SAP HANA Predictive Analysis Library (PAL)

PAL_SINGLESMOOTH_STATISTICS_TBL:
Related Information
Forecast Accuracy Measures [page 365]
3.5.9 Double Exponential Smoothing
Double Exponential Smoothing model is suitable to model the time series with trend but without seasonality. In
the model there are two kinds of smoothed quantities: smoothed signal and smoothed trend.
PAL provides two methods of double exponential smoothing: Holt's linear exponential smoothing and additive
damped trend Holt's linear exponential smoothing. The Holt’s linear exponential smoothing displays a
constant trend indefinitely into the future. Empirical evidence shows that the Holt's linear method tends to
over-forecast. A parameter that is used to damp the trend could improve the situation.
Holt's Linear Exponential Smoothing
Let S t and b t be the smoothed value and smoothed trend for the (t+1)-th time period, respectively. The
following rules are satisfied:
S 0 = x 0
b 0 = x 1 – x 0
S t = αx t + (1 – α) (S t-1 + b t-1 )
b t = β (S t – S t–1 ) + (1 – β) b t-1
Where α, β∈(0,1) are two user specified parameters. The model can be understood as two coupled Single
Exponential Smoothing models, and forecast can be made by the following equation:
F T+m = S T + mb T
Additive Damped Trend Holt's Linear Exponential Smoothing
Let S t and b t be the smoothed value and smoothed trend for the (t+1)-th time period, respectively. The
following rules are satisfied:
S 0 = x 0
b 0 = x 1 – x 0
S t = αx t + (1 – α) (S t-1 + Φb t-1 )
b t = β (S t – S t–1 ) + (1 – β) Φb t-1
Where α, β, Φ∈(0,1) are three user specified parameters. Forecast can be made by the following equation:
F T+m = S T + (Φ + Φ 2 + ... + Φ m )b T
400 P U B L I C
SAP HANA Predictive Analysis Library (PAL)
PAL Functions