Conditional heteroskedasticity is
residual variance related to level of X’s
Serial correlation is
correlated residuals
Multicollinearity is
two or more X’s are correlated
Effect of conditional heteroskedasticity
Type I errors
high t stat, caused by low std errors
Effect of serial correlation
Type I errors
positive correlation
Effect of multicollinearity
type II errors
Detection of conditional heteroskedasticity
Breusch-Pagan Test
Chi-Square Test
Detection of serial correlation
Durbin-Watson test
Detection of multicollinearity
Conflicting t and F stats
Correlations among ind variables if k=2
Correcting conditional skedasticity
white-correct std errors
Correction serial correlation
Hansen method
Correcting multicollinearity
Drop a correlated variable
Functional Form Misspecifications
- important variables omitted
- variables not transformed properly
- data pooled improperly
Time-Series Misspecification
- X is lagged Y with serial correlation present
- Forecasting the past
- Measurement error
Probit model
estimates probability of default given values of X based on normal dist
Logit Models
estimates probability of default given values of X based on logistic dist (computationally easier than normal dist).
Logistic dist NOT logarthimic
Discriminant models
produces a score or rank used to classify into categories
ex- bankrupt, not bankrupt
Economic Significance
not significant just because of statistical significance
-commissions, taxes, risk, etc.
If a time series is mean reverting
the value of the dependent variable tends to fall when above its mean; and rise when below its mean
Mean Reverting Level Formula
b0/ (1 - b1)
Forecasting Accuracy of ARCH measured by
root of mean squared error.
Use model with lowest RMSE based on out-of-sample forecasting
Without a mean reverting level, the time series is
non-stationary
Dickey-Fuller Tests for
unit root
Dickey Fuller Test method
subtract x(t-1) from both sides; first differencing where g1 = (b1 - 1)
If there is a unit root in AR(1) model , g1 will be 0.
