Exponential Smoothing Calculator

Image to Crop

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 - 1

For 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 set
Sum of Values/nexponential smoothingCreate smoothed data using exponential functions
αxt - 1 + (1 - α)st - 1

Exponential Smoothing Calculator Video


Tags:

Add This Calculator To Your Website

ncG1vNJzZmivp6x7rq3ToZqepJWXv6rA2GeaqKVfmsWxu9KmpqismGO9qbyep6ymdVtmcnOPkV5pfGtVZ5B1cZF8bF%2BZnKW1oomKaWVtXqChioSty5yspZmkmg%3D%3D