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ISYE 6402
ISYE 6402 Final Exam Part 1 & 2 |
Qs & As| Grade A| 100% Correct
(NEW 2025/ 2026)
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. - ANS ✓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. - ANS ✓True
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. - ANS ✓True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. - ANS ✓FALSE (The statement would
only be true if you knew the two variables were independent.)
ISYE 6402
, 2
ISYE 6402
If the mean of a time series doesn't depend on time t, then the time series is stationary. -
ANS ✓False. (While constant mean is a necessary condition for stationarity, non-
constant variance or significant auto-correlation may be present.)
For a random walk process St=∑tj=1Xjwhere Xt∼IID(0,σ2), we have that Var(St) >
Var(St-1) - ANS ✓True
The mean of a random walk process depends on time. - ANS ✓False
All auto-regressive processes are stationary. - ANS ✓False
Consecutive observations in a white noise process are independent. - ANS ✓False
The random walk process is not variance stationary. - ANS ✓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). - ANS ✓True
If the correlation between variables XX and YY is 0, then the two variables must be
independent. - ANS ✓False
ISYE 6402
ISYE 6402
ISYE 6402 Final Exam Part 1 & 2 |
Qs & As| Grade A| 100% Correct
(NEW 2025/ 2026)
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. - ANS ✓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. - ANS ✓True
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. - ANS ✓True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. - ANS ✓FALSE (The statement would
only be true if you knew the two variables were independent.)
ISYE 6402
, 2
ISYE 6402
If the mean of a time series doesn't depend on time t, then the time series is stationary. -
ANS ✓False. (While constant mean is a necessary condition for stationarity, non-
constant variance or significant auto-correlation may be present.)
For a random walk process St=∑tj=1Xjwhere Xt∼IID(0,σ2), we have that Var(St) >
Var(St-1) - ANS ✓True
The mean of a random walk process depends on time. - ANS ✓False
All auto-regressive processes are stationary. - ANS ✓False
Consecutive observations in a white noise process are independent. - ANS ✓False
The random walk process is not variance stationary. - ANS ✓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). - ANS ✓True
If the correlation between variables XX and YY is 0, then the two variables must be
independent. - ANS ✓False
ISYE 6402
