Week 2

Question 1

How is a VAR(p) process defined?

Answer 1

Question 2

What is the companion form of a VAR(p) process?

Answer 2

Question 3

When is a VAR(p) process stable? How is it easier to check?

Answer 3

Question 4

What is the infinite moving average representation of a VAR(p) process? What is the autocovariance at lag h?

Answer 4

Question 5

How do you again get y_t from the companion form of a VAR(p) process?

Answer 5

Question 6

When is a VAR(p) process weakly stationary?

Answer 6

i.e., just if it's stable

Question 7

What is the prediction error representation of a VAR(p) process?

Answer 7

Question 8

How can Φ be calculated for a VAR(p) process? Explain the derivation.

Answer 8

Question 9

How to compute the autocorrelations of a VAR(p) process?

Answer 9

Question 10

What are two options of estimation for a VAR(p) process?

Answer 10

• Multivariate Least Squares
• Maximum likelyhood

Question 11

Describe the notation of the letters describing estimation of a multivariate VAR(p) least squares.

Answer 11

Question 12

Describe the vec operation.

Answer 12

Question 13

Describe the Kronicker product.

Answer 13

Question 14

Name the 6 (or 7) rules of the vec and Kronicker product.

Not all rules include the vec operation

Answer 14

Question 15

What is the derivation of the least squeres estimation of a VAR(p) model?

Answer 15

Question 16

How are the LLN and CLT shown for the LS estimator of a VAR(p) model?

Answer 16

Question 17

How is consistency proved for a VAR(p) model (which is stable obv.)?

Answer 17

Question 18

How is asymptotic normality proved for a stable VAR(p) process?

Answer 18

Question 19

What is the log-likelyhood of VAR(p) process?

Answer 19

Question 20

Why is the optimum of a ML estimation and LS optimization the same?

Of a VAR(p) process

Answer 20

Question 21

What is the sigma of the ML estimation? Why is it biased?

Of a VAR(p) process

Answer 21