Using Math To Find Speculative Bubbles

Science Blog, via nc links:

The key characteristic in determining a bubble is the volatility of an asset’s price, which, in the case of bubbles is very high. The authors estimate the volatility by applying state of the art estimators to real-time tick price data for a given stock. They then obtain the best possible extension of this data for large values using a technique called Reproducing Kernel Hilbert Spaces (RKHS), which is a widely used method for statistical learning.
“First, one uses tick price data to estimate the volatility of the asset in question for various levels of the asset’s price,” Protter explains. “Then, a special technique (RKHS with an optimization addition) is employed to extrapolate this estimated volatility function to large values for the asset’s price, where this information is not (and cannot be) available from tick data. Using this extrapolation, one can check the rate of increase of the volatility function as the asset price gets arbitrarily large. Whether or not there is a bubble depends on how fast this increase occurs (its asymptotic rate of increase).”
If it does not increase fast enough, there is no bubble within the model’s framework.
The authors test their methodology by applying the model to several stocks from the dot-com bubble of the nineties. They find fairly successful rates in their predictions, with higher accuracies in cases where market volatilities can be modeled more efficiently. This helps establish the strengths and weaknesses of the method.

I tend to think things are in a bubble when the price chart appears to go parabolic.  Also, when mainstream media outlets are full of reports about wonderful ways to make easy money with little or no risk of price decreases, you're in a bubble.  I usually call the bubble too soon, but I thought it was pretty easy to tell something was wrong, both in tech stocks and real estate.  Today, I think we are somewhere along the lifecycle of bubbles in commodities, farm land prices, shale oil and gas field investment and all things China.  Don't ask me when they'll pop, but I think they will sometime.  Just a random guess, I'll put commodities peak in late 2012, farm land in early to mid 2013, China in mid-to-late 2013 and shale energy in 2014.  Technically, they are all linked, and may come down from peak at about the same time, but I think the latter two will see more bargain-hunters swooping in to keep them going longer.