12-FinEcon-Model Sel Page 349 Wednesday, February 4, 2004 12:59 PM
Financial Econometrics: Model Selection, Estimation, and Testing 349SUMMARY
■ Model selection cannot be completely automated because the search
space is too large.
■ Econometrics constrains the search for an optimal model within model
classes.
■ If a family of models can fit data with arbitrary accuracy, then criteria
for choosing the optimal model complexity are needed.
■ Overfitting occurs when a model is too complex and thus fits unpre-
dictable noise.
■ Akaike Information Criteria and Bayesian Information Criteria are
complexity selection criteria based on information theory.
■ The Vapnik-Chervonenkis theory of learning has given a rigorous theo-
retical basis to the principles of statistical learning.
■ An estimator is a random variable function of the sample data that
approximates a given parameter of a distribution.
■ The Cramer-Rao bound prescribes lower bounds for the variance of
estimators.
■ Maximum Likelihood Estimate (MLE) chooses those parameters that
maximize likelihood on samples.
■ For unconstrained regressions, MLE coincides with Ordinary Least
Square estimation.
■ MLE estimators are efficient estimators, that is, they attain the Cramer-
Rao variance lower bound.
■ The simplest asset price model is the random walk.
■ A multivariate correlated random walk is a model for the joint price
process of a set of asset prices.
■ A large set of price processes exhibits nearly random variance-covari-
ance matrix of the return process.
■ Factor models reduce the dimensionality of the variance-covariance
matrix of the return process.
■ Principal component analysis identifies a generally small number of sta-
ble factors.
■ Vector Autoregressive (VAR) models capture the dynamics of time
series.
■ It is impossible to describe large sets of asset price processes with unre-
stricted VAR models because the number of parameters is too high and
therefore not stable.
■ Cointegration captures common stable trends thus implementing a
dimensionality reduction.
■ Cointegrated time series can be represented with a constrained Error
Correction VAR model.
■ State-space models are equivalent to Error Correction models.