Frontmatter Page viii Monday, March 8, 2004 10:06 AM
viii ContentsCHAPTER 12
Financial Econometrics: Model Selection, Estimation, and Testing 315
Model Selection 315
Learning and Model Complexity 317
Maximum Likelihood Estimate 319
Linear Models of Financial Time Series 324
Random Walk Models 324
Correlation 327
Random Matrices 329
Multifactor Models 332
CAPM 334
Asset Pricing Theory (APT) Models 335
PCA and Factor Models 335
Vector Autoregressive Models 338
Cointegration 339
State-Space Modeling and Cointegration 342
Empirical Evidence of Cointegration in Equity Prices 343
Nonstationary Models of Financial Time Series 345
The ARCH/GARCH Family of Models 346
Markov Switching Models 347
Summary 349
CHAPTER 13
Fat Tails, Scaling, and Stable Laws 351
Scaling, Stable Laws, and Fat Tails 352
Fat Tails 352
The Class L of Fat-Tailed Distributions 353
The Law of Large Numbers and the Central Limit Theorem 358
Stable Distributions 360
Extreme Value Theory for IID Processes 362
Maxima 362
Max-Stable Distributions 368
Generalized Extreme Value Distributions 368
Order Statistics 369
Point Process of Exceedances or Peaks over Threshold 371
Estimation 373
Eliminating the Assumption of IID Sequences 378
Heavy-Tailed ARMA Processes 381
ARCH/GARCH Processes 382
Subordinated Processes 383
Markov Switching Models 384
Estimation 384
Scaling and Self-Similarity 385
Evidence of Fat Tails in Financial Variables 388
On the Applicability of Extreme Value Theory in Finance 391
Summary 392