ISYE 6402 Final – question with answers
A white noise process has zero auto-covariance for all lags including lag zero.
- -False
-If a time series is Gaussian then it is non-stationary. - -False
-AR(p) processes are always invertible. - -True
-The ACF plot can always be used to determine the order q of ARMA(p,q)
models. - -False
-In some cases, the PACF plot can be used to determine the order p of
ARMA(p,q) models. - -True
-The PACF of an ARMA(p,q) process cuts off after lag p. - -False. (The PACF of
an ARMA(p,q) process tails off, while the PACF of an AR(p) process cuts off
after lag p.)
-MA(q) processes are always causal. - -True
-If Xt and Ytϕ1 are independent AR(1) processes, then Xt+Yt ϕ1 is an AR(2)
process. - -False. (The order of the sum of two independent AR processes is
not necessarily the sum of each individual processes' order.)
-Let Wt be a white noise process. Then Xt=Wt−Wt−1 is stationary. - -True
-An ARIMA(p,0,q) model is always stationary. - -False
-There is no auto-correlation in an ARIMA(1,d,q) process. - -False
-The best ARIMA(p,d,q) model to choose is always the one with the lowest
AIC score. - -False. (If two models have very similar scores but different
coefficient counts, it is often best practice to select the simpler model.
Additionally, we may wish to use a measure that penalizes coefficient counts
more (e.g. BIC).)
-A pure MA(q) process always has constant variance. - -True. (All MA(q)
processes are stationary.)
-A pure AR(p) process always has significant autocorrelation. - -True.
-If an ARMA(p,q) process in causal and invertible then is must also be
stationary. - -True
A white noise process has zero auto-covariance for all lags including lag zero.
- -False
-If a time series is Gaussian then it is non-stationary. - -False
-AR(p) processes are always invertible. - -True
-The ACF plot can always be used to determine the order q of ARMA(p,q)
models. - -False
-In some cases, the PACF plot can be used to determine the order p of
ARMA(p,q) models. - -True
-The PACF of an ARMA(p,q) process cuts off after lag p. - -False. (The PACF of
an ARMA(p,q) process tails off, while the PACF of an AR(p) process cuts off
after lag p.)
-MA(q) processes are always causal. - -True
-If Xt and Ytϕ1 are independent AR(1) processes, then Xt+Yt ϕ1 is an AR(2)
process. - -False. (The order of the sum of two independent AR processes is
not necessarily the sum of each individual processes' order.)
-Let Wt be a white noise process. Then Xt=Wt−Wt−1 is stationary. - -True
-An ARIMA(p,0,q) model is always stationary. - -False
-There is no auto-correlation in an ARIMA(1,d,q) process. - -False
-The best ARIMA(p,d,q) model to choose is always the one with the lowest
AIC score. - -False. (If two models have very similar scores but different
coefficient counts, it is often best practice to select the simpler model.
Additionally, we may wish to use a measure that penalizes coefficient counts
more (e.g. BIC).)
-A pure MA(q) process always has constant variance. - -True. (All MA(q)
processes are stationary.)
-A pure AR(p) process always has significant autocorrelation. - -True.
-If an ARMA(p,q) process in causal and invertible then is must also be
stationary. - -True
