matt mullens gulsah gunenc alex keyfes gaoyuan tian andrew booth
Post on 22-Dec-2015
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TRANSCRIPT
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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Residual Actual Fitted
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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DGDP_US
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GDP_US
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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DGDP_USF ± 2 S.E.
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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DSDLNGDPCH
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LNGDPCH
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SDLNGDPCH
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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DSDLNGDPCHF ± 2 S.E.
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