1 takehome one 2010. 2 3 4 5 excaus:price of us $ in canadian $
Post on 20-Dec-2015
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Takehome One2010
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Excaus:Price of US $ in Canadian $
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Is excaus evolutionary?
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Spreadsheet
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Histogram
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Series: EXCAUSSample 1971:01 2010:04Observations 472
Mean 1.233909Median 1.218750Maximum 1.599700Minimum 0.962300Std. Dev. 0.167021Skewness 0.210250Kurtosis 2.173970
Jarque-Bera 16.89653Probability 0.000214
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correlogram
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Unit root test
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Based on evidence Trace Histogram Correlogram Unit root test Conclude it is evolutionary First difference, or take logs and first
difference
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Spreadsheet dexcaus
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Trace dexcaus
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DEXCAUS
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Histogram dexcaus
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-0.05 0.00 0.05 0.10
Series: DEXCAUSSample 1971:02 2010:04Observations 471
Mean -1.40E-05Median 0.000000Maximum 0.126500Minimum -0.074200Std. Dev. 0.017065Skewness 0.418085Kurtosis 10.10121
Jarque-Bera 1003.354Probability 0.000000
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Correlogram dexcaus
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Unit root test dexcaus
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Is dexcaus stationary? Based on the evidence
Trace Histogram Correlogram Unit root test
Yes, so model
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How to model dexusca? # of observations = 471
~4001/2 = 20 1/20 = 0.05 So 95% confidence intervals~ 0.10
Based on pacf Probably significant at lag 1, maybe lag 4 and lag
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Based on acf Probably significant at lag 1, maybe lag 4
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Model conjectures
Ar(1) ar(4) ar(10) Ar(1) ar(4) ma(10) Ma(1) ma(4) Arma(1,1)
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Model dexcaus c ar(1) ar(4), ser= 0.0165
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Correlogram of residuals, BG F=0.38
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Model dexcaus c ar(1) ar(4) ma(11), ser = 0.0164
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Correlogram of residuals, BG F =0.43
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Model dexcaus c ar(1) ma(1), ser=0.0165
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Correlogram of residuals, BG F=0.12
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Model dexcaus c ar(1) ma(4),ser= 0.0164
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Correlogram of residuals, BG F=0.99
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Conclude: two clean models
Dexcaus c ar(1) ma(4) Dexcaus c ar(1) ar(4) ma(11)
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One more test; correlogram of residuals squared for dexusca c ar(1) ma(4)
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ARCH LM test
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Within Sample forecast
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Estimation
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forecast
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EViews forecast plot
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09:05 09:07 09:09 09:11 10:01 10:03
DEXCAUSF ± 2 S.E.
Forecast: DEXCAUSFActual: DEXCAUSSample: 2009:05 2010:04Include observations: 12
Root Mean Squared Error 0.025644Mean Absolute Error 0.019996Mean Abs. Percent Error 100.1694Theil Inequality Coefficient 0.804653 Bias Proportion 0.446219 Variance Proportion 0.514724 Covariance Proportion 0.039057
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spreadsheet
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forecastdex
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Generate upper and lower
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Quick show
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Forecast within sample
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DEXCAUSFORECASTDEX
UPPERLOWER
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Sample 2000.01 2010.04
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Forecast within sample
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DEXCAUSFORECASTDEX
UPPERLOWER
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Estimate ar(1) ma(4) model for full sample
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Procs expand range, change sample
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Forecast out of sample
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EViews out of sample forecast
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DEXCAUSF2 ± 2 S.E.
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Gen upper and lower
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Forecastd2
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Quick show dexcaus forecastd2 upper2 lower2
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DEXCAUSFORECASTD2
UPPER2LOWER2
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Recolor: excausf(t) = excausf(t-1) + dexcausf2; excausf(2010.04) = excaus(201004)
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Forecast 2010.05- 2011.04
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EXCAUS EXCAUSF
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Forecast with confidence Intervalsquick show EXCAUS
EXCAUSFEXCAUSF+2*SEF2EXCAUSF-2*SEF2
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EXCAUSEXCAUSF
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Forecast of Canadian price of the US $: 2010.05-2011.04
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Forecast excaus: 2010.05 -2011.04
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EXCAUSEXCAUSF
EXCAUSF+2*SEF2EXCAUSF-2*SEF2
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Model dexcaus c ar(1) ma(4),ser= 0.0164
Dexcaus(t) = c+ resid(t)
Resid(t) = 0.26*resid(t-1) + wn(t)+0.12*wn(t-4)
Dexcaus(t) = 0.26*dexcaus(t-1) + wn(t) + 0.12*wn(t-4)