1. Statistics for Managers using Microsoft Excel 3rd Edition
Chapter 13
Time Series Analysis
© 2002 Prentice-Hall, Inc.

2. Chapter Topics The importance of forecasting
Component factors of the time-series model
Smoothing of annual time series
Moving averages
Exponential smoothing
Least square trend fitting and forecasting
Linear, quadratic and exponential models
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3. Chapter Topics Autoregressive models
(continued)
Autoregressive models
Choosing appropriate forecasting models
Time series forecasting of monthly or quarterly data
Pitfalls concerning time-series analysis
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4. The Importance of Forecasting
Government needs to forecast unemployment, interest rates, expected revenues from income taxes to formulate policies
Marketing executives need to forecast demand, sales, consumer preferences in strategic planning
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5. The Importance of Forecasting
(continued)
College administrators need to forecast enrollments to plan for facilities and for faculty recruitment
Retail stores need to forecast demand to control inventory levels, hire employees and provide training
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6. Time-Series Numerical data obtained at regular time intervals
The time intervals can be annually, quarterly, daily, hourly, etc.
Example:
Year:
Sales:
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7. Time-Series Components
Trend
Cyclical
Time-Series
Seasonal
Random
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8. Trend Component Overall upward or downward movement
Data taken over a period of years
Upward trend
Sales
Time
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9. Cyclical Component Upward or downward swings May vary in length
Usually lasts years
1 Cycle
Sales
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10. Seasonal Component Upward or downward swings Regular patterns
Observed within 1 year
Sales
Summer
Winter
Spring
Fall
Time (Monthly or Quarterly)
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11. Random or Irregular Component
Erratic, nonsystematic, random, “residual” fluctuations
Due to random variations of
Nature
Accidents
Short duration and non-repeating
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12. e.g.: Quarterly Retail Sales with Seasonal Components
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13. e.g.: Quarterly Retail Sales with Seasonal Components Removed
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14. Multiplicative Time-Series Model
Used primarily for forecasting
Observed value in time series is the product of components
For annual data:
For quarterly or monthly data:
Ti = Trend
Ci = Cyclical
Ii = Irregular
Si = Seasonal
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15. Moving Averages Used for smoothing
Series of arithmetic means over time
Result dependent upon choice of L (length of period for computing means)
To smooth out cyclical component, L should be multiple of the estimated average length of the cycle
For annual time-series, L should be odd
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16. Moving Averages Example: Three-year moving average First average:
(continued)
Example: Three-year moving average
First average:
Second average:
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17. Moving Average Example
John is a building contractor who has constructed 24 single-family homes over a six-year period. Provide John with a three-year Moving Average Graph.
Year Units Moving Ave NA NA
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18. Moving Average Example Solution
Year Response Moving Ave NA NA
Sales
L = 3 8 6 4 2
No MA for the first and last (L-1)/2 years
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19. Moving Average Example Solution in Excel
Use excel formula “=average (cell range containing the data for the years to average)”
Excel spreadsheet for the single family home sales example
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20. e.g.: 5-point Moving Averages of Quarterly Retail Sales
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21. Exponential Smoothing
Weighted moving average
Weights decline exponentially
Most recent observation weighted most
Used for smoothing and short term forecasting
Weights are:
Subjectively chosen
Ranges from 0 to 1
Close to 0 for smoothing out unwanted cyclical and irregular components
Close to 1 for forecasting
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22. Exponential Weight: Example
Year Response Smoothing Value Forecast (W = .2, (1-W)=.8) NA
(.2)(5) + (.8)(2) =
(.2)(2) + (.8)(2.6) =
(.2)(2) + (.8)(2.48) =
(.2)(7) + (.8)(2.384) =
(.2)(6) + (.8)(3.307) =
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23. Exponential Weight: Example Graph
Sales 8 6 4 2
Data
Smoothed
Year
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24. Exponential Smoothing in Excel
Use tools | data analysis | exponential smoothing
The damping factor is (1-W )
Excel spreadsheet for the single family home sales example
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25. Example: Exponential Smoothing of Real GNP
The EXCEL spreadsheet with the real GDP data and the exponentially smoothed series
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26. The Least Squares Linear Trend Model
Year Coded X Sales (Y)
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27. The Least Squares Linear Trend Model
(continued)
Excel Output
Projected to year 2001
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28. The Quadratic Trend Model
Year Coded X Sales (Y)
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29. The Quadratic Trend Model
(continued)
Excel Output
Projected to year 2001
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30. The Exponential Trend Modelor
Year Coded X Sales (Y)
Excel Output of Values in logs
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31. The Least Squares Trend Models in PHStat
Use PHStat | simple linear regression for linear trend and exponential trend models and PHStat | multiple regression for quadratic trend model
Excel spreadsheet for the single family home sales example
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32. Model Selection Using Differences
Use a linear trend model if the first differences are more or less constant
Use a quadratic trend model if the second differences are more or less constant
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33. Model Selection Using Differences
(continued)
Use an exponential trend model if the percentage differences are more or less constant
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34. Autoregressive Modeling
Used for forecasting
Takes advantage of autocorrelation
1st order - correlation between consecutive values
2nd order - correlation between values 2 periods apart
Autoregressive model for p- th order:
Random Error
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35. Autoregressive Model: Example
The Office Concept Corp. has acquired a number of office units (in thousands of square feet) over the last eight years. Develop the second order Autoregressive model.
Year Units
94 3
97 2
98 2
99 4
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36. Autoregressive Model: Example Solution
Develop the 2nd order table
Use Excel to estimate a regression model
Year Yi Yi Yi-2
Excel Output
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37. Autoregressive Model Example: Forecasting
Use the second order model to forecast number of units for 200x:
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38. Autoregressive Model in PHStat
PHStat | multiple regression
Excel spreadsheet for the office units example
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39. Autoregressive Modeling Steps
1. Choose p : note that df = n - 2p - 1
2. Form a series of “lag predictor” variables
Yi-1 , Yi-2 , … ,Yi-p
3. Use excel to run regression model using all p variables
4. Test significance of Ap
If null hypothesis rejected, this model is selected
If null hypothesis not rejected, decrease p by 1 and repeat
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40. Selecting A Forecasting Model
Perform a residual analysis
Look for pattern or direction
Measure sum of square error - SSE (residual errors)
Measure residual error using MAD
Use simplest model
Principle of parsimony
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41. Cyclical effects not accounted for
Residual Analysis e e T T
Random errors
Cyclical effects not accounted for e e T T
Trend not accounted for
Seasonal effects not accounted for
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42. Measuring Errors
Choose a model that gives the smallest measuring errors
Sum square error (SSE)
Sensitive to outliers
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43. Measuring Errors Mean Absolute Deviation (MAD)
(continued)
Mean Absolute Deviation (MAD)
Not sensitive to extreme observations
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44. Principal of Parsimony
Suppose two or more models provide good fit for data
Select the simplest model
Simplest model types:
Least-squares linear
Least-square quadratic
1st order autoregressive
More complex types:
2nd and 3rd order autoregressive
Least-squares exponential
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45. Forecasting With Seasonal Data
Use categorical predictor variables with least-square trending fitting
Exponential model with quarterly data:
The bi provides the multiplier for the i-th quarter relative to the 4th quarter.
Qi = 1 if i-th quarter and 0 if not
Xj = the coded variable denoting the time period
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46. Forecasting With Quarterly Data: Example
Standards and Poor’s Composite Stock Price Index:
Quarter
Excel Output
r2 is .98
Appears to be an excellent fit.
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47. Forecasting With Quarterly Data: Example
(continued)
Excel Output
Regression Equation for the first quarter:
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48. Forecasting with Quarterly Data in PHStat
Use PHStat | multiple regression
Excel spreadsheet for the stock price index example
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49. Pitfalls Regarding Time-Series Analysis
Assuming the mechanism that governs the time series behavior in the past will still hold in the future
Using mechanical extrapolation of the trend to forecast the future without considering personal judgments, business experiences, changing technologies, and habits, etc.
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50. Chapter Summary Discussed the importance of forecasting
Addressed component factors of the time-series model
Performed smoothing of data series
Moving averages
Exponential smoothing
Described least square trend fitting and forecasting
Linear, quadratic and exponential models
© 2002 Prentice-Hall, Inc.

51. Chapter Summary Addressed autoregressive models
(continued)
Addressed autoregressive models
Described procedure for choosing appropriate models
Addressed time series forecasting of monthly or quarterly data (use of dummy variables)
Discussed pitfalls concerning time-series analysis
© 2002 Prentice-Hall, Inc.