ISYE 6402 MIDTERM PREP Questions with Correct Solutions
Question:
1. Getting a 3 variable VAR model from summary(model) output of a VAR(1) model
Answer:
first matrix: first row are coefficients for Xt1, second row are coefficients for Xt2, etc...
second matrix is Xt-1, i b/c this is a VAR(1) model last matrix are the constants eta_t is
covariance matrix, direct copy
Question:
2. (c) Based on the fitted model, is there contemporaneous cross-correlation? Is there lagged
cross-correlation? Is there lagged auto-correlation? Explain.
Answer:
contemporaneous cross-correlation is NOT present if the variance-covariance matrix is a
diagonal matrix there is lagged correlation if the order p of the VAR(p) model > 0
Question:
3. T/F - Differencing the data might not make the series stationary in the presence of
cointegration.
Answer:
True
Question:
4. Cointegration and long-run equilibrium
Answer:
See image
Question:
5. Does cov(x,x) = var(x)?
, Answer:
You betcha
Question:
6. Autocovariance T/F
Answer:
see image
Question:
7. T/F - The AR(1) process is causal if and only if the autoregressive parameter phi is between
0 and
1. However, it is always invertible.
Answer:
FALSE! the absolute value of phi must lie b/w -1 and 1
Question:
8. T/F - A linear process is a special case of the moving average model.
Answer:
FALSE - the moving average is a special case of a linear process.
Question:
9. T/F - A guassian time series is always stationary
Answer:
false - guassian processes can have varying means
Question:
10. T/F 'In autoregressive models the current value of dependent variable is influenced by
past values of both dependent and independent variables.'
Answer:
FALSE - there are no analogies of dependent/independent variables w/ AR models, as there
are w/ regression models
Question:
11. in AR models the current value of the dependent variable is affected by the past values of
both dependent and independent variables
Answer:
False - We don't have dependent and independent variables in AR models like we do in
regression models
Question:
1. Getting a 3 variable VAR model from summary(model) output of a VAR(1) model
Answer:
first matrix: first row are coefficients for Xt1, second row are coefficients for Xt2, etc...
second matrix is Xt-1, i b/c this is a VAR(1) model last matrix are the constants eta_t is
covariance matrix, direct copy
Question:
2. (c) Based on the fitted model, is there contemporaneous cross-correlation? Is there lagged
cross-correlation? Is there lagged auto-correlation? Explain.
Answer:
contemporaneous cross-correlation is NOT present if the variance-covariance matrix is a
diagonal matrix there is lagged correlation if the order p of the VAR(p) model > 0
Question:
3. T/F - Differencing the data might not make the series stationary in the presence of
cointegration.
Answer:
True
Question:
4. Cointegration and long-run equilibrium
Answer:
See image
Question:
5. Does cov(x,x) = var(x)?
, Answer:
You betcha
Question:
6. Autocovariance T/F
Answer:
see image
Question:
7. T/F - The AR(1) process is causal if and only if the autoregressive parameter phi is between
0 and
1. However, it is always invertible.
Answer:
FALSE! the absolute value of phi must lie b/w -1 and 1
Question:
8. T/F - A linear process is a special case of the moving average model.
Answer:
FALSE - the moving average is a special case of a linear process.
Question:
9. T/F - A guassian time series is always stationary
Answer:
false - guassian processes can have varying means
Question:
10. T/F 'In autoregressive models the current value of dependent variable is influenced by
past values of both dependent and independent variables.'
Answer:
FALSE - there are no analogies of dependent/independent variables w/ AR models, as there
are w/ regression models
Question:
11. in AR models the current value of the dependent variable is affected by the past values of
both dependent and independent variables
Answer:
False - We don't have dependent and independent variables in AR models like we do in
regression models
