Matt MullensGulsah Gunenc

Alex KeyfesGaoyuan TianAndrew Booth

Motivation Background Data sources Models Model Validations Results Conclusions Questions

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

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.

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

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

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

Pre-Whitening Process Needed to be logged and first differenced

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LNGDP

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DLNGDP

Model Validation As seen from the correlogram more work is needed

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

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

More Model Validation Actual, Fitted, Residuals

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Forecast for the rest of 2009

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DLNGDPF ± 2 S.E.

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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GDPF GDP

Possible Forecast Bias Long time period upward trend

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

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

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GDP_US

Data had linear trend Needed first difference

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Model Validation Looking at the

correlogram more work was needed

Try ARMA model

Final ARMA Model

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

Q-stats

Forecast of the rest of 2009

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Recoloring of the model

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GDP_US GDP_USF

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

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

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

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Model Validation Correlogram Needs some work Try ARMA model

Final ARMA Model

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

Q-stats Appears valid

Rest of 2009

Forecast (China)

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Forecast (China)

Recoloring Model

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Results

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

agriculture economy in China

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

Fin

Any Questions? anyone

Any Comments? anyone