I have a VAR model with five macro-economic variables, y[1], y[2], y[3], y[4],
y[5]. They are related to each other in following manner.
y[1,t] = alpha[1,0] + beta[1,1, 1]*y[1,t-1]+............+beta[1,1,
12]*y[1,t-12] + beta[1,2, 1]*y[2,t-1]+............+beta[1,2, 12]*y[2,t-12] +
e[1,t]
y[2,t] = alpha[2,0] + beta[2,2, 1]*y[2,t-1]+............+beta[2,2,
12]*y[2,t-12] + e[2,t]
y[3,t] = alpha[3,0] + beta[3,1, 1]*y[1,t-1]+............+beta[3,1,
12]*y[1,t-12]
+ beta[3,2, 1]*y[2,t-1]+............+beta[3,2, 12]*y[2,t-12]
+ beta[3,3, 1]*y[3,t-1]+............+beta[3,3, 12]*y[3,t-12]
+ beta[3,4, 1]*y[4,t-1]+............+beta[3,4, 12]*y[4,t-12] + e[3,t]
y[4,t] = alpha[4,0] + beta[4,3, 1]*y[3,t-1]+............+beta[4,3,
12]*y[3,t-12]
+ beta[4,4, 1]*y[4,t-1]+............+beta[4,4, 12]*y[4,t-12] + e[4,t]
y[5,t] = alpha[5,0] + beta[5,3, 1]*y[3,t-1]+............+beta[5,3,
12]*y[3,t-12]
+ beta[5,5, 1]*y[5,t-1]+............+beta[5,5, 12]*y[4,t-12] + e[5,t]
All variables are stationary
Now I want to estimate the coefficients under a VAR[12] framework. Is it
mathematically correct to estimate coefficients of each equaltion with simple
OLS separately? Or how I can use R [mAr.est() function) to estimate them?
Regards,
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