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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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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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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

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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

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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

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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)