1 Power Nine Econ 240C. 2 Outline Lab Three Exercises Lab Three Exercises –Fit a linear trend to retail and food sales –Add a quadratic term –Use both.

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Presentation transcript:

1 Power Nine Econ 240C

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

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15 Correlogram of residuals from Linear trend model

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17 One Period Ahead Forecast E retailnfoodales ( ) = 159, *171 E retailnfoodales ( ) = 159, *171 E retailnfoodales ( ) = E retailnfoodales ( ) E retailnfoodales ( ) = E retailnfoodales ( ) E retailnfoodales ( ) = = /- 2*ser E retailnfoodales ( ) = = /- 2*ser Ser =18932 Ser =18932

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21 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

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

23 Add the quadratic term

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33 Now we know another way to forecast Seasonal difference retail Seasonal difference retail

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46 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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50 Note trend from Spike in pacf at Lag one; seasonal Pattern in ACF

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53 Log transform is fix for trend in Var

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

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56 Note seasonal peaks at, 12 24, etc.

57 No unit root, but Correlogram shows Seasonal Dependence on time

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61 Note: sddlnbjpass is normal

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

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65 Satisfactory Model from Q-stats

66 And the residuals from the model are normal

67 How to use the model to forecast Forecast sddlnbjpass Forecast sddlnbjpass recolor recolor

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