Additive Saison, exponentieller Trend

Additive season, exponential trend

In this Time Series model, the simp­le expo­nen­ti­al smoot­hing fore­casts are “enhan­ced” both by an expo­nen­ti­al trend com­po­nent (inde­pendent­ly smoot­hed with para­me­ter g) and an addi­ti­ve sea­so­nal com­po­nent (smoot­hed with para­me­ter d). For exam­p­le, sup­po­se we wan­ted to fore­cast the month­ly reve­nue for a resort area. Every year, reve­nue may increase by a cer­tain per­cen­ta­ge or fac­tor, resul­ting in an expo­nen­ti­al trend in over­all reve­nue. In addi­ti­on, the­re could be an addi­ti­ve sea­so­nal com­po­nent, for exam­p­le a par­ti­cu­lar fixed (and slow­ly chan­ging) amount of added reve­nue during the Decem­ber holi­days.

To com­pu­te the smoot­hed values for the first sea­son, initi­al values for the sea­so­nal com­pon­ents are neces­sa­ry. By default, the Time Series modu­le will esti­ma­te tho­se values (for all models inclu­ding a sea­so­nal com­po­nent) from the data via Clas­si­cal sea­so­nal decom­po­si­ti­on. Also, to com­pu­te the smoot­hed value (fore­cast) for the first obser­va­ti­on in the series, both esti­ma­tes of S0 and T0 (initi­al trend) are neces­sa­ry. By default, the­se values are com­pu­ted as:

T0 = exp((log(Mk) - log(M1))/p)

whe­re

k is the num­ber of com­ple­te sea­so­nal cycles
Mk is the mean for the last sea­so­nal cycle
M1 is the mean for the first sea­so­nal cycle
p is the length of the sea­so­nal cycle

and S0 = exp(log(M1) - p*log(T0)/2)

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Sasha Shiran­gi (Head of Sales)