You are using an exponential smoothing on an annual time series concerning total revenues (in $millions). You decide to use a smoothing coefficient of W = .2, and the exponentially smoothed value for 2017 is E[2017] = (.2)(12.1) + (.8)(9.4).
What is the smoothed value of this series in 2018 if the value of the series in that year is $11.5 million?
To find the smoothed value of the series in 2018, we need to use the exponential smoothing formula:
E[2018] = α * X[2018] + (1 - α) * E[2017]
Given that the smoothing coefficient is W = 0.2, we have:
E[2018] = 0.2 * 11.5 + (1 - 0.2) * (0.2 * 12.1 + 0.8 * 9.4)
Simplifying the equation:
E[2018] = 2.3 + 0.8 * 10.824
E[2018] = 2.3 + 8.6592
E[2018] = 10.9592
Therefore, the smoothed value of the series in 2018 is $10.9592 million.