Although Zhou and Sornette  presented a general methodology under which to incorporate fundamental economic factors (e.g., interest rate, interest spread, historical volatility, implied volatility, and exchange rates) into the theory of herding to describe bubbles and antibubbles, the most surprising result is that the best model is the second-order LPPL model without any factors.
Substituting (3) into (2) and integrating yields the LPPL equation for the price:
Sornette, "The volatility-confined LPPL model: a consistent model of 'explosive' financial bubbles with mean-reverting residuals," International Review of Financial Analysis, vol.
They also argued that most financial crashes are the climax of the so-called log-periodic power law signatures (LPPLS) associated with speculative bubbles .
The predictive power of LPPLS was first discovered in acoustic emissions prior to rupture and in identifying the precursors of earthquakes [2, 3].
This means that universal LPPLS sufficiently reflect the fundamental tendency of investors to speculate and herd.
Marc's performance at the event lived up to expectations - his play, in a field of more than 100 players representing 10 teams from across the UK and Ireland, helped Team LPPL to finish seventh.
I couldn't have imagined the experiences I've enjoyed since I started playing LPPL poker and I highly recommend it to any poker player out there.