Week 1

Question 1

What is the idea of a conditional mean? What is the conditional mean of a basic linear regression?

Answer 1

Question 2

What is a white noise sequence?

Answer 2

Question 3

What is an AR(1) model?

Give the definition

Answer 3

Question 4

What is the conditional mean and conditional distribution of an AR(1) model?

Answer 4

Question 5

1. When is a time series weakly stationary?
2. When is an AR(1) model weakly stationary?
3. What does this mean?

Answer 5

Question 6

What is a random walk?

Answer 6

Question 7

What needs to be shown to claim that stock prices behave like random walks?

Answer 7

Question 8

1. What are log returns?
2. What are some of their appealing properties?

Answer 8

Question 9

Why can we not predict (log) returns?

Answer 9

Question 10

1. What do we try to predict in Financial Econometrics?
2. How do we predict it?

Answer 10

Volalility

Question 11

What is the definition of an ARCH(1) model?

Answer 11

Question 12

What is the observation equation and the updating equation of a ARCH(1) model?

Answer 12

Question 13

What is the

of an ARCH(1) model (though should hold for all similar models)

Answer 13

Question 14

Answer 14

Question 15

Show the derivation of the conditional mean and conditional variance of an ARCH(1) model.

Answer 15

Question 16

How can the conditional distribution of an ARCH(1) model be used?

Answer 16

Question 17

Name the 6 properties from a model of which the log-returns are generated by an ARCH(1) model.

Answer 17

Question 18

Show that the returns from an ARCH(1) model have unconditional mean 0.

Answer 18

Question 19

Show that the returns from an ARCH(1) model are uncorrelated.

Answer 19

Question 20

Show how an ARCH(1) model can be refactored in an AR(1) model.

Answer 20

Question 21

Derive the unconditional variance of an ARCH(1) model.

Answer 21

Question 22

1. What is the definition of kurtosis?
2. When does a distribution have “fat tails”?

Answer 22

Question 23

Show that an ARCH(1) model has “fat tails”.

Answer 23

Question 24

What is the definition of an ARCH(q) model?

Answer 24

Question 25

How can an ARCH(q) model be rewritten into an AR(q) model?

Answer 25

Question 26

What is the unconditional variance of an ARCH(q) model?

Answer 26

Question 27

Why do we (usually) use GARCH models over ARCH models?

Answer 27

Question 28

1. What is the definition of a GARCH(1,1) model?
2. What does GARCH stand for?

Answer 28

Question 29

What are the properties of a GARCH(1,1) model?

Name 5

Answer 29

Question 30

What is the ARMA represensitation of a GARCH model?

Answer 30

Question 31

What is the unconditional variance of a GARCH(1,1) model?

Answer 31

Question 32

Why is data generated by a GARCH(1,1) model stationary?

Answer 32

Question 33

How can a GARCH(1,1) model be rewriten in an ARCH(∞) model?

Answer 33

Question 34

What is the definition of a GARCH(p,q) model?

Answer 34

Question 35

What are the stochastic properties of a GARCH(p,q) model?

There are 5

Answer 35

Question 36

What is the ARMA reprensitation of a GARCH(p,q) model?

Answer 36

Question 37

When are GARCH(p,q) results stationary?

Answer 37