What is the idea of a conditional mean? What is the conditional mean of a basic linear regression?
What is a white noise sequence?
What is an AR(1) model?
Give the definition
What is the conditional mean and conditional distribution of an AR(1) model?
- When is a time series weakly stationary?
- When is an AR(1) model weakly stationary?
- What does this mean?
What is a random walk?
What needs to be shown to claim that stock prices behave like random walks?
- What are log returns?
- What are some of their appealing properties?
Why can we not predict (log) returns?
- What do we try to predict in Financial Econometrics?
- How do we predict it?
Volalility
What is the definition of an ARCH(1) model?
What is the observation equation and the updating equation of a ARCH(1) model?
What is the
of an ARCH(1) model (though should hold for all similar models)
Show the derivation of the conditional mean and conditional variance of an ARCH(1) model.
How can the conditional distribution of an ARCH(1) model be used?
Name the 6 properties from a model of which the log-returns are generated by an ARCH(1) model.
Show that the returns from an ARCH(1) model have unconditional mean 0.
Show that the returns from an ARCH(1) model are uncorrelated.
Show how an ARCH(1) model can be refactored in an AR(1) model.
Derive the unconditional variance of an ARCH(1) model.
- What is the definition of kurtosis?
- When does a distribution have “fat tails”?
Show that an ARCH(1) model has “fat tails”.
What is the definition of an ARCH(q) model?
