# by Andrew Jim

*DISCLAIMER; This post and its contents should in no way be considered investment advice.*

# SUMMARY

The **Log-Periodic Power Law (LPPL)** model gave a good forward indication of the burst of the speculative Bitcoin bubble from its lofty $20,000 highs in mid- December 2017 and hinted at it’s subsequent ~70% drop. By using a 90 day forward test, this study will use the same model in ‘reverse’ to see if it can indicate a future point of a more aggressive price rebound by year end. Unfortunately, the short answer is *no*: simulations estimated the median ‘Critical Time’ to be about 46 days from now (around Dec 2, 2018) for a ‘price trough’ of ~$5262 (-19% from current levels) with a 90 day final forward price of ~$7707 (+16% from current levels).

**Introduction**Bitcoin (BTC) has run up from $400 in early 2016 to a price peak of ~$20,000 by late 2017 for a exponential ~50X return. An LPPL model captured the exponentially increasing oscillations indicated by swings in investor sentiment that eventually led to a point of failure (

*Critical Time*). A quick recap of the theory and LPPL equation can be seen here in the original note: https://mynabla.com/2017/11/30/bubble-trouble-exploring-an-lppl-model-for-bitcoin/ where a heuristic search algorithm was used to find an approximate global solution for the LPPL cost function.

**Drawdowns**To put things in perspective, BTC has experienced only 10 drawdowns greater than 30% since 2010 and with 3 in the latter half of 2017. The worst drawdown of -93% lasted 623 days. The current one we are in is the 4th largest and has lasted a slow 306 days so far for a drawdown of about -70%. The 3rd largest drawdown was also about -70% but hit the bottom in a week!

**Top 10 Drawdowns ranked by depth:**

**Top BTC Drawdowns:**(y- axis: drawdown range)

Given the depth and length of this current drawdown, we apply this same LPPL model in ‘reverse’ to see if there is a possibility in a forward Critical Time period that a ‘price trough’ will emerge (as opposed to a ‘price peak’ in the normal model).

**Data setup:**

Aggregated daily trading data from 2017–12–01 to 2018–10–17 was used for BTC price giving a total of 321 observations. This data captures BTC’s peak price on 2017–12–17 as well as its subsequent sell off (drawdown). The LPPL model was used to generate simulations to provide a median Critical Time (** Tc**) for a price trough using a 90 day forward looking timeframe — effectively till the end of the year.

**Reverse LPPL simulations (90 Days Forward Estimate)**(y-axis:

*Log*BTC price)

The corresponding number of “Trading days to the trough” from the simulations can be summarized in a frequency plot below:

A frequency plot for the ‘price trough levels’ was also generated from the simulations:

From the above frequency plots the median estimate of the number of days till expected price trough is **~46 days** (ie. till ‘Critical Time’) with a **median equivalent price bottom of ~$5262.**

**Results**The final curve plot below corresponds to the optimal parameters found during the global metaheuristic algorithm search with the shaded blue area representing the 80% confidence level for the Critical Time.

**Reverse LPPL model using 90 day forward estimates:**

The optimal estimated parameters are:

or LPPL equation:

giving:

**Summary**

The reverse LPPL model has 7 parameters to estimate making a precise calibration tricky at best. The simulation results suggest continued slow sideways trading with a negative bias to below the $6000 level which is plausible given that notably lower recent price volatility. Actual current 30 day volatility is now ~40% has already hit a 19 month low.

Rolling 30 day volatility chart for BTC:

However, rather than projecting an explosive rebound after hitting a trough price of ~$5262 at Critical Time, the model forecasts a gentler upward oscillating trajectory to close out the 90 days forecast at around **~$7707** (approx mid Jan 2019). This goes against popular expectation (hope!) that we may see a much stronger rebound into November and December. In retrospect, the climb to Bitcoin’s peak of $20,000 was certainly exponential but the subsequent -70% crash was not and it was also spread over a longer time period. The reverse LPPL model reflected this decelerating sell off accordingly.

** Caveats:** The model obviously does not take into account events that may add an external shock to the system. For example: ICE’s (Intercontinental Exchange) plan to list Bakkt Bitcoin Daily Futures on Dec 12, 2018 — the first physically delivered BTC futures contracts will be a key one to watch. Game on!

**Disclaimer:** This is not investment advice and is a practical example for illustrative purposes only. Please note that historical gains may not be representative of future returns. And as always, please thoroughly *#DoYourOwnResearch*

DISCLAIMER; This post and its contents should in no way be considered investment advice. We may individually hold positions in some of the assets we discuss. Any projections, conclusions, analysis, views are to be considered hypothetical & for informational purposes only & not meant as recommendations for investment. Anyone considering an investment in crypto should only invest what they can afford to lose. You alone are responsible for evaluating the risks & merits of our content.