Question 1 1/1p
Which of the following statements about an ARMA(2,1) process with white noise
normal errors are true?
The roots of the characteristic equation for the AR component must lie on the unit
circle.
o The process can be represented as a combination of AR and MA processes with
appropriate constraints for stationarity.
o The invertibility condition ensures the MA component has a unique representation in
terms of past residuals.
The process can always be expressed as a finite-order AR process.
A stationary ARMA(2,1) process combines AR and MA components under
constraints that ensure stationarity (roots of the AR characteristic equation
outside (not on!) the unit circle). The MA invertibility condition is required for
uniqueness in representing the process.
,Question 2 0.5/ 1 pts
For the time series S; = Eizl X, where X, ~ IID (0, 02) , which of the
following statements are correct?
-> The series is non-stationary.
o The autocorrelation decreases with increasing lag.
-> The variance of S; grows linearly with ¢.
The series has constant mean E[S;] = 0.
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, Question 3 0. pts
For an AR(2) process X; = 0.5X;_1 4+ 0.2X; o + Z;, where Z; is white noise,
which of the following statements are true?
o The PACF cuts off after lag 2.
The ACF oscillates for all lags.
-> The roots of the characteristic equation determine stationarity.
o The process is stationary.
The stationarity of the AR(2) process depends on the roots of its characteristic
equation being outside the unit circle, and in that case the PACF cuts off at lag
2.
Which of the following statements about an ARMA(2,1) process with white noise
normal errors are true?
The roots of the characteristic equation for the AR component must lie on the unit
circle.
o The process can be represented as a combination of AR and MA processes with
appropriate constraints for stationarity.
o The invertibility condition ensures the MA component has a unique representation in
terms of past residuals.
The process can always be expressed as a finite-order AR process.
A stationary ARMA(2,1) process combines AR and MA components under
constraints that ensure stationarity (roots of the AR characteristic equation
outside (not on!) the unit circle). The MA invertibility condition is required for
uniqueness in representing the process.
,Question 2 0.5/ 1 pts
For the time series S; = Eizl X, where X, ~ IID (0, 02) , which of the
following statements are correct?
-> The series is non-stationary.
o The autocorrelation decreases with increasing lag.
-> The variance of S; grows linearly with ¢.
The series has constant mean E[S;] = 0.
Error parsing MathML: error on line 1 at column 817: Opening and ending tag mismatch: img lint
, Question 3 0. pts
For an AR(2) process X; = 0.5X;_1 4+ 0.2X; o + Z;, where Z; is white noise,
which of the following statements are true?
o The PACF cuts off after lag 2.
The ACF oscillates for all lags.
-> The roots of the characteristic equation determine stationarity.
o The process is stationary.
The stationarity of the AR(2) process depends on the roots of its characteristic
equation being outside the unit circle, and in that case the PACF cuts off at lag
2.
