1. 1 Power Nine Econ 240C

2. 2 Outline Lab Three Exercises Lab Three Exercises –Fit a linear trend to retail and food sales –Add a quadratic term –Use both models to forecast 1 period ahead Lab Five Preview Lab Five Preview –Airline passengers

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8. 8 Lab Three Exercises Process Identification Identification –Spreadsheet –Trace –Histogram –Correlogram –Unit root test Estimation Estimation Validation Validation

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17. 17 One Period Ahead Forecast E 2008.02 rsafnsa (2008.03) = 156,647.8 + 1127.496*194 E 2008.02 rsafnsa (2008.03) = 156,647.8 + 1127.496*194 E 2008.02 rsafnsa (2008.03) = E 2008.02 rsafnsaf (2008.02) + 1127.496 E 2008.02 rsafnsa (2008.03) = E 2008.02 rsafnsaf (2008.02) + 1127.496 E 2008.02 rsafnsa (2008.03) = 374255 + 1127.496 = 375380.5 +/- 2*ser E 2008.02 rsafnsa (2008.03) = 374255 + 1127.496 = 375380.5 +/- 2*ser Ser =20014 Ser =20014

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22. 22 Lab Three Exercises Process Identification Identification –Spreadsheet: check variable values –Trace: trended series and seasonal –Histogram: –Correlogram: similar to a “random walk” –Unit root test: evolutionary Estimation Estimation Validation Validation

23. 23 Process Validating the model Validating the model –Actual, fitted, residual –Correlogram of the residuals –Histogram of the residuals

24. 24 Add the quadratic term

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27. 27 Seasonal dummies

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34. 34 Now we know another way to forecast Seasonal difference retail Seasonal difference retail

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50. 50 Preview of Lab Five A Box-Jenkins famous time series: airline passengers A Box-Jenkins famous time series: airline passengers –Trend in mean –Trend in variance –seasonality Prewhitening Prewhitening –Log transform –First difference –Seasonal difference

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54. 54 Note trend from Spike in pacf at Lag one; seasonal Pattern in ACF

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57. 57 Log transform is fix for trend in Var

58. 58 First difference for trend in mean Looks more stationary but is it?

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60. 60 Note seasonal peaks at, 12 24, etc.

61. 61 No unit root, but Correlogram shows Seasonal Dependence on time

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65. 65 Note: sddlnbjpass is normal

66. 66 Closer to white Noise; proposed Model ma(1), ma(12)

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69. 69 Satisfactory Model from Q-stats

70. 70 And the residuals from the model are normal

71. 71 How to use the model to forecast Forecast sddlnbjpass Forecast sddlnbjpass recolor recolor

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