ISYE 6402 FINALS QUIZZES WITH
DETAILED VERIFIED AND 100%
ACCURATE SOLUTIONS
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.
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.
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.
True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables.
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.
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)
, True
The mean of a random walk process depends on time.
False
All auto-regressive processes are stationary.
False
Consecutive observations in a white noise process are independent.
False
The random walk process is not variance stationary.
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).
True
If the correlation between variables XX and YY is 0, then the two variables must be
independent.
False
If the correlation between X and Y is 1, then one variable must cause the other.
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.
DETAILED VERIFIED AND 100%
ACCURATE SOLUTIONS
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.
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.
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.
True
Var(X+Y)=Var(X)+Var(Y) for any X and Y variables.
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.
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)
, True
The mean of a random walk process depends on time.
False
All auto-regressive processes are stationary.
False
Consecutive observations in a white noise process are independent.
False
The random walk process is not variance stationary.
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).
True
If the correlation between variables XX and YY is 0, then the two variables must be
independent.
False
If the correlation between X and Y is 1, then one variable must cause the other.
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.
