Lectures for Part II: Time Series Models in Finance

2. If X 1 = X 2 > 0, then X= (X 1 , X 2 ) is multivariate regularly varying
with index α and spectral distribution
P( θ = (1/√2, 1/√2) ) = 1.
3. AR(1): X t = .9 X t-1 + Z t , {Z t }~IID symmetric stable (1.8)
{
±(1,.9)/sqrt(1.81), W.P. .9898
Distr of θ:
±(0,1), W.P. .0102
Figure: plot of (X t ,
X t+1 ) for realization
of 10,000.
x_{t+1}
-10 0 10 20 30
MaPhySto Workshop 9/04
-10 0 10 20 30
x_t
87