Lectures for Part II: Time Series Models in Finance

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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 18
Log returns for IBM 1/3/62-11/3/00 (blue=1961-1981) 100*log(returns) -20 -10 0 10 MaPhySto Workshop 9/04 1962 1967 1972 1977 1982 1987 1992 1997 time 19
Page 1 and 2: Nonlinear Time Series Modeling Part
Page 3 and 4: 1. Classification of White Noise As
Page 5 and 6: 2. Examples (1) All-pass processs.
Page 7 and 8: 2. Examples (cont) MaPhySto Worksho
Page 13 and 14: 2. Examples (cont) Likelihood funct
Page 15 and 16: 2. Examples (cont) The sample ACF.
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Page 21 and 22: ACF of squares for IBM (a) 1961-198
Page 23 and 24: Hill’s estimator of tail index Th
Page 25 and 26: Hill’s plot of tail index for IBM
Page 27 and 28: 4. ARCH and GARCH Models (cont) MaP
Page 37 and 38: 4. ARCH and GARCH Models (cont) i M
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Page 41 and 42: 4. ARCH and GARCH Models (cont) SS
Page 49 and 50: Parameter Estimation for Finite-Var
Page 67 and 68: 5. Forecasting with GARCH (cont) Ma
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7. Stochastic Volatility Models MaP
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7. Stochastic Volatility Models (co
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MaPhySto Workshop 9/04 81
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8. Regular variation and applicatio
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8.2 Regular variation — multivari
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2. If X 1 = X 2 > 0, then X= (X 1 ,
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8.3 Applications of multivariate re
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8.4 Applications of theorem 1. Kest
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8.4 Examples (cont) Example of ARCH
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8.6 Extremes for GARCH and SV proce
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8.6 Extremes for GARCH and SV proce
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8.7 Summary of results for ACF of G
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Sample ACF for Squares of GARCH (10
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Example: Amazon returns May 16, 199
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Lectures for Part II: Time Series Models in Finance

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