ISyE 6402 Midterm Prep - Questions With Correct
Solutions
Getting a 3 variable VAR model from summary(model) output of a
VAR(1) model Correct Ans - 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
(c) Based on the fitted model, is there contemporaneous cross-
correlation? Is there lagged cross-correlation? Is there lagged auto-
correlation? Explain. Correct Ans - 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
T/F - Differencing the data might not make the series stationary in
the presence of cointegration. Correct Ans - True
Cointegration and long-run equilibrium Correct Ans - See
image
Does cov(x,x) = var(x)? Correct Ans - You betcha
Autocovariance T/F Correct Ans - see image
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.
, Correct Ans - FALSE! the absolute value of phi must lie b/w -1
and 1
T/F - A linear process is a special case of the moving average model.
Correct Ans - FALSE - the moving average is a special case of a
linear process.
T/F - A guassian time series is always stationary Correct Ans -
false - guassian processes can have varying means
T/F 'In autoregressive models the current value of dependent
variable is influenced by past values of both dependent and
independent variables.' Correct Ans - FALSE - there are no
analogies of dependent/independent variables w/ AR models, as
there are w/ regression models
in AR models the current value of the dependent variable is affected
by the past values of both dependent and independent variables
Correct Ans - False - We don't have dependent and independent
variables in AR models like we do in regression models
how do ACF and PACF differ? Correct Ans - TBD
what in an ACF plot would show non-stationarity? Correct Ans -
slowly decreasing lags
what in an ACF and PACF plot would show stationary? Correct Ans
- few lags outside of confidence bands, quickly decreasing
can confidence intervals be used for significance? Correct Ans -
you bet - should all be same sign for significance
Solutions
Getting a 3 variable VAR model from summary(model) output of a
VAR(1) model Correct Ans - 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
(c) Based on the fitted model, is there contemporaneous cross-
correlation? Is there lagged cross-correlation? Is there lagged auto-
correlation? Explain. Correct Ans - 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
T/F - Differencing the data might not make the series stationary in
the presence of cointegration. Correct Ans - True
Cointegration and long-run equilibrium Correct Ans - See
image
Does cov(x,x) = var(x)? Correct Ans - You betcha
Autocovariance T/F Correct Ans - see image
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.
, Correct Ans - FALSE! the absolute value of phi must lie b/w -1
and 1
T/F - A linear process is a special case of the moving average model.
Correct Ans - FALSE - the moving average is a special case of a
linear process.
T/F - A guassian time series is always stationary Correct Ans -
false - guassian processes can have varying means
T/F 'In autoregressive models the current value of dependent
variable is influenced by past values of both dependent and
independent variables.' Correct Ans - FALSE - there are no
analogies of dependent/independent variables w/ AR models, as
there are w/ regression models
in AR models the current value of the dependent variable is affected
by the past values of both dependent and independent variables
Correct Ans - False - We don't have dependent and independent
variables in AR models like we do in regression models
how do ACF and PACF differ? Correct Ans - TBD
what in an ACF plot would show non-stationarity? Correct Ans -
slowly decreasing lags
what in an ACF and PACF plot would show stationary? Correct Ans
- few lags outside of confidence bands, quickly decreasing
can confidence intervals be used for significance? Correct Ans -
you bet - should all be same sign for significance
