Post on 22-Dec-2015
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Basic Concepts in Forecasting
• Forecast error is the difference between the observed value of the time series and the forecast, or At – Ft .
Mean Square Error (MSE)
Mean Absolute Deviation Error (MAD)
Mean Absolute Percentage Error (MAPE)
Σ(At – Ft )2
MSE = [11.1]T
MAD = [11.2]׀ At – Ft׀T
Σ׀(At – Ft )/At ׀ X 100MAPE = [11.3]
T
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Solved Problem
Develop three-period and four-period moving-average forecasts and single exponential smoothing forecasts with a = 0.5. Compute the MAD, MAPE, and MSE for each. Which method provides a better forecast?
Period Demand Period Demand
1 86 7 91
2 93 8 93
3 88 9 96
4 89 10 97
5 92 11 93
6 94 12 95
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Based on these error metrics (MAD, MSE, MAPE), the 3-month moving average is the best method among the three.
80
82
84
86
88
90
92
94
96
98
1 2 3 4 5 6 7 8 9 10 11 12
Period
Moving Average Forecasts
Solved Problem
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Single Exponential Smoothing
• Single Exponential Smoothing (SES) is a forecasting technique that uses a weighted average of past time-series values to forecast the value of the time series in the next period.
Ft+1 = At + (1 – )Ft = Ft + (At – Ft)
[11.5]
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Regression as a Forecasting Approach
• Regression analysis is a method for building a statistical model that defines a relationship between a single dependent variable and one or more independent variables, all of which are numerical.
Yt = a + bt (11.7)- Simple linear regression finds the best values of a and b using
the method of least squares.- Excel provides a very simple tool to find the best-fitting
regression model for a time series by selecting the Add Trendline option from the Chart menu.