Does the LPPLS bubble model identify tops?

LPPLS (log-periodic power law singularity) comes from Didier Sornette and colleagues, from the 1990s. It looks for a price rising faster and faster, with swings that get quicker as they go, and fits a curve that says when that run must end. That end date is called the critical time.

We fit it every day to 8 lookback periods, from 120 days to 730 days. Each fit either passes a set of published quality checks, fixed before we tested anything, or it does not. The model’s confidence is the share that pass; half or more is a signal. Each fit uses only prices known on that day, so nothing looks ahead. We built our own implementation and publish it.

Signal days within a week of each other count as one signal: 18 signals, 561 days in all. For each signal day we ask whether price fell 40% within the next year. To judge whether that is better than chance, we place signals of the same lengths at random 10,000 times and score them the same way. Placing whole blocks rather than single days keeps the clustering honest.

A 40% fall followed 28.0% of signal days and 35.0% of ordinary days. Random signals scored anywhere from 14% to 56%, so this result is what a signal with no information in it would produce. In 69 of 100 random draws, a meaningless signal did at least this well.

LPPLS does not say how far price will fall. It says when the run ends. So the fairest test is its own claim: on the day it fired, did the year’s top land near the date it named? We count one try per signal, not per day.

At every distance the model did slightly worse than random dates. One note on counting: if you score every signal day instead of every signal, the model looks good, about one hit in five. That is misleading, because the days inside one signal share the same date and the same year ahead, so they are one try counted many times.

A stricter version, with tighter quality checks, never fired once in the whole history. It is not a harder test the model fails; under it the model is simply silent.

The bottom-finding version looks for accelerating falls instead, claiming a bottom is near. It fired on 35 days in 2 signals. Price doubled within a year after 97% of them, but two signals are far too few to mean anything.

This is our implementation with one published set of quality checks. Other versions of LPPLS exist, and this result is not a verdict on all of them.

And it does not mean the threshold itself was chosen fairly. Every rule in this registry was specified by someone who had already seen bitcoin’s history, so the cut-off is fitted to the record it is being judged against. The interval above measures sampling variation between independent trials and nothing else: not the choice of threshold, not that cycle turns are few and related, and not that thirty-six rules were tested in total. Only the forward record, which fixes a rule before its answer is known, avoids this.

More signals, which only time provides; a different set of quality checks fixed in advance by someone else; or a run of hits like 2021. At 18 signals, one more striking hit would move the date result noticeably.