ISYE 6402 Final Questions With 100% Correct Solutions.

ISYE 6402 Final
If Xt and Ytϕ1 are independent AR(1) processes, then Xt+Yt ϕ1 is an AR(2) process. -
ANSWER-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. - ANSWER-True

An ARIMA(p,0,q) model is always stationary. - ANSWER-False

There is no auto-correlation in an ARIMA(1,d,q) process. - ANSWER-False

A white noise process has zero auto-covariance for all lags including lag zero. -
ANSWER-False

If a time series is Gaussian then it is non-stationary. - ANSWER-False

AR(p) processes are always invertible. - ANSWER-True

The ACF plot can always be used to determine the order q of ARMA(p,q) models. -
ANSWER-False

In some cases, the PACF plot can be used to determine the order p of ARMA(p,q)
models. - ANSWER-True

The PACF of an ARMA(p,q) process cuts off after lag p. - ANSWER-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. - ANSWER-True


The best ARIMA(p,d,q) model to choose is always the one with the lowest AIC score. -
ANSWER-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. - ANSWER-True. (All MA(q)
processes are stationary.)

A pure AR(p) process always has significant autocorrelation. - ANSWER-True.