SIMPLE EXPONENTIAL SMOOTHING AND THE HOLT MODELING SYSTEM

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SIMPLE EXPONENTIAL SMOOTHING AND
THE HOLT MODELING SYSTEM

• Marlow Bakken
• Matthias Held
• Aurore Poulain
• Dominika
  Wabinska

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Define it !

• Exponential Smoothing
• Its based on averaging past values of
  series
• in a decreasing manner.
• New forecast
  ?(new observation)
  (1-?)(old forecast)

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We cannot work without some math
or

• Old forecast adjusted by ? times the error in
  the old forecast
• It continually revises an estimate in the light
  of more recent experiences?Autopilot

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a ?0 Groundhog Day Phil saysToday is
tomorrow a ?1 substantial error
adjustment
WANTED!!! ?
weighting factor

• determines how much current data influences the
  forecast value
• can be found somewhere between
• 0 and 1
• REWARD Valuable forecast!!!

http//groundhog.org/about/predictions.php
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• How to estimate ? ???
• hunch
• MSE

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CRUTIAL MATTER INITIAL VALUE
How do we start? the first estimate of
smoothed series the first observation
just average! ( use an
average of first 5 or 6 observation)
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Tracking signal
A tracking signal involves computing a measure of
the forecast errors over time and setting limits
, so that when cumlative errors goes outside
those limits the forecaster is alerted !
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HOLTS METHOD

• Holts two-parameter method,
• 1957
• Smoothes the level and the slope,
• using constants
• Constants provide estimates of level and slope,
  adapt over time as new observations become
  available
• Great deal of flexibility in selecting of the
  rates at which the level and trend are changed.

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Three equations

• The current level estimate
• Lt a Yt (1-a) (Lt-1 Tt-1)
• Trend estimate
• Tt ß(Lt Lt-1) (1- ß)Tt-1
• Forecast p periods into the future
• Ytp Lt pTt

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?

• Used to smooth the trend estimate
• 0 ß 1
• ß 0 Simple exponential smoothing
• Trend 0
• ß 1
• Trend value difference
• between the last 2
• level forecast values

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The Weight ? and ?

• Subjectively or by minimizing an error such as
  the MSE

• Small values
• less rapid changes

• Large values
• more rapid changes

The larger the weights, the more the smoothed
values follow the data
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• Grid of value of ? and ?
• Select a combination lowest MSE
• ( Marlows graph)

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CRUCIAL MATTER INITIAL VALUE

• How do we start?
• the first estimate of the smoothed
  series the first observation Ti 0
• once again just average!
• (use an average of first 5 or 6
  observation)