Brown’s Double Exponential Smoothing

Local Algorithm - One-Dimensional Algorithm

The basic formulas of the Brown’s Double Exponential Smoothing algorithm are stated as follows:

(1)s′0=Y0,
(2)s0″
(3) \quad s^{'}_t = \alpha Y_t + (1-\alpha) s^{'}_{t-1} \, \text{,}
(4) \quad s^{''}_t = \alpha s^{'}_t + (1-\alpha) s^{''}_{t-1} \, \text{,}
(5) \quad a_t = 2 s^{'}_t - s^{''}_t \, \text{,}
(6) \quad b_t = \frac{\alpha}{1-\alpha} (s^{'}_t - s^{''}_t) \, \text{,}
(7) \quad \hat{Y}_{t+m} = a_t + m b_t \, \text{,}

where Y is the data sequence beginning at time t = 0 and \hat{Y}_{t+m} is the smoothed forecast for time t + m.

Input Parameters

Parameter Type Constraint Description Remarks
Y Y \in \mathbb R^N N \in \mathbb{N} Input data sequence of length N  
\alpha \alpha \in \mathbb R 0 \leq \alpha \leq 1    

Output Parameters

Parameter Type Constraint Description Remarks
\hat{Y} \hat{Y} \in \mathbb R^N      

Tool Support

Single Steps using the Algorithm

References