ISYE 6402 FINALS QUIZZES WITH DETAILED VERIFIED AND 100% ACCURATE SOLUTIONS

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.