What is an accurate technique for implementing moving variance?

Yoshua Bengio wrote (p.c.):

My preferred style of moving average is the following. Let's say you have a series x_t and you want to estimate the mean m of previous (recent) x's:

m <-- m - (2/t) (m - x_t)

Note that with (1/t) learning rate instead of (2/t) you get the exact historical average. With a larger learning rate (like 2/t) you give a bit more importance to recent stuff, which makes sense if x's are non-stationary (very likely here). With a constant learning rate (independent of t) you get an exponential moving average.

What is an accurate technique for computing the moving variance?

You can estimate a running average of the variance, using the running averages of the mean and of the square of the difference to the moving mean. However, I read a blog post (can't find the URL, unfortunately) that argues that this estimate has high error.

Is there a better technique for computing the moving variance?