Week 3 Flashcards
4 Properties of OLS for Linear model and show
Wether to use Yule Walker equations for AR(p), MA(q), ARMA(p,q)
YW estimators are optimal for AR(p) as they coincide w OLS (which are optimal)
YW estimators are suboptimal for MA(q) and ARMA(p,q)
When to use conditional least squares
To estimate parameters of a time series model that doesn’t start at an infinite point in the past
Conditional least squares for MA(1)
Conditional least squares for ARMA(2,1)
Difference between OLS and BLP
OLS is used to estimate parameters by minimising sum of squares of residuals
BLP is used to predict next values for time series
How and when to use BLP
Properties of BLP
Key difference of MLE to OLS and when to use MLS
MLE requires dist of f(Xt | Ft-1)
Useful for ARMA models (as they’re of state space form)
Useful for non linear models (GARCH, EGARCH)
Method of moments ?
Using estimators, equate theoretical moments to sample moments and solve for parameters of model
AIC
You want to minimise AIC
Where L(Ψ^) is the likelihood function of param vector
θ^ ~ Ψ^ here
p* is the total number of parameters (for ARMA(p,q) p* = p+q)
General results for kurtosis that seems to come up a lot
Crucially the E[ε^4]/Ε[ε^2]^2 factor is = 3
