind of these approaches. We discuss them and their impact on forecasting in this chapter. 9 is devoted to “expert mining”, that is, methods for extracting knowledge from experts. Models trained from data can serve as artificial “experts” along with or in place of human experts. 10 describes background mathematical facts about the restoration of monotone Boolean functions.

For some time series, differencing can reflect a meaningful empirical operation with real world objects. These series are called integrated. For instance, trade volume measures the cumulative effect of all buy/sell transactions. An I(1) or ARIMA(0,1,0) model can be viewed as an autoregressive model, AR(1) or ARIMA(1,0,0), with a regression coefficient In this model (called random walk), each next value is only a random step D(t) away from the previous value. See chapter 1 for a financial interpretation of this model.

This shows that ARIMA models and statistical models, in general, are sensitive to expert decisions about parameters. 7 summarizes many of the differences between a variety of data mining methods. The ARIMA method was evaluated in the category of statistical methods (SM) in the column marked ST. According to [Dhar, Stein, 1977] this column indicates the two strongest features of SM: embeddability and independence of an expert in comparison with other methods. Embeddability of SM into application software systems is really its most attractive and indisputable feature.

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