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LPPL Tracker is a technical tool for fitting the Log-Periodic Power Law model to crypto, stock, and commodity price series. It helps identify bubble-like price behavior, estimate a critical time window, and compare fit quality across assets.

LPPL stands for Log-Periodic Power Law. The model is also known as the JLS model, after Johansen, Ledoit, and Sornette.

What LPPL Models

The LPPL model describes financial bubbles as positive-feedback processes. During a bubble, price may rise faster than an exponential trend while showing oscillations that become more frequent as the market approaches a critical time.

LPPL does not predict an exact crash date. It estimates a high-risk window where the current price regime is more likely to break or change.

Core Formula

$$\ln[p(t)] = A + B(t_c-t)^m + C(t_c-t)^m\cos[\omega\ln(t_c-t)+\phi]$$

Parameters

Symbol	Meaning	Notes
$p(t)$	Asset price at time $t$	The model fits the natural log of price.
$t$	Current time	Usually normalized to days in this project.
$t_c$	Critical time	Estimated time window where the bubble is most likely to break or change state.
$A$	Expected log price near $t_c$	The project uses $\exp(A)$ as the predicted critical price.
$B$	Power-law trend coefficient	For a rising bubble, the usual constraint is $B < 0$.
$C$	Oscillation amplitude	Controls how strongly price oscillates around the trend.
$m$	Power-law exponent	Usually constrained to $0 < m < 1$.
$\omega$	Log-periodic frequency	Controls how many oscillations appear before $t_c$.
$\phi$	Phase	Sets the starting phase of the oscillation.

How to Read the Result

• Fit quality: lower RMSE means the fitted curve is closer to the observed log price, but RMSE alone is not enough.
• Critical date: the estimated center of a high-risk window, not a deterministic forecast.
• Predicted critical price: derived from $\exp(A)$, with a simple confidence interval when the fit supports it.
• Confidence: based on nested-window scans. Higher values mean more windows produced valid LPPL fits under the configured filters.

Important Limits

• LPPL is a risk signal, not a trading signal.
• The model is sensitive to the selected time window and initial conditions.
• False positives are possible, especially outside clear bubble regimes.
• Historical bubbles often fit LPPL well after the fact. Real-time prediction is harder and should be treated cautiously.

Documentation

• LPPL Guide
• Stock API Setup Guide