ISYE 6402 Final - Part 1 Questions and Answers Best rated A+ Guaranteed Success Latest Update

ISYE 6402 Final - Part 1
A time series generally can be decomposed into three components mt, st and Xt. Where
mt is the trend, st is the seasonality, and Xt is a residual time process after accounting
for trend and seasonality. - ANSWER-True

Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. - ANSWER-FALSE (The statement
would only be true if you knew the two variables were independent.)

If the mean of a time series doesn't depend on time t, then the time series is stationary.
- ANSWER-False. (While constant mean is a necessary condition for stationarity, non-
constant variance or significant auto-correlation may be present.)


If the time series YtYt can be represented as trend plus Gaussian white noise with
Yt=βt+ϵtYt=βt+ϵt , then its expectation is E( Yt ) = β. - ANSWER-False. It would be E(Yt)
= E(βt) + E(εt) = βt + 0.

If {Xt} is a stationary process, then its autocorrelation function has an expected value of
0 for lag values greater than 0. - ANSWER-True


For a random walk process St=∑tj=1Xjwhere Xt∼IID(0,σ2), we have that Var(St) >
Var(St-1) - ANSWER-True

The mean of a random walk process depends on time. - ANSWER-False

All auto-regressive processes are stationary. - ANSWER-False

Consecutive observations in a white noise process are independent. - ANSWER-False

The random walk process is not variance stationary. - ANSWER-True

Whether or not X and Y are independent, we have
Cov(a+bX,c+dY)=bdCov(X,Y)Cov(a+bX,c+dY)=bdCov(X,Y). - ANSWER-True


The condition that the covariance between Yi and Yi−j depends only on j is sufficient for
the process to be stationary. - ANSWER-False. (This condition is necessary, but not
sufficient. Presence of a trend or non-constant variance would result in a violation of
stationarity assumptions.)