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)