# Technical Forecasting

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```					Technical Forecasting

Week 5 (Chapter 4/5)
Winters Triple Exponential
Smoothing
Classical Decomposition
Elements of a Time Series
   Trend
   Seasonal variation (one year)
   Cyclical variation (long cycle)
   Random variation
   Other
Dealing with Seasonality
   Seasonality Index (SI)
• Indicates how much this period typically
deviates from the annual average
•   Requires at least one full season of data
   Multiplicative seasonality
• Level and trend estimates are multiplied by
the SI to generate forecast
•   Realistically represents increasing variation
Seasonal Forecasting Methods
   Winter’s Triple Exponential Smoothing
   Time Series Decomposition
Winter’s (Triple) Exponential
Smoothing
   L=level estimate
   T=trend estimate
   S=seasonality estimate (SI)
   Three are combined to generate a forecast
   Multiplicative model is most common
Triple Exponential Formulas

 1   Lt 1  Tt 1 
Yt
Lt  
St  s
Tt   Lt  Lt 1   1   Tt 1

 1   St  s
Yt
St  
Lt
Y  L  T S
ˆ
t 1     t     t   t  s 1
Selecting Smoothing Constant γ
   Constant seasonal pattern (small γ)
   Changing seasonal pattern (large γ)
   Useful to experiment with different α, β,
and γ values
Getting Started
   Choose α, β, γ
   Calculate values for the first year:
• L is the average for the year
• T is 0
• S is Y/L for each period
Minimizing Forecast Error
   Nonlinear optimization problem
   Calculate objective function based on
MPE, MAPE
   Adjust α, β, and γ to minimize objective
   Excel solver works well
Time Series Decomposition
   Decompose series into elements
• Trend
• Seasonality
• Other
   Can be used to seasonally adjust data
Steps
   Seasonally adjust the data
   Extract the trend
   Generate the forecast
   Calculate yearly averages
   Calculate one-year SI values
   Calculate two-year SI values
   Use two-year values to adjust data:
Yt
Yt 
St
where : St is 2  year SI
Extracting Trend
   Use at least one year of adjusted data
   Use linear regression
   Excel forecast( ) function
Generating the Forecast
   Multiplicative combination of trend and
seasonality:

ˆ       ˆ
Yt 1  Tt 1St s 1
Comparing the Two Methods
   Winter’s
• Parameters give adjustment
• Parameters hard to determine
• More complex
   Decomposition
• Seasonal adjustment is informative
• Simpler
• No adjustments to improve error

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 views: 8 posted: 3/12/2012 language: pages: 15