Lectures for Part II: Time Series Models in Finance

3. “Stylized Facts” of Financial Returns
Define X t = 100*(ln (P t ) - ln (P t-1 )) (log returns)
• heavy tailed
P(|X 1 | > x) ~ C x -α , 0 < α < 4.
• uncorrelated
ˆ
ρ X
( h)
near 0 for all lags h > 0 (MGD sequence?)
• |X t | and X t2 have slowly decaying autocorrelations
ρˆ ( ) and ˆ
| X |
h ρ 2 ( h)
• process exhibits ‘stochastic volatility’.
X
converge to 0 slowly as h increases.
MaPhySto Workshop 9/04
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