EViews.com

I'm running variance ratio test on three time series:

1. lkoh, original time series of LKOH stock prices. Data specification --> exponential random walk (the rest is default)
2. ll, which is log(lkoh). Data specification --> random walk
3. dl, which is dlog(lkoh). Data specification --> random walk innovations.

The results of the first two tests are identical, not surprisingly; the results of the third differ and the difference becoming bigger as I increase the number of observations.

I should also note that an equivalent test for jp from wright.wf1, example you use in User Guide, would have produced three identical results.

Not sure if this is a bug in the code or shortcoming of the algorithm.

Regards

You'll notice that there are more observations being used in the first two cases than in the third.

The reason is that in the third case, you give us the data in differences and then ask us to compute differences at various lags. We do so by computing sums of the differenced data for the appropriate lag. In the case where there are no internal missings in the data, this procedure fully recovers the lag differences. This is, however, not the case when there are internal missings. In this setting, a particular lagged data difference might be available in the original data but not available in the cumulative sum of the differenced data since a nearby first-lag missing value will propagate through the sum.

You can probably see where I am going with this. Your data has internal missings which propagate when we do the cumulative differences.

The bottom line is that while we can generally do pretty well reconstructing the lagged differences from the first differences, we can't do as well as knowing the original data when there are internal missings...

Got it.
Quite interesting.
Thanks.