Casestudie Breakdown prediction Contell PILOT - Transumo

Figure 5-4: Sales of an Industrial Heater [Chatfield04]
A decomposition of a time series y = t , s , o , i ) like that allows a nearly complete
t
(
t t t t
description. Deviations are very small and have to be classified as other irregular
fluctuations. A prediction, based on such a time series, leads to much better results
than regression because the regular variations t, s, and o are taken into account.
To be able to identify these components it is first of all necessary to define the
interaction of the single components. In general, two models do exist. Formula 5-8
pictures the additive one and Formula 5-9 pictures the multiplicative one.
([Bourier03], p. 158-159)
y = t + s + o + i
t
t
Formula 5-8: The Additive Component Model
t
t
t
y
t
= t ⋅ s ⋅o
⋅i
t
t
t
t
Formula 5-9: The Multiplicative Component Model
The first model is normally used, if cyclic variations with constant amplitude are
assumed. By contrast, the multiplicative model is used, if cyclic components are on
the increase over time. ([Eckey02], p. 188)
The first step of a time series analysis is the identification of a possible trend. A very
common approach to identify a trend is the usage of the least squares method, as
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