How can the 30 day average on http://bitcoin.sipa.be/ be so high.

[nibor]

Looking at:
http://bitcoin.sipa.be/speed-lin-ever.png

The point on the 30 day average at start of Aug 2011 is higher than the 7 day average had EVER been at that point.

This is impossible. The 30 day average is at the end of the day just the average of the previous 4 and a bit 7 day periods.

And the average of 4 numbers can never be higher then the max!

14 day average also look wrong, as it should always be reasonable close the the difficult at the instant it changes.

[Pieter Wuille]

It does not report averages, it reports estimates.

The problem with a 30-day average, is that it on average reports data that is 15 days old.

The graphs shown use a limited extrapolation to estimate the current hash rate based on data from 30 days ago (and other window sizes). If the hash rate seems consistently rising, it will report numbers that assume this rising continued.

[nibor]

OK - that explains it (although would have to see maths to be sure).

I understand what you are trying to do, but looks like around that period it did not achieve the aims, although other times looks reasonable.

No doubt there is someone out there that has written a thesis on estimating the current value of a poison distributed variable with changing mean from historical data.
But not even Google is up to answering such badly phrased questions yet without a lot of help from a human...