Issue 6402 Midterm Prep Exam Questions and
Answers.
Getting a 3 variable VAR model from summary (model) output of a VAR (1) model -
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
teat 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. - 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. - ANS True
Cointegration and long-run equilibrium - ANS See image
Does cov(x,x) = var(x)? - ANS You betcha
Autocovariance T/F - 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. - 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. - ANS FALSE -
the moving average is a special case of a linear process.
T/F - A guassian time series is always stationary - 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.' - 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 - 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? - ANS TBD
what in an ACF plot would show non-stationarity? - ANS slowly decreasing lags
what in an ACF and PACF plot would show stationary? - ANS few lags outside of
confidence bands, quickly decreasing
can confidence intervals be used for significance? - ANS you bet - should all be same
sign for significance
in a VAR model w/ seasonality for twelve months, how many seasonality dummy
variables will you have? - ANS just 11 - # of categories - 1
T/F 1. Time series processes generally can be decomposed into a component modeling
systematic variation (trend and seasonality) and a component modeling stochastic
stationary variation. - ANS TRUE! stochastic, like white noise
In mathematics and statistics, a stationary process (a.k.a. a strict/strictly stationary
process or strong/strongly stationary process) is a stochastic process whose
unconditional joint probability distribution does not change when shifted in time.
Consequently, parameters such as mean and variance also do not change over time.
T/F Consecutive observations in time series data are independent and identically
distributed. - ANS FALSE - otherwise, you wouldn't have to consider autocorrelation
T/F - Var(a+bY) = b * Var(Y) - ANS FALSE - Var(a+bY) = b^2 * Var(Y)
T/F - One model for the trend component of a time series is the simple linear regression
model in which time is used as an explanatory variable. - ANS TRUE
T/F - If Cov(X,Y)=0 then X and Y are independent - ANS FALSE - If X and Y are
independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY =
E(X)E(Y ) − µXµY = 0
The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are
not independent
T/F If ρ=Corr(X,Y)=0, then X and Y are independent - ANS FALSE - However, if X and
Y are uncorrelated, then they can still be dependent
T/F If X and Y are independent random variables, then we have that Var(X+Y)≠Var(X)
+Var(Y). - ANS FALSE
Answers.
Getting a 3 variable VAR model from summary (model) output of a VAR (1) model -
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
teat 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. - 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. - ANS True
Cointegration and long-run equilibrium - ANS See image
Does cov(x,x) = var(x)? - ANS You betcha
Autocovariance T/F - 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. - 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. - ANS FALSE -
the moving average is a special case of a linear process.
T/F - A guassian time series is always stationary - 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.' - 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 - 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? - ANS TBD
what in an ACF plot would show non-stationarity? - ANS slowly decreasing lags
what in an ACF and PACF plot would show stationary? - ANS few lags outside of
confidence bands, quickly decreasing
can confidence intervals be used for significance? - ANS you bet - should all be same
sign for significance
in a VAR model w/ seasonality for twelve months, how many seasonality dummy
variables will you have? - ANS just 11 - # of categories - 1
T/F 1. Time series processes generally can be decomposed into a component modeling
systematic variation (trend and seasonality) and a component modeling stochastic
stationary variation. - ANS TRUE! stochastic, like white noise
In mathematics and statistics, a stationary process (a.k.a. a strict/strictly stationary
process or strong/strongly stationary process) is a stochastic process whose
unconditional joint probability distribution does not change when shifted in time.
Consequently, parameters such as mean and variance also do not change over time.
T/F Consecutive observations in time series data are independent and identically
distributed. - ANS FALSE - otherwise, you wouldn't have to consider autocorrelation
T/F - Var(a+bY) = b * Var(Y) - ANS FALSE - Var(a+bY) = b^2 * Var(Y)
T/F - One model for the trend component of a time series is the simple linear regression
model in which time is used as an explanatory variable. - ANS TRUE
T/F - If Cov(X,Y)=0 then X and Y are independent - ANS FALSE - If X and Y are
independent variables, then their covariance is 0: Cov(X, Y ) = E(XY ) − µXµY =
E(X)E(Y ) − µXµY = 0
The converse, however, is not always true. Cov(X, Y ) can be 0 for variables that are
not independent
T/F If ρ=Corr(X,Y)=0, then X and Y are independent - ANS FALSE - However, if X and
Y are uncorrelated, then they can still be dependent
T/F If X and Y are independent random variables, then we have that Var(X+Y)≠Var(X)
+Var(Y). - ANS FALSE
