# Interpretation of VAR results on R

I am trying to run VAR on the first differences of XLE and Brent futures. Prior to this I have already tested that the series in levels are I(1) and are not cointegrated.

Below are my results using VAR in the VARS package in R and I'm not really sure what I should be looking at - could someone shed some light on the interpretation please? Many thanks!

> Diff1VAR<-VAR(data.frame(XLE.Diff1,Brent.Diff1),type=c("const"),p=2)
> summary(Diff1VAR)

VAR Estimation Results:
=========================
Endogenous variables: XLE.Diff1, Brent.Diff1
Deterministic variables: const
Sample size: 175
Log Likelihood: 470.915
Roots of the characteristic polynomial:
0.3968 0.3968 0.3812 0.3514
Call:
VAR(y = data.frame(XLE.Diff1, Brent.Diff1), p = 2, type = c("const"))

Estimation results for equation XLE.Diff1:
==========================================
XLE.Diff1 = XLE.Diff1.l1 + Brent.Diff1.l1 + XLE.Diff1.l2 + Brent.Diff1.l2 + const

Estimate Std. Error t value Pr(>|t|)
XLE.Diff1.l1    0.024898   0.101310   0.246    0.806
Brent.Diff1.l1 -0.043074   0.073885  -0.583    0.561
XLE.Diff1.l2    0.087136   0.100689   0.865    0.388
Brent.Diff1.l2  0.045034   0.070635   0.638    0.525
const           0.005842   0.004818   1.212    0.227

Residual standard error: 0.06313 on 170 degrees of freedom
Multiple R-Squared: 0.01663,    Adjusted R-squared: -0.006507
F-statistic: 0.7188 on 4 and 170 DF,  p-value: 0.5802

Estimation results for equation Brent.Diff1:
============================================
Brent.Diff1 = XLE.Diff1.l1 + Brent.Diff1.l1 + XLE.Diff1.l2 + Brent.Diff1.l2 + const

Estimate Std. Error t value Pr(>|t|)
XLE.Diff1.l1    0.254914   0.137533   1.853   0.0655 .
Brent.Diff1.l1  0.069256   0.100301   0.690   0.4908
XLE.Diff1.l2    0.275127   0.136690   2.013   0.0457 *
Brent.Diff1.l2 -0.099845   0.095890  -1.041   0.2992
const           0.005070   0.006541   0.775   0.4394
---
Signif. codes:  0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1

Residual standard error: 0.0857 on 170 degrees of freedom
Multiple R-Squared: 0.07946,    Adjusted R-squared: 0.0578
F-statistic: 3.669 on 4 and 170 DF,  p-value: 0.006809

Covariance matrix of residuals:
XLE.Diff1 Brent.Diff1
XLE.Diff1    0.003985    0.003544
Brent.Diff1  0.003544    0.007344

Correlation matrix of residuals:
XLE.Diff1 Brent.Diff1
XLE.Diff1      1.0000      0.6551
Brent.Diff1    0.6551      1.0000

• What are you looking for? Are you conducting a descriptive / explanatory / predictive study? – Richard Hardy Nov 17 '15 at 10:49

Note that the model's $R^2$ is very low (adjusted $R^2$ is even negative) and the $F$-statistic is not statistically significant. Hence, a model including only an intercept in each equation could be superior to your current model. This should not come as a big surprise since oil price (or changes in oil price, as in this model) is notoriously difficult to predict. I would be more surprised if a VAR model was successful here.
• I mean $y_t=\beta_0+\varepsilon_t$, the simplest possible model. – Richard Hardy Nov 19 '15 at 6:03