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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
Seasonality Adjustment
   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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