arch-garch ppifgs. producer price index finished goods 1982=100
Post on 15-Jan-2016
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Arch-GarchPPIFGS
Producer Price Index Finished Goods
1982=100
Transform to the monthly inflation rate
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
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
How to Model?Try arma(1,1)
Stationary monthly inflation rate?
-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
Correlogram of residuals
Correlogram of residuals squared
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
Modeling the variance
Is model satisfactory?
Corrrelogram of square of standardized residuals
Ordinary residual: e(t)Equation Window: Procs, make residual
e(t) =wn(t)*h(t)1/2
ordinary residual = standardized residual*conditional standard deviation
Residuals: ordinary & Standard
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
Equation window: Procs Make Garch Variance Series
e(t) =wn(t)*h(t)1/2
-4
-2
0
2
4
6
-4 -2 0 2 4 6
RESIDSTD
ST
DR
ES
ID
Residstd & stdresid
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)