SAP HANA Predictive Analysis Library (PAL)

3.5.10 Triple Exponential Smoothing
Triple exponential smoothing is used to handle the time series data containing a seasonal component. This
method is based on three smoothing equations: stationary component, trend, and seasonal. Both seasonal
and trend can be additive or multiplicative. PAL supports multiplicative triple exponential smoothing and
additive triple exponential smoothing. For additive triple exponential smoothing, an additive damped method is
also supported.
Multiplicative triple exponential smoothing is given by the below formula:
Additive triple exponential smoothing is given by the below formula:
S t = α × (X t − C t−L ) + (1 − α) × (S t−1 + B t−1 )
B t = β × (S t − S t−1 ) + (1 − β) × B t−1
C t = γ × (X t − S t ) + (1 − γ) × C t−L
F t+m = S t + m × B t + C t−L+1+((m−1)mod L)
The additive damped method of additive triple exponential smoothing is given by the below formula:
S t = α × (X t − C t−L ) + (1 − α) × (S t−1 + Φ × B t−1 )
B t = β × (S t − S t−1 ) + (1 − β) × Φ × B t−1
C t = γ × (X t − S t ) + (1 − γ) × C t−L
F t+m = S t + (Φ + Φ 2 + ... + Φ m ) × B t + C t−L+1+((m−1)mod L)
Where:
Table 290:
α Data smoothing factor. The range is 0 < α