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GARCH. Generalized Autoregressive Conditional Heteroskedastic Models. UNR * STAT 758 * Spring2010. Standard and Poor index (S&P500). Standard and Poor index (S&P500) : Returns (first difference). Standard and Poor index (S&P500): Log transform. - PowerPoint PPT Presentation
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1990 1995 2000 2005
200
600
1000
1400
Time
SP
500
Standard and Poor index (S&P500)
Standard and Poor index (S&P500) : Returns (first difference)
1990 1995 2000 2005
-50
050
Time
Ret
urns
Standard and Poor index (S&P500): Log transform
1990 1995 2000 2005
2.4
2.6
2.8
3.0
3.2
Time
Loga
rithm
of S
&P
500
Standard and Poor index (S&P500): Log returns
1990 1995 2000 2005
-0.0
3-0
.01
0.01
0.02
Time
Log-
Ret
urns
Autocorrelation function: S&P500
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
F
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
FAutocorrelation function: (log10(S&P500))
0 20 40 60 80 100
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
F
Autocorrelation function: [(log10(S&P500))]2
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
FARIMA(2,1,1) for log10 (S&P500): ACF of squared residuals
ARCH(1) for ARIMA residuals: ACF of squared residuals
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
F
ARCH(9) for ARIMA residuals: ACF of squared residuals
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
F
GARCH(1,1) for ARIMA residuals: ACF of squared residuals
0 5 10 15 20 25 30 35
0.0
0.2
0.4
0.6
0.8
1.0
Lag
AC
F
