ISYE 6402 Final Exam - Questions With Verified
Solutions
ISYE 6402 Final - Part 1
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. Correct 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. Correct 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.
Correct Ans - True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. Correct Ans -
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. Correct 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) Correct Ans - True
The mean of a random walk process depends on time. Correct Ans
- False
, All auto-regressive processes are stationary. Correct Ans -
False
Consecutive observations in a white noise process are independent.
Correct Ans - False
The random walk process is not variance stationary. Correct 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). Correct
Ans - True
If the correlation between variables XX and YY is 0, then the two
variables must be independent. Correct Ans - False
If the correlation between X and Y is 1, then one variable must cause
the other. Correct Ans - False
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. Correct Ans - True
The condition that the covariance between Yi and Yi−j depends only
on j is sufficient for the process to be stationary. Correct Ans -
False. (This condition is necessary, but not sufficient. Presence of a
trend or non-constant variance would result in a violation of
stationarity assumptions.)
If {Xt} is white noise, then {−Xt} is stationary. Correct Ans -
True
The main benefit of parametric models is that they have higher
degrees of freedom. Correct Ans - False
Solutions
ISYE 6402 Final - Part 1
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. Correct 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. Correct 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.
Correct Ans - True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables. Correct Ans -
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. Correct 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) Correct Ans - True
The mean of a random walk process depends on time. Correct Ans
- False
, All auto-regressive processes are stationary. Correct Ans -
False
Consecutive observations in a white noise process are independent.
Correct Ans - False
The random walk process is not variance stationary. Correct 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). Correct
Ans - True
If the correlation between variables XX and YY is 0, then the two
variables must be independent. Correct Ans - False
If the correlation between X and Y is 1, then one variable must cause
the other. Correct Ans - False
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. Correct Ans - True
The condition that the covariance between Yi and Yi−j depends only
on j is sufficient for the process to be stationary. Correct Ans -
False. (This condition is necessary, but not sufficient. Presence of a
trend or non-constant variance would result in a violation of
stationarity assumptions.)
If {Xt} is white noise, then {−Xt} is stationary. Correct Ans -
True
The main benefit of parametric models is that they have higher
degrees of freedom. Correct Ans - False
