True or false? You do not have to provide explanations. (a) Any moving average (MA) process is co...
True or false? You do not have to provide explanations.
(a) Any moving average (MA) process is covariance stationary.
(b) Any autoregressive (AR) process is invertible.
(c) The autocorrelation function of an MA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off.
(d) Suppose yt is a general linear process. The optimal 2-step-ahead prediction error follows MA(2) process.
(e) Any autoregressive moving average (ARMA) process is invertible because any moving average (MA) process is invertible.
(f) The autocorrelation function of any ARMA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off.
(g) Any ARMA(p,q) process can be represented as a general linear process.
Homework Answers
(a) Any moving average (MA) process is covariance stationary.
False
(b) Any autoregressive (AR) process is invertible.
Yes
(c) The autocorrelation function of an MA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off.
True
(d) Suppose yt is a general linear process. The optimal 2-step-ahead prediction error follows MA(2) process.
True
(e) Any autoregressive moving average (ARMA) process is invertible because any moving average (MA) process is invertible.
False
(f) The autocorrelation function of any ARMA process decays gradually while the partial autocorrelation function exhibits a sharp cut-off.
True
(g) Any ARMA(p,q) process can be represented as a general linear process.
True
Add Answer to:
True or false? You do not have to provide explanations. (a) Any moving average (MA) process is co...
a) Consider the following moving average process, MA(2):
a) Consider the following moving average process, MA(2): Yt = ut + α1ut-1 + α2ut-2 where ut is a white noise process, with E(ut)=0, var(ut)=σ2 and cov(ut,us)=0 . Derive the mean, E(Yt), the variance, var(Yt), and the covariances cov( Yt,Yt+1 ) and cov(Yt,Yt+2 ), of this process. b) Give a definition of a (covariance) stationary time series process. Is the MA(2) process (covariance) stationary?
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