SAP HANA Predictive Analysis Library (PAL)

B
Trend factor
C
Seasonal index
F
The forecast at m periods ahead
t
The index that denotes a time period
Note
α, β, and γ are the constants that must be estimated in such a way that the MSE of the error is minimized.
PAL uses two methods for initialization. The first is the following formula:
To initialize trend estimate B L−1 :
To initialize the seasonal indices C i for i = 0,1,...,L−1 for multiplicative triple exponential smoothing:
To initialize the seasonal indices C i for i = 0,1,...,L−1 for additive triple exponential smoothing:
c i = x i - S L-1 0≤i≤L-1
Where
Note
S L−1 is the average value of x in the L cycle of your data.
The second initialization method is as follows:
1. Get the trend component by using moving averages with the first two CYCLE observations.
2. The seasonal component is computed by removing the trend component from the observations. For
additive, use the observations minus the trend component. For multiplicative, use the observations divide
the trend component.
3. The start values of C t are initialized by using the seasonal component calculated in Step 2. The start values
of S t and B t are initialized by using a simple linear regressing on the trend component, S t is initialized by
intercept and B t is initialized by slope.
408 P U B L I C
SAP HANA Predictive Analysis Library (PAL)
PAL Functions