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Quantitative Business Forecasting
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Quantitative Forecasting
• Regression Models
• Time Series Models
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Procedure for Forecasting with Time Series Model
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Time SeriesTrend and Seasonsality
• Calculate the deseasonalized data from the original time series
• Construct a least squares line through the deseasonalized data.
• Calculate the forecast for the time period T+1
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Exponential Smoothing
• This technique uses all the preceding observations to determine a smoothed value for a particular time period.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Exponential Smoothing
1)1( ttt SAAyS
St = Smoothed value for time period t
t = 2, 3, 4, . . . . .
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Simple Exponential Smoothing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Simple Exponential Smoothing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Linear Exponential Smoothing
Procedures for Summarizing the Results
• Procedure 1:– b1 = 0 Provided you have a large number of
years, this procedure provides an adequate initial estimate for the trend.
• Procedure 2:– use the first five years to estimate the initial
trend. Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Linear Exponential Smoothing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Forecasting Using Linear and Seasonal Exponential Smoothing• Procedure 1:
– Set the initial seasonal factors equal to 1.– Set the initial trend estimate equal to 0.– Set the initial smoothed value for quarter 4 (t)
equal to the actual value for quarter 4 (t+1).
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Forecasting Using Linear and Seasonal Exponential Smoothing• Procedure 2:
– Use the first two years of data to determine the seasonal indexes.
– Deseasonalize the datat for the first two years and calculate the least squares line through these deseasonalized values.
– The initial smoothed value for quarter 4 (t). So is the forecast value for each of the 4 quarters in year t+1.Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Forecasting Using Linear and Seasonal Exponential Smoothing
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Comparison of the Procedures
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Time as a Factor for Choosing the Appropriate Forecasting Procedure
• Length of the forecast– short term forecast: one to three months– Medium-range forecast: four months to two years– Long-range forecast: two or more years
• Exponential smoothing procedures are excellent for short-term forcasts, whereas the component decomposition is useful for medium- and long-range forecastingIntroduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
“Fit” as a Factor for Choosing the Appropriate Forecasting Procedure
• MAD - mean absolute deviation
• MAPE - mean absolute percentage error
• MSE - mean square error
• There is no consensus among statisticians as to which measure is preferable.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
“Fit” as a Factor for Choosing the Appropriate Forecasting Procedure
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Autoregressive Forecasting
• Used when the time series variable is related to past values of itself.
• We can expect the autoregressive technique to perform well for a time series that (1) is not extremely volatile and (2) requires a short-term or medium-range forecast.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Autocorrelation
DW(et et 1)2
t2
T
et2
t1
T
Durbin-Watson Statistic
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Autocorrelation
Ho: no autocorrelation existsHa: positive autocorrelation exists
DW(et et 1)2
t2
T
et2
t1
T
Reject Ho if DW < dL
Fail to Reject Ho if DW < dU
The test is inconclusive if dL DW dU
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Procedures for Correcting Autocorrelated Errors
zt yt yt 1
yt1
100
1. Replace yt by the first differenceyt = yt - yt-1
2. Replace yt by the percentage change during year t
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing
Procedures for Correcting Autocorrelated Errors
3. Include the lagged dependent variables as predictors of y.4. Attempt to discover other significant predictor variables.5. Model the error term in much the same way we handled the situation of autocorrelated observations.
Introduction to Business Statistics, 5e
Kvanli/Guynes/Pavur
(c)2000 South-Western College Publishing