Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth.
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Transcript of Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth.
![Page 1: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d7e5503460f94a610aa/html5/thumbnails/1.jpg)
Matt MullensGulsah Gunenc
Alex KeyfesGaoyuan TianAndrew Booth
![Page 2: Matt Mullens Gulsah Gunenc Alex Keyfes Gaoyuan Tian Andrew Booth.](https://reader038.fdocuments.in/reader038/viewer/2022103022/56649d7e5503460f94a610aa/html5/thumbnails/2.jpg)
Motivation Background Data sources Models Model Validations Results Conclusions Questions
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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
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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.
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USA data gathered from: http://www.bea.gov/national/index.htm#gdp
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Chinese data gathered from: http://www.stats.gov.cn/eNgliSH/statisticaldata/Quarterlydata/
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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
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Pre-Whitening Process Needed to be logged and first differenced
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LNGDP
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DLNGDP
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Model Validation As seen from the correlogram more work is needed
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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
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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
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More Model Validation Actual, Fitted, Residuals
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Residual Actual Fitted
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Forecast for the rest of 2009
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2009:2 2009:3 2009:4
DLNGDPF ± 2 S.E.
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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
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Possible Forecast Bias Long time period upward trend
According to our model it will increase, only time will tell
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Examine just the past few years in an attempt to eliminate upward time trend
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GDP_US
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Data had linear trend Needed first difference
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DGDP_US
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GDP_US
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Model Validation Looking at the
correlogram more work was needed
Try ARMA model
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Final ARMA Model
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Model Validation A much better looking model High P-values for
Q-stats
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Forecast of the rest of 2009
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DGDP_USF ± 2 S.E.
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Recoloring of the model
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GDP_US GDP_USF
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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
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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
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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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SDLNGDPCH
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Model Validation Correlogram Needs some work Try ARMA model
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Final ARMA Model
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Model Validation A much better looking model High P-values for
Q-stats Appears valid
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Rest of 2009
Forecast (China)
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DSDLNGDPCHF ± 2 S.E.
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Forecast (China)
Recoloring Model
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GDPCH GDPCHF
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Results
China continues with an increasing seasonal trend This can be accounted for by the large
agriculture economy in China
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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
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Fin
Any Questions? anyone
Any Comments? anyone