Hi,I am trying to test the price process of commodities for a trending behaviour. Using a variance ratio test, can I interpret that a significantly higher than one variance ratio indicates a trend?[b/]I have read in A non random walk down Wall Street (1999) by Lo that under heteroskedasctic increments the measure of the variance ratio would be <sum(for j=1_to_q-1) of [2(q-j)/q]*autocorrelation(j)> where q is the aggregation period.If I assume that the increments of my commodity price series are heteroskedastic:Would it make sense to calculate the variance ratio over a total sample size of one year by using aggregated period of 3 months and comparing them to weekly variances?[b/]If I find out that my variance ratio is significantly higher than 1, should I keep on calculating variance ratios by rolling over my yearly samples? (i.e: sample 1: t=o->t=252, sample 2: t=1->t=253,...)Also, what software do you recommend for variance ratios?Thanks for the insights

I used to have my own little test for mean reversion based upon variances of time series using different sampling periods - this test must be equivalent.Let me try to put your question into trader speak: "if I calculate the annualized variance of a series of returns using daily, weekly and monthly data over the same overall time period, and I get the ratio of (for example) weekly variance to daily variance significantly larger than one, does this indicate trending?"I think the answer is "probably". Did I understand your question right?The result of my tests were often a little fuzzy ...Let's let a stats expert wade in here.

Yes this was my question. What were you assuming for your time series: homoskedastic and no autocorrelation.heteroskedastic and no autocorrelation.I have read that this was changing the variance ratio calculation to be used and I am wondering which assumption would be more realistic for commodities.I am using backward adjusted data provided by the CSI. Any recommendations to apply the variance ratio test on this data?

To be honest I found the best thing to simulate is the potential trading strategy itself.I didn't particularly apply much high powered math - I simply calculated the variance of the returns and used this as a rough indicator which determined whether it was worth running a full P&L simulation.

Modified Variance Ratio paperI believe the above paper has been presented here before.

Has anyone already used the software called R to calculate the variance ratio?I am comparing my results with the Lo.Mac function in R but they differ significantly.Would anyone be aware of the formula the software uses to calculate the M2 statistic (variance ratio under heteroskedasticity)?Is it the weighted average of autocorrelations with lag j = 1 to q-1 where q is the aggregation period?Cassius