[R-SIG-Finance] Estimating variance ratio test result

[David Chang]

I'm testing whether a null hypothesis that a time series is random
walk is true. I use Auto.VR() and Lo.Mac() from R package "vrtest" for
variance ratio test to EURUSD. EURUSD log returns were the input.

> head(returns)
                  Close
2002-01-08 -0.005035595
2002-01-09  0.001905318
2002-01-10 -0.002017508
2002-01-11  0.001009263
2002-01-14  0.002462807
2002-01-15 -0.001118706

Where Auto.VR() gave me
> Auto.VR(returns)
$stat
[1] 54.50223
$sum
[1] 2.843879

Lo.Mac() gave me
> Lo.Mac(returns, 2)
$Stats
           M1        M2
k=2 -2.083685 -1.733119

How do we evaluate the result from Auto.VR() or Lo.Mac()? In other
words, how can we say that the null hypothesis is rejected from those
results?

David