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Power NinePower Nine

Econ 240CEcon 240C

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OutlineOutline• Lab Three ExercisesLab Three Exercises

– Fit a linear trend to retail and food salesFit a linear trend to retail and food sales– Add a quadratic termAdd a quadratic term– Use both models to forecast 1 period Use both models to forecast 1 period

aheadahead

• Lab Five PreviewLab Five Preview– Airline passengersAirline passengers

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RSAFSNA

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Series: RSAFSNASample 1992:01 2008:02Observations 194

Mean 265451.2Median 262622.5Maximum 433319.0Minimum 146737.0Std. Dev. 66378.42Skewness 0.248616Kurtosis 2.198377

Jarque-Bera 7.192855Probability 0.027422

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Lab Three ExercisesLab Three ExercisesProcessProcess

• IdentificationIdentification– SpreadsheetSpreadsheet– TraceTrace– HistogramHistogram– CorrelogramCorrelogram– Unit root testUnit root test

• EstimationEstimation• ValidationValidation

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Series: ResidualsSample 1992:01 2008:02Observations 194

Mean 1.88E-11Median 537.6320Maximum 63871.33Minimum -47196.84Std. Dev. 19962.12Skewness 0.557862Kurtosis 4.202766

Jarque-Bera 21.75617Probability 0.000019

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One Period Ahead ForecastOne Period Ahead Forecast

• EE2008.02 2008.02 rsafnsa (2008.03) = 156,647.8 rsafnsa (2008.03) = 156,647.8 + 1127.496*194+ 1127.496*194

• EE2008.02 2008.02 rsafnsa (2008.03) = Ersafnsa (2008.03) = E2008.02 2008.02

rsafnsaf (2008.02) + 1127.496rsafnsaf (2008.02) + 1127.496

• EE2008.02 2008.02 rsafnsa (2008.03) = 374255 + rsafnsa (2008.03) = 374255 + 1127.496 = 375380.5 +/- 2*ser1127.496 = 375380.5 +/- 2*ser

• Ser =20014Ser =20014

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RSAFSNAF ± 2 S.E.

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Lab Three ExercisesLab Three ExercisesProcessProcess

• IdentificationIdentification– Spreadsheet: Spreadsheet: check variable valuescheck variable values– Trace: Trace: trended series and seasonaltrended series and seasonal– Histogram: Histogram: – Correlogram: Correlogram: similar to a “random walk”similar to a “random walk”– Unit root test: Unit root test: evolutionaryevolutionary

• EstimationEstimation• ValidationValidation

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ProcessProcess

• Validating the modelValidating the model– Actual, fitted, residualActual, fitted, residual– Correlogram of the residualsCorrelogram of the residuals– Histogram of the residualsHistogram of the residuals

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Add the quadratic termAdd the quadratic term

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Seasonal dummiesSeasonal dummies

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Series: ResidualsSample 1992:01 2008:02Observations 194

Mean 4.06E-11Median -659.2587Maximum 25911.03Minimum -25469.32Std. Dev. 8375.957Skewness 0.110874Kurtosis 3.373720

Jarque-Bera 1.526452Probability 0.466160

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Now we know another way to Now we know another way to forecastforecast• Seasonal difference retailSeasonal difference retail

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SDRSAFSNA

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Series: SDRSAFSNASample 1993:01 2008:02Observations 182

Mean 13892.13Median 13111.50Maximum 31395.00Minimum -7022.000Std. Dev. 6624.846Skewness 0.085951Kurtosis 3.433944

Jarque-Bera 1.652088Probability 0.437778

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DSDRSAFSNA

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Series: DSDRSAFSNASample 1993:02 2008:02Observations 181

Mean 84.32044Median -357.0000Maximum 28078.00Minimum -18089.00Std. Dev. 6951.430Skewness 0.210084Kurtosis 3.777211

Jarque-Bera 5.887011Probability 0.052681

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Preview of Lab FivePreview of Lab Five• A Box-Jenkins famous time series: A Box-Jenkins famous time series:

airline passengersairline passengers– Trend in meanTrend in mean– Trend in varianceTrend in variance– seasonalityseasonality

• PrewhiteningPrewhitening– Log transformLog transform– First differenceFirst difference– Seasonal differenceSeasonal difference

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Note trend fromSpike in pacf atLag one; seasonal Pattern in ACF

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Log transform is fix for trend in Var

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First difference for trend in meanLooks more stationary but is it?

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Note seasonal peaks at, 1224, etc.

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No unit root, butCorrelogram showsSeasonal Dependence ontime

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Note: sddlnbjpass is normal

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Closer to whiteNoise; proposedModel ma(1), ma(12)

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SatisfactoryModel from Q-stats

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And the residuals from the model are normal

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How to use the model to How to use the model to forecastforecast• Forecast sddlnbjpassForecast sddlnbjpass

• recolorrecolor

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