Question

6. Consider a VAR(1) process {(X1,t, X2,t)} defined by X1,t = 0.9X1,t−1 + phi X2,t−1 + W1,t, X2,t = phi X1,t−1 + 0.9X2,t−1 + W2,t, where phi is a real constant and {(W1,t, W2,t)} is a bivariate white noise with mean vector 0 and covariance matrix Sigma . For what values of phi is {(X1,t, X2,t)} a stationary process? Justify your answer. [Total 10 marks]

Name: 6 consider a var1 process x1t x2t defined by x1t 09x1t1 phi x2t1 w1t x2t phi x1t1 09x2t1 w2t where phi is a real constant and w1t w2t is a bivariate white noise with mean vector 0 and covari 37342
Uploaded: 2023-08-25T21:27:43-08:00
Duration: 7 min 42 s
Channel: Sri K
Description: 6 consider a var1 process x1t x2t defined by x1t 09x1t1 phi x2t1 w1t x2t phi x1t1 09x2t1 w2t where phi is a real constant and w1t w2t is a bivariate white noise with mean vector 0 and covari 37342

          6. Consider a VAR(1) process {(X1,t, X2,t)} defined by 
X1,t = 0.9X1,t−1 + phi X2,t−1 + W1,t, 
X2,t = phi X1,t−1 + 0.9X2,t−1 + W2,t, 
where phi  is a real constant and {(W1,t, W2,t)} is a bivariate white noise with mean vector 0 and covariance matrix Sigma . For what values of phi   is {(X1,t, X2,t)} a stationary process? Justify your answer. 
[Total 10 marks]

Added by Joel W.

Elementary Statistics a Step by Step Approach

Allan G. Bluman 9th Edition

Instant Answer

Solved by Expert Sri K

08/25/2023

Step 1

The parameters of interest are the autoregressive coefficients (0.9 for each variable's own lag and \(\phi\) for the other variable's lag) and the innovations which are assumed to be white noise with a mean vector of 0 and a covariance matrix \(\Sigma\). Show more…

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6. Consider a VAR(1) process {(X1,t, X2,t)} defined by X1,t = 0.9X1,t−1 + phi X2,t−1 + W1,t, X2,t = phi X1,t−1 + 0.9X2,t−1 + W2,t, where phi is a real constant and {(W1,t, W2,t)} is a bivariate white noise with mean vector 0 and covariance matrix Sigma . For what values of phi is {(X1,t, X2,t)} a stationary process? Justify your answer. [Total 10 marks]