Lectures for Part II: Time Series Models in Finance
Lectures for Part II: Time Series Models in Finance
Lectures for Part II: Time Series Models in Finance
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8.7 Summary of results <strong>for</strong> ACF of GARCH(p,q) and SV models<br />
GARCH(p,q)<br />
α∈(0,2):<br />
α∈(2,4):<br />
α∈(4,∞):<br />
d<br />
( ρˆ<br />
X<br />
( h))<br />
h= , K , m<br />
⎯⎯→(<br />
Vh<br />
/ V0<br />
)<br />
h=<br />
1, K,<br />
1 m<br />
1−2/<br />
α<br />
d −1<br />
( n ρ ( h)<br />
) ⎯⎯→ γ (0)( V ) .<br />
ˆ<br />
X h=<br />
1, K , m<br />
X h h=<br />
1, K,<br />
m<br />
1/2<br />
d −1<br />
( n ρ ( h)<br />
) ⎯⎯→<br />
(0)( G ) .<br />
ˆ<br />
X<br />
γ<br />
h= 1, K , m<br />
X h h=<br />
1, K,<br />
m<br />
,<br />
Remark: Similar results hold <strong>for</strong> the sample ACF based on |X t | and<br />
X t2 .<br />
MaPhySto Workshop 9/04<br />
98
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