Week 4 & 5

Question 1

What is the idea of VECM models?

Answer 1

Question 2

What are the mean, variance, autocovariance and autocorrelations of a AR(1) random walk process?

Answer 2

Question 3

When is a process integrated with an order of 1? How can it be made stable? How can this be generalized?

Answer 3

Question 4

When is differencing components in a time series process d times (i.e., where d is the number roots in the unit circle), not ideal?

Answer 4

Question 5

What is the idea of a cointegrated process?

Answer 5

Question 6

What is the idea of a cointegrated process?

Answer 6

Question 7

Describe a general (simple) ECM model.

Answer 7

Question 8

How to write a VECM model as a VAR model? What does this mean?

Answer 8

Question 9

How to rewrite a (unstable) VAR(2) to a VECM model?

Answer 9

Question 10

Why is cointegration important?

Answer 10

Question 11

When is a VAR(p) process called cointegrated?

Answer 11

Question 12

What are the other options for r (the rank of matrix Pi)?

Answer 12

Question 13

What is the VECM representation? What are the parameters of a VAR process (using the variables of a VECM)?

Answer 13

Question 14

How is a constant included in a VECM model?

Answer 14

Question 15

How to interpret estimates of a VECM model?

Answer 15

Question 16

What is a vector space?

Answer 16

Question 17

What is a vector subspace?

Answer 17

Question 18

What is the orthogonal complement?

Answer 18

Question 19

What is a projection?

Answer 19

Question 20

What is the Frisch-Waugh-Lovell theorem?

Answer 20

Question 21

Why is the Frisch-Waugh-Lovell theorem needed?

Answer 21

Question 22

Describe a VECM without deterministic terms.

I.e., what is the notation

Answer 22

Question 23

What is the VECM in stacked matrix notation?

Answer 23

Question 24

How can we estimate a VECM using LS? When and or why would we do this?

Answer 24

Question 25

Do the two asymptotic properties hold with a VECM estimation? If they do, why and when?

Answer 25

Question 26

What could be the advantage of ML estimation for a VECM? What are some of its additional assumptions?

Answer 26

Question 27

What is the likelyhood function of an ML estimation of a VECM?

What do we maximize

Answer 27

Question 28

How to concentrate Γ out of the likelyhood function?

Of VECM obv.

Answer 28

Question 29

How to concentrate Σ_u out of the likelyhood function?

Of VECM

Answer 29

Question 30

How to concentrate out 𝛼 out of the likelyhood function?

Of VECM

Answer 30

Question 31

How to maximize β of the likelyhood function?

Of the VECM part

Answer 31

Question 32

What is the maximalized likelyhood function of a VECM model?

Answer 32

Question 33

In short: What are the values of the variables of the maximized likelyhood function?

Answer 33

Question 34

How to select the lag order for a VECM model?

Answer 34

Question 35

How do you test for the cointegration rank?

VECM

Answer 35