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Arch-GarchPPIFGS
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Producer Price Index Finished Goods
1982=100
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Transform to the monthly inflation rate
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Noisy episodic inflation rate
-0.04
-0.02
0.00
0.02
0.04
50 55 60 65 70 75 80 85 90 95 00 05 10
DLNPPIFGS
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Kurtotic monthly inflation rate
0
50
100
150
200
250
-0.0250 -0.0125 0.0000 0.0125 0.0250
Series: DLNPPIFGSSample 1947:05 2010:04Observations 756
Mean 0.002558Median 0.002558Maximum 0.034635Minimum -0.028606Std. Dev. 0.005766Skewness 0.285270Kurtosis 7.214761
Jarque-Bera 569.8264Probability 0.000000
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How to Model?Try arma(1,1)
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Stationary monthly inflation rate?
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-0.04
-0.02
0.00
0.02
0.04
-0.04
-0.02
0.00
0.02
0.04
50 55 60 65 70 75 80 85 90 95 00 05 10
Residual Actual Fitted
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Correlogram of residuals
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Correlogram of residuals squared
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Residuals squared trace
0.0000
0.0002
0.0004
0.0006
0.0008
0.0010
50 55 60 65 70 75 80 85 90 95 00 05 10
RESSQ
-0.04
-0.02
0.00
0.02
0.04
50 55 60 65 70 75 80 85 90 95 00 05 10
DLNPPIFGS
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Modeling the variance
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Is model satisfactory?
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Corrrelogram of square of standardized residuals
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Ordinary residual: e(t)Equation Window: Procs, make residual
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e(t) =wn(t)*h(t)1/2
ordinary residual = standardized residual*conditional standard deviation
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Residuals: ordinary & Standard
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h(t)1/2 : conditional standard deviation
0.000
0.005
0.010
0.015
0.020
50 55 60 65 70 75 80 85 90 95 00 05 10
conditional standard deviation
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Equation window: Procs Make Garch Variance Series
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e(t) =wn(t)*h(t)1/2
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-4
-2
0
2
4
6
-4 -2 0 2 4 6
RESIDSTD
ST
DR
ES
ID
Residstd & stdresid
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Estimated Conditional Variance h(t) = α0 + α1 [e(t-1)]2 + β1 h(t-1) h(t) = 1.56X10-6 + 0.219 [e(t-1)]2 + 0.734 h(t-
1)