What is the formula used to calculate the value of bt in the linear trend equation Ft+k = at + btk while using double exponential smoothing?
A) bt = βbt - bt-1) + 1 -β)bt-1
B) bt = αFt-1 + 1 - α)at +1 + bt+1)
C) bt = αFt + 1 - α)at -1 + bt-1)
D) bt = βat - at-1) + 1 -β)bt-1

Question

Quizplus · Accepted Answer

The correct formula for calculating the value of $b_t$ in the context of the linear trend equation $F_{t+k} = a_t + b_tk$ when using double exponential smoothing is $b_t = \beta(a_t - a_{t-1}) + (1 - \beta)b_{t-1}$. This formula adjusts the trend component of the forecast by blending the most recent trend (as indicated by the difference between the last two levels, $a_t - a_{t-1}$) with the previous trend estimate ($b_{t-1}$), weighted by the smoothing parameter $\beta$.

What Is the Formula Used to Calculate the Value of Bt