Global Warming: Is It True?

Peter Fuller

Odeliah GreeneAmanda Smith

May Zin

What is Global Warming?

Global warming is the increase in the average temperature of the

Earth's near-surface air and oceans since the mid-twentieth

century, and its projected continuation.

Data We’re Using

Our data showed monthly average

temperatures in England

from 1850-2008

Forecasting Goal

Our purpose is to explore the validity of Global Warming with

regards to temperature change in England.

Trace

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TEMP

Histogram

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Series: TEMPSample 1850:01 2008:04Observations 1900

Mean 48.79893Median 48.02000Maximum 66.74000Minimum 28.22000Std. Dev. 8.358940Skewness 0.059055Kurtosis 1.848781

Jarque-Bera 106.0244Probability 0.000000

Correlogram

Unit Root TestADF Test Statistic -14.22821 1% Critical Value* -3.4368

5% Critical Value -2.8635 10% Critical Value -2.5679

*MacKinnon critical values for rejection of hypothesis of a unit root.

Augmented Dickey-Fuller Test EquationDependent Variable: D(TEMP)Method: Least SquaresDate: 06/02/08 Time: 03:02Sample(adjusted): 1850:02 2008:04Included observations: 1899 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. TEMP(-1) -0.191971 0.013492 -14.22821 0.0000C 9.374922 0.668019 14.03391 0.0000R-squared 0.096427 Mean dependent var 0.006635Adjusted R-squared 0.095950 S.D. dependent var 5.168794S.E. of regression 4.914569 Akaike info criterion 6.023338Sum squared resid 45818.22 Schwarz criterion 6.029182Log likelihood -5717.159 F-statistic 202.4420Durbin-Watson stat 1.081641 Prob(F-statistic) 0.000000

How we go about fixing the data

We seasonally differenced the model using a new variable:

SDTemp=Temp-Temp(-12)

Our best model

Our best model is:

SDTemp C AR(1) AR(2) MA(12) AR(19)w/ ARCH (1) and GARCH (0)

Estimation Output

Actual, Fitted Residual Graph

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Residual Actual Fitted

Histogram

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Series: Standardized ResidualsSample 1852:08 2008:04Observations 1869

Mean -0.013779Median 0.005741Maximum 3.380337Minimum -4.559005Std. Dev. 1.000174Skewness -0.313048Kurtosis 3.806190

Jarque-Bera 81.14096Probability 0.000000

Correlogram

ARCH LM TestARCH Test:F-statistic 7.80E-05 Probability 0.992956Obs*R-squared 7.81E-05 Probability 0.992951

Test Equation:Dependent Variable: STD_RESID^2Method: Least SquaresDate: 06/02/08 Time: 03:41Sample(adjusted): 1852:09 2008:04Included observations: 1868 after adjusting endpoints

Variable Coefficient Std. Error t-Statistic Prob. C 1.000582 0.045274 22.10045 0.0000STD_RESID^2(-1) -0.0002040.023149 -0.0088300.9930R-squared 0.000000 Mean dependent var 1.000378Adjusted R-squared -0.000536 S.D. dependent var 1.681044S.E. of regression 1.681494 Akaike info criterion 3.878313Sum squared resid 5275.970 Schwarz criterion 3.884236Log likelihood-3620.344 F-statistic 7.80E-05Durbin-Watson stat 2.000032 Prob(F-statistic) 0.992956

Within Sample Forecast

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SDT EMP SDT EMPF

Recoloring our Within Sample Forecast

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RC T EMPORG

Forecasting Ahead

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SDT EMPF SDT EMP

Recoloring our Forecast of the Future

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T EMP T EMPORG

Seasonal DummiesDependent Variable: TEMPMethod: Least SquaresDate: 06/01/08 Time: 16:07Sample: 1850:01 2008:12Included observations: 1908

Variable Coefficient Std. Error t-Statistic Prob.

TIME -0.006932 0.000305 -22.71867 0TIME*FALL 0.008374 0.000326 25.72431 0TIME*SPRING 0.005936 0.000326 18.19238 0TIME*SUMMER 0.015827 0.000326 48.56036 0C 48.23872 0.253971 189.9378 0

R-squared 0.561056 Mean dependent var 48.8192Adjusted R-squared 0.560133 S.D. dependent var 8.360092S.E. of regression 5.54462 Akaike info criterion 6.26615Sum squared resid 58503.56 Schwarz criterion 6.280704Log likelihood -5972.907 F-statistic 608.1003Durbin-Watson stat 1.04374 Prob(F-statistic) 0

Conclusion

We must look to other data such as rainfall, sea levels, ocean

temperatures, C02 data to say that global warming does exist.