Download - ForecastIT 7. Decomposition
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Decomposition
Lesson #7
Decomposition Method
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Decomposition
Model Introduction• Assumes that every time series is composed of four components:
– Trend, seasonality, cyclical, and random• Method decomposes the time series in to its basic components• Uses the estimated component factors to forecast future values• Method format:
– Y = T × S × C
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Decomposition
Model Details• Method characteristics
– Decomposes a time series in to its parts– Estimates each component of the time series individually and
then combines then together to generate a forecast for the future.
• When to use method– Any time series can be decomposed
• When not to use– Not applicable
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Decomposition
Forecasting Steps1. Set an objective2. Build model3. Evaluate model4. Use model
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Decomposition
Objective Setting• Simpler is better• Decomposition allows to test whether a breaking down of the time
series works as a model. Objectives should take that principal under consideration
• Example objectives for New One Family Homes Sold (see next slide):– Test if New One Family Homes Sold can be fit to a
decomposition model– If One Family Homes Sold exhibits a statistically significant fit,
review and interpret results– If model looks good, create a forecast based off model
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Decomposition
Example: Houses Sold
1962-12-20 1968-06-11 1973-12-02 1979-05-25 1984-11-14 1990-05-07 1995-10-28 2001-04-19 2006-10-100
200
400
600
800
1000
1200
1400
1600
New One Family Houses Sold: United States (Thousands)
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Decomposition
Build Model• Model breaks down time series in to its appropriate parts,
independently estimates each part, and then combines the estimated parts together to forecast future values
1962-12-20 1968-06-11 1973-12-02 1979-05-25 1984-11-14 1990-05-07 1995-10-28 2001-04-19 2006-10-100
200400600800
1000120014001600
New One Family Houses Sold: United States (Thousands)
VALUE Forecast
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Decomposition
Evaluate Model• Descriptive Statistics
– Mean– Variance & Standard Deviation
• Accuracy / Error– SSE– RMSE– MAPE– R2; Adjusted R2
• Statistical Significance– F-Test– P-Value F-Test
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Decomposition
ExampleDescriptive Statistics
• Mean– 5.88
• Variance– 0.34
• Standard Deviation– 0.58
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Decomposition
ExampleAccuracy / Error
• SSE– 1.97
• RMSE– 0.22
• MAPE– 2.78%
• R2; Adjusted R2
– 84.80%– 84.39%
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Decomposition
ExampleStatistical Significance
• F-Test– 55.80
• P-Value F-Test– 0.000021
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Decomposition
Compare Multiple Models• Skip this step until have knowledge of multiple methods• Will use accuracy/error statistics to compare multiple models to
find best models
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Decomposition
Use Model
• Understand limitations of model• Answer objectives
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Decomposition
Example• Forecasts
– 4.888234437
