# Time series Analysis : Vector autoregression in R

#### TheMonkster

##### New Member
I am finding relation between two time series M & M1.
M and M1 both found to be stationary at first difference and also cointegrated at first difference.
Using VARselect in R,I found out 4 as lag length for M and 6 as lag length for M1.

Then I have tested for Granger and I got :
M=f(M1,lag=4){p value=0.001} & M1 != f(M,lag=6) {p value=0.001}

Then I applied VAR with lag length = 4 and I got following result:

Roots of the characteristic polynomial:
0.9853 0.9463 0.4623 0.4623 0.4389 0.4389 0.3293 0.3293
Call:
VAR(y = Vardata, p = 4, type = "const")

Estimation results for equation M:
=====================================
M = M.l1 + M1.l1 + M.l2 + M1.l2 + M.l3 + M1.l3 + M.l4 + M1.l4 + const

Estimate Std. Error t value Pr(>|t|)
M.l1 0.970703 0.032298 30.054 < 2e-16 ***
M1.l1 0.121400 0.016714 7.263 7.76e-13 ***
M.l2 0.042422 0.044823 0.946 0.34417
M1.l2 -0.057860 0.023364 -2.476 0.01344 *
M.l3 -0.125813 0.044741 -2.812 0.00502 **
M1.l3 -0.025420 0.023436 -1.085 0.27833
M.l4 0.075556 0.031006 2.437 0.01500 *
M1.l4 -0.004158 0.017338 -0.240 0.81052
const 2.135886 2.746256 0.778 0.43691
---
Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 7.744 on 968 degrees of freedom
Multiple R-Squared: 0.9863, Adjusted R-squared: 0.9862
F-statistic: 8738 on 8 and 968 DF, p-value: < 2.2e-16

As I need to put their relation in terms of eqution,Could someone help me with following questions? It would really help me to progress further in modeling relationship.

1) Which lag length (Max or min of both) should I apply during VAR?
2) Is the equation I got the actual relation between M and M1? What should I interpret from coefficient results?
3) Am I right in using VAR over VECM?

My questions might sound stupid but I have tried looking for answers on internet but still not able to find them.Thanks for your time.