Using exponential smoothing, list all terms for the following time series
{1,2,3,4,5} using α = 0.4
t = 1
s1 = x0
s1 = 1
t = 2
st = αxt - 1 + (1 - α)st - 1
s2 = αx2 - 1 + (1 - α)s2 - 1
s2 = 0.4(x1) + (1 - 0.4)s1
s2 = 0.4(x1) + (0.6)s1
s2 = 0.4(2) + (0.6)1
s2 = 0.8 + 0.6
s2 = 1.4
t = 3
st = αxt - 1 + (1 - α)st - 1
s3 = αx3 - 1 + (1 - α)s3 - 1
s3 = 0.4(x2) + (1 - 0.4)s2
s3 = 0.4(x2) + (0.6)s2
s3 = 0.4(3) + (0.6)1.4
s3 = 1.2 + 0.84
s3 = 2.04
t = 4
st = αxt - 1 + (1 - α)st - 1
s4 = αx4 - 1 + (1 - α)s4 - 1
s4 = 0.4(x3) + (1 - 0.4)s3
s4 = 0.4(x3) + (0.6)s3
s4 = 0.4(4) + (0.6)2.04
s4 = 1.6 + 1.224
s4 = 2.824
t = 5
st = αxt - 1 + (1 - α)st - 1
s5 = αx5 - 1 + (1 - α)s5 - 1
s5 = 0.4(x4) + (1 - 0.4)s4
s5 = 0.4(x4) + (0.6)s4
s5 = 0.4(5) + (0.6)2.824
s5 = 2 + 1.6944
s5 = 3.6944
Final Answer
Our 5 smoothed values are {1, 1.4, 2.04, 2.824, 3.6944}
You have 1 free calculations remaining
What is the Answer?
Our 5 smoothed values are {1, 1.4, 2.04, 2.824, 3.6944}
How does the Exponential Smoothing Calculator work?
Free Exponential Smoothing Calculator - Performs exponential smoothing on a set of data.
This calculator has 2 inputs.
What 1 formula is used for the Exponential Smoothing Calculator?
αxt - 1 + (1 - α)st - 1For more math formulas, check out our Formula Dossier
What 2 concepts are covered in the Exponential Smoothing Calculator?
averageA number expressing the central value of a setSum of Values/nexponential smoothingCreate smoothed data using exponential functions
αxt - 1 + (1 - α)st - 1
Exponential Smoothing Calculator Video
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