Exercises Part 1 Flashcards
How we you compute autocovariances of an MA process?
See example, but steps are:
0. Rewrite from Lag notation to normal notation
1. Compute gamma_0 = E[y_t^2]
2. Compute gamma_1 = E[y_t y_{t-1}]
etc.
How to check if an AR(p) process is stationary?
How do you compute autocovariances of an AR(p) process?
Essentially get first autocovariances first and then solve the system.
What are the three conditions neccesary for the stationarity of a VAR process?
What is the stability condition of a VAR(1) process?
What is the stability condition for a VAR(p) process?
What is the unconditional mean of a VAR(p) process?
What is the unconditional variance of a VAR(1) process? How is it derived?
How can a VMA (Vector MA) be derived? Just answer with steps
- Start with the initial equation
- Write out what happens in case you switch x_{t-1} with its definition
- Continue until you can create some sort of sum
What is the quadratic formula?
What is the chacteristic equation for the difference notation? What for time series?
The difference with time series is that it is exactly the inverse as for time series
What is block-exogeneity?
Only b
Only c
What is the structural form of the VAR model?
How to convert structural VAR to reduced VAR?
What is the definition of mixing?
If a dynamic time series process satisfies the stability condition that is discussed in the lecture then we say that this process is stationary.
If a random time series sequence, {xt}, is mixing. Then, the realization of the se- quence at time t does not contain any information about the realization at time t−1.
If a sequence is “mixing” then the pair x_t and x_{t−j} that is taken from the sequence tends to independence as j → ∞.
A stationary time series is automatically mixing.
Ensemble mean is the expectation of a process that is for fixed t across all possible realizations of the sequence.
Thusfar unclear, please think of the answer now.
Ergodicity is the property of a stationary series, that ensures that time average of the sequence is converging in probability to the mean of the sequence.
True, however stationarity is also needed.
Companion form can be used to rewrite an AR(1) in terms of a MA(∞) model.
Weak exogeneity is a relation between two variables that ensures that one variable is independent of the other.
The statement is incorrect. Weak exogeneity does not imply that one variable is independent of another. It is a property about the sufficiency of information in the conditional distribution for parameter estimation.
An adapted sequence, {x_t, F_t} is a martingale difference sequence only if it is sta-
tionary.
The property of martingale difference sequence is weaker than independence and also weaker than uncorrelatedness.
