**Link of the Week - Bubble Science**
Very interesting stuff - applying nonlinear dynamical models to sales data:

"...Best-selling books typically reach their sales peaks in one of two ways. The less potent way is by what Sornette calls an "exogenous shock," which is brief and abrupt. An example is "Strong Women Stay Young" by Dr. Miriam Nelson, which peaked on the list the day after a favorable review in the Sunday New York Times. A second example is Sornette's own 2002 book, "Why Stock Markets Crash: Critical Events in Complex Financial Systems," which spiked following a favorable review by Jon Markman on CNBC and TheStreet.com. "On Jan. 17, 2003, my book was ranked 2,000-something and then suddenly it was No. 17," Sornette recalled. "A few hours later, it was in the top 10. As a physicist, it looked to me like an exogenous shock to the system."

Sales are typically greater, however, when a book benefits from what Sornette calls an "endogenous shock," which progressively accelerates over time, and is illustrated in the book business by favorable word-of-mouth. Such books rise slowly, but the sales results are more enduring, and the decline in sales is slower and more much gradual, he found.

An example includes "The Divine Secrets of the Ya-Ya Sisterhood," which reached the best-seller list two years after it was published, without the benefit of a major marketing campaign. The book was popular with book clubs and inspired women to form "Ya-Ya Sisterhood" groups of their own. A second example is Nora Roberts' novel, "Heaven and Earth (Three Sisters Island Trilogy)," which peaked only after a slow rise and also fell slowly, which Sornette attributes to word of the book spreading among friends and family.

The slower peaks tend to generate more sales over time, Sornette said.

"Word-of-mouth can spread like an epidemic," he said.

The trajectories of many books' rankings are combinations of both kinds of peaks, Sornette says, which suggests that an effective, well-timed marketing campaign could combine with a strong network to enhance sales.

..."Is it possible to derive a quantitative law of how book sales behave?" Sornette asks. "We have derived a law of how a sale's shock to the system will jump up and decline over time. The books we analyzed behaved the same way. We can statistically predict how the system will evolve, how sales peaks can emerge, and we can predict the expected decline slope for books that rise sharply."

Basically, a quick read of these models tells me they apply sandpile (ie avalanche) models to expectations - this creates oscillating positive feedback in herding, which is a nice model for bubbles.

More links: Sornette's site. Interesting essay 1. Interesting essay 2. Interview:

"...What we have found in our studies [Johansen and Sornette, 2002] is that basically 2/3 of all shocksï¿½of all dramatic crashes--can be attributed to an endogenous origin as opposed to exogenous origin.

...

**When this 30% drop is analyzed statistically at the daily scale, as is usually done in standard statistical analysis, it becomes three independent events of 10% drop**. A 10% drop for example on the NASDAQ occurs once every four years statistically. It is an event that has a probability of one in one thousand to occur at any given day. It is not that rare. In contrast, what is very rare is to witness three such daily losses occurring in a run of three consecutive days, cumulating into a 30% drawdown. It is such drawdown that is hurting your portfolio, not really the daily losses, but the runs of losses. This is why I stress in my research the important of looking at these drawdowns which are much better measures of the large risks and the crashes. Now the probability of three such 10% drop events to occur in a run is the probability of one event -- times the probability of the second event -- times the probability of the third event. That is one in one thousand to the power cube. That gives a probability of one in one billion. Translated into the time of recurrence of such a run or a drawdown of 30%, it corresponds to one event in four million years.

Thus, people who are not taking into account the fact that you have a run or drawdown, which gives rise to the dramatic drawdowns, are providing an incorrect description of the event because they would predict that such events would occur once in four million years. Such large recurrence time means that such an event is practically impossible and one should never observe it. In reality, drawdowns of 30% or more are seen very often these days. So, what is the solution of this puzzle?

**It is that the market is characterized by the existence of strong dependencies between successive days**. Such strong dependencies are however rare and difficult to qualify and detect by standard statistical techniques. We have developed specific tools to quantify them. We say that these strong dependencies occur intermittently in pockets of predictability."