Part 1

Question 1

What is the conditional mean of a VAR(1) process?

Answer 1

Question 2

What is the usual representation of a VAR(1) process?

Answer 2

Question 3

What are the four properties of the innovations epsilon from a VAR(1) process?

Answer 3

Question 4

What is the conditional variance of epsilon_t of a VAR(1) process?

Answer 4

Question 5

What is the reduced form and structural form of a VAR model? How can one be written as the other?

Answer 5

First, structural, then reduced

Question 6

What do we need to ensure that E[x_t] and Var[X_t] behave nicely?

Answer 6

Question 7

How is the stability condition of a VAR process derived? (Specifically what specific condition do we need to hold for the process to be stable)

Answer 7

Question 8

What is the scalar equation of a matrix A?

Answer 8

Question 9

Which condition needs to hold for a VAR(1) model to be stable?

Answer 9

Question 10

What is the closed form solution of the unconditional expectation of x_t? When does this hold? (Of a VAR model)

Answer 10

Question 11

Derive the unconditional variance of a VAR model (until the sum of Lambda Omega Lambda)

Answer 11

Question 12

Derive the autocovariance of a VAR model

Answer 12

Question 13

What does the following thm imply?

Answer 13

A linear combination of Gaussian variables is also Gaussian

Question 14

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

Answer 14

Question 15

What is the characteristic equation of a VAR(p) process?

Answer 15

Question 16

What is the stability condition of a VAR(p) process?

Answer 16

Question 17

What is the definition of stationarity in the wide sence and stationarity in the strict sence?

Answer 17

Question 18

What are the three conditions for stationarity of a VAR process?

Answer 18

Question 19

Why is the mixing property useful?

Answer 19

Question 20

What does ergodic mean?

Answer 20

Question 21

What is the ergodic theorem?

Answer 21

Question 22

What is the definition of the DGP of the entire economy? What could be said about this theoretical DGP?

Answer 22

Question 23

What are the three types of variables in the DGP of the entire economy?

Answer 23

Question 24

What is usually meant by treat z_t as given? What are thre three consequences?

Answer 24

Question 25

How can the joint density of the entire economy be factorized?

Answer 25

Question 26

When are variables said to be variation free?

Answer 26

Question 27

What are the three assumptions that econometric analysis of D_{y|z} rely on?

Answer 27

Question 28

If the three assumptions that D_{y|z} rely on are fulfilled, which conclusion can be reached?

Answer 28

Question 29

What are nuisance parameters? What are parameters of intrest?

Answer 29

Question 30

Answer 30

Question 31

What is the definition of weakly exogenous?

Answer 31

Question 32

What is the definition of (non)-granger causality?

Answer 32

Question 33

What is the difference between real causality and Granger causality?

Answer 33

Question 34

What is the definition of strong exogeneity?

Answer 34

Question 35

What is the definition of super exogeneity?

Answer 35

Question 36

What are the three notions of exogeneity? What do they enable?

Answer 36

Question 37

What is the idea behind the lag-operator?

Answer 37

Question 38

What is the one period difference operator? What is the n-period difference operator? What is the nth order-difference operator?

Answer 38

Question 39

What is the inverting lag polynomial?

Answer 39

Question 40

Give an example of how to invert lag polynomials:

Answer 40

Question 41

How can an AR(p) model be written using lag-polynomials?

Answer 41

Question 42

Write a MA process in terms of a Lag operator.

Answer 42

Question 43

Write an ARMA process in terms of a Lag operator.

Answer 43

Question 44

How can autocovariance be analyzed? (name 2)

Answer 44

Question 45

What is the definition of an Integrated process?

Answer 45

Question 46

How can a VAR(p) model be written with a Lag operation? How a VARMA?

Answer 46

Question 47

How can a matrix polynomial be inverted? Why is this usefull?

Answer 47

Question 48

What are the three methods of writing down the stability conditions?

Answer 48

Question 49

What is the simplest dynamic model?

Answer 49

Question 50

What is the definition of filtration?

Answer 50

Question 51

What is the definition of adaption?

Answer 51

Question 52

What is the definition of a martingale?

Answer 52

Question 53

What is the definition of a martingale difference sequence?

Answer 53

Question 54

What does a mds imply with regarding lagged values?

Answer 54

Question 55

How can a martingale sequence always be created?

Answer 55

Question 56

What is the LLN for mds?

Answer 56

Question 57

What is the clt for mds?

Answer 57