matt mullens gulsah gunenc alex keyfes gaoyuan tian andrew booth

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Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

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Page 1: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Matt MullensGulsah Gunenc

Alex KeyfesGaoyuan TianAndrew Booth

Page 2: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Motivation Background Data sources Models Model Validations Results Conclusions Questions

Page 3: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

We wanted to first off see what a forecast of the United States GDP will be for the rest of the year Thought it was relevant given current

economic state We also wanted to compare the GDP of

two dissimilar countries Compared USA and China

Page 4: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

The US is considered to be a long established industrialized country

China is considered to be an emerging or developing nation

We figured that the US and China models would be different.

Page 5: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

USA data gathered from: http://www.bea.gov/national/index.htm#gdp

Page 6: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Chinese data gathered from: http://www.stats.gov.cn/eNgliSH/statisticaldata/Quarterlydata/

Page 7: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Quarterly data from 1947 first quarter -2009 first quarter

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GDP

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Series: GDPSample 1947:1 2009:1Observations 249

Mean 4063.241Median 2150.000Maximum 14412.80Minimum 237.2000Std. Dev. 4155.574Skewness 0.974405Kurtosis 2.724373

Jarque-Bera 40.19100Probability 0.000000

Page 8: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Pre-Whitening Process Needed to be logged and first differenced

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LNGDP

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DLNGDP

Page 9: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation As seen from the correlogram more work is needed

Page 10: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Final ARMA model

Dependent Variable: DLNGDPMethod: Least SquaresDate: 05/29/09 Time: 15:28Sample(adjusted): 1947:3 2009:1Included observations: 247 after adjusting endpointsConvergence achieved after 10 iterationsBackcast: 1942:3 1947:2

Variable Coefficient Std. Error t-Statistic Prob. C 0.015809 0.001984 7.969583 0.0000

AR(1) 0.383838 0.064384 5.961659 0.0000MA(2) 0.171806 0.058702 2.926745 0.0038MA(5) -0.162338 0.056908 -2.852644 0.0047MA(9) 0.047766 0.055652 0.858292 0.3916MA(10) 0.151226 0.054837 2.757725 0.0063MA(11) 0.124731 0.057034 2.186981 0.0297MA(16) 0.213311 0.059270 3.598973 0.0004MA(18) 0.208413 0.058542 3.560054 0.0004MA(20) 0.343491 0.056335 6.097299 0.0000

R-squared 0.375007 Mean dependent var 0.016476Adjusted R-squared 0.351273 S.D. dependent var 0.011296S.E. of regression 0.009098 Akaike info criterion -6.521832Sum squared resid 0.019618 Schwarz criterion -6.379752Log likelihood 815.4463 F-statistic 15.80045Durbin-Watson stat 1.958212 Prob(F-statistic) 0.000000Inverted AR Roots .38Inverted MA Roots .97 -.18i .97+.18i .83+.44i .83 -.44i

.60+.71i .60 -.71i .43+.82i .43 -.82i .15+.96i .15 -.96i -.13+.92i -.13 -.92i -.43+.82i -.43 -.82i -.63+.69i -.63 -.69i -.84 -.48i -.84+.48i -.95 -.17i -.95+.17i

Page 11: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation

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Series: ResidualsSample 1947:3 2009:1Observations 247

Mean 1.21E-06Median -0.000126Maximum 0.029393Minimum -0.026420Std. Dev. 0.008930Skewness 0.155128Kurtosis 3.956949

Jarque-Bera 10.41526Probability 0.005475

Page 12: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

More Model Validation Actual, Fitted, Residuals

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Residual Actual Fitted

Page 13: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Forecast for the rest of 2009

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DLNGDPF ± 2 S.E.

Page 14: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Recoloring of GDP Recoloring: Lngdpf=lngdp (2009:1 2009:1) lngdpf=lngdpf(-1)+dlngdpf (2009:2 2009:4) gdpf=exp(lngdpf) (2009:2 2009:4)

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Page 15: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Possible Forecast Bias Long time period upward trend

According to our model it will increase, only time will tell

Page 16: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Examine just the past few years in an attempt to eliminate upward time trend

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GDP_US

Page 17: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Data had linear trend Needed first difference

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DGDP_US

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GDP_US

Page 18: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation Looking at the

correlogram more work was needed

Try ARMA model

Page 19: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Final ARMA Model

Page 20: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation A much better looking model High P-values for

Q-stats

Page 21: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Forecast of the rest of 2009

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DGDP_USF ± 2 S.E.

Page 22: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Recoloring of the model

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GDP_US GDP_USF

Page 23: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

A better estimation as the long time upward trend is less of a bias Due to economic changes over the past decades a data set that includes only

more recent data is more accurate for forecasting More relevant to current economy Reflects current issues without previous bias

Page 24: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Looking at the past few years of China’s GDP Highly seasonal due to large economic dependence

on seasonal agriculture of 900 million farmers

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GDPCH

Page 25: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Pre-Whitening Needed both log and seasonal differencing Also used from 1998-2008 and first differenced

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DSDLNGDPCH

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LNGDPCH

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Page 26: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation Correlogram Needs some work Try ARMA model

Page 27: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Final ARMA Model

Page 28: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Model Validation A much better looking model High P-values for

Q-stats Appears valid

Page 29: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Rest of 2009

Forecast (China)

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DSDLNGDPCHF ± 2 S.E.

Page 30: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Forecast (China)

Recoloring Model

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Page 31: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Results

China continues with an increasing seasonal trend This can be accounted for by the large

agriculture economy in China

Page 32: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Conclusions

Not surprising that USA and China did not have similar models USA historic leading economy China is a recent world economy

Long term upward trends indicate USA economy will improve Shorter term model is less generous

Page 33: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth

Fin

Any Questions? anyone

Any Comments? anyone