# Variance Ratio Test in R

I would like to conduct a variance ratio test for a financial time series in order to examine whether I can apply the square root rule for the variance with the software R. I used the Automatic Variance Ratio Test vrtest::Auto.Vr and got a statistic of -0.01. Now I am wondering, is that the z-score, which is distributed standard normal under the Null hypothesis, that this ratio is 1 (or equivalent that there is no autocorrelation)? It is not specified in the describtion, I just found this:

Usage:
Auto.VR(y)
Arguments:
y financial return time series
Value:
stat Automatic variance ratio test statistic


TL;DR: the test statistic's distribution is $N(0,1)$

$H_0$: ${\Delta}r_t$ is serially uncorrelated (where ${\Delta}r_t=r_t-r_{t-1}$)
$H_1$: ${\Delta}r_t$ is serially correlated
The test statistic is $VR=\sqrt{T/l}[\hat{VR}(l)-1]/\sqrt{2} \quad {\xrightarrow{d}} \quad N(0,1)$
The $d$ over the arrow is important, i.e. the $VR$ converges in distribution to standard normal (hence $d$ does not imply the convergence in mean square or convergence in probability) as $T$, $l$ and $T/l$ approach infinity. The $l$ is the lag truncation point. The paper has detail on formulae for both $VR$ and $l$.