# Maximum-entropy Spectrum Maximum-entropy Spectrum is an indicator on [Vela](https://vela.luxalgo.com/chart), our next-generation charting platform, written in Pine Script®. Estimates the dominant market cycle with Burg's maximum-entropy method: a 12th-order autoregressive model is fitted to 64 conditioned samples each bar and its spectrum scanned over 8-48 bar periods. The smoothed dominant period plots as a line, the live spectrum draws as a heat profile beside the last bar, and alerts flag sharp or flat spectrum transitions and cycle shifts. - Indicator in the LuxAlgo Library, by LuxAlgo, published Jun 14, 2026. - Access: free. - Concepts: [Maximum-entropy Spectrum](https://www.luxalgo.com/library/concept/maximum-entropy-spectrum/) (primary) - Open on Vela: https://vela.luxalgo.com/chart?pineScriptCodeId=aoc0zen5f3gby2xrew518kym - Page: https://www.luxalgo.com/library/indicator/maximum-entropy-spectrum/ **Maximum-entropy Spectrum** measures which cycle currently dominates a market, and whether the reading deserves trust. Each bar the build high-passes the source, fits an autoregressive model with Burg's recursion, and evaluates its power spectrum across a period grid: the [maximum-entropy spectrum](https://www.luxalgo.com/library/concept/maximum-entropy-spectrum/), prized for sharp peaks on short windows. The smoothed dominant period plots as a line in bars, the spectrum as a heat profile beside the last bar. ## How to Trade the Maximum-entropy Spectrum? - **Sharp rhythm**: peak power at or above the Sharpness Threshold times the spectral average means one rhythm dominates; below it the dashboard reads flat or drifting and the line deserves less weight. - **Cycle shifts**: a jump in the smoothed dominant period beyond the shift threshold fires its own alert. - **Half cycle**: the optional half-period plot is the traditional choice when setting oscillator lengths from a measured cycle. ## Maximum-entropy Spectrum Settings - **Source** (default close) with **Conditioning** (default First Difference) and **Detrend Length** (default 48): high-pass preparation so trend cannot pose as a very long cycle. - **Sample Window** (default 64): shorter tracks drifting cycles faster, longer stabilizes the spectrum. - **AR Order** (default 12): too low blurs neighboring peaks, too high can split a real cycle; capped below half the window. - **Minimum Period** (default 8) and **Maximum Period** (default 48): the evaluated grid. - **Cycle Smoothing** (default 3): median-smooths the readouts. - **Sharpness Threshold** (default 4.0) and **Cycle Shift Threshold** (default 5.0): the alert levels. - **Calculation Bars** (default 2000), **Show Spectrum Profile** (on) with **Profile Width** (default 30), **Show Half Cycle** (off), plus dashboard toggles. ## Frequently Asked Questions ### How does this compare to the Hilbert Transform for cycle work? The [Hilbert Transform](https://www.luxalgo.com/library/indicator/hilbert-transform/) derives one instantaneous period from the analytic signal's phase: responsive, but a single estimate. The maximum-entropy spectrum lays out the whole period landscape, including the dashboard's second peak, so competing rhythms stay visible. ### Why fit a model instead of transforming the data directly? A direct transform needs long samples to separate nearby periods and treats its window as if it looped forever. The autoregressive route extrapolates the measured structure instead, producing sharp peaks from a few dozen bars. ### What does the profile beside the last bar show? The current spectrum as horizontal heat bars on the shared period axis, the strongest peak claiming the full width. It is a snapshot of the latest fit and redraws as new bars update the model. ## Related indicators - [Spline Quantile Regression Channel](https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel/) (Polynomial Regression): markdown at https://www.luxalgo.com/library/indicator/spline-quantile-regression-channel.md - [Bitcoin Power Law](https://www.luxalgo.com/library/indicator/bitcoin-power-law/) (Linear Regression): markdown at https://www.luxalgo.com/library/indicator/bitcoin-power-law.md - [Recursive Least Squares Forecast](https://www.luxalgo.com/library/indicator/recursive-least-squares-forecast/) (Linear Regression): markdown at https://www.luxalgo.com/library/indicator/recursive-least-squares-forecast.md - [Adaptive Harmonic Forecast](https://www.luxalgo.com/library/indicator/adaptive-harmonic-forecast/) (FFT/spectral Analysis): markdown at https://www.luxalgo.com/library/indicator/adaptive-harmonic-forecast.md - [Kalman Filter](https://www.luxalgo.com/library/indicator/kalman-filter/) (Statistics): markdown at https://www.luxalgo.com/library/indicator/kalman-filter.md - [Bitcoin Expectile Model](https://www.luxalgo.com/library/indicator/bitcoin-expectile-model/) (Quantile Regression): markdown at https://www.luxalgo.com/library/indicator/bitcoin-expectile-model.md - [Rolling Segment](https://www.luxalgo.com/library/indicator/rolling-segment/) (Linear Regression): markdown at https://www.luxalgo.com/library/indicator/rolling-segment.md - [Daily Polynomial Regressions](https://www.luxalgo.com/library/indicator/daily-polynomial-regressions/) (Polynomial Regression): markdown at https://www.luxalgo.com/library/indicator/daily-polynomial-regressions.md --- Source: https://www.luxalgo.com/library/indicator/maximum-entropy-spectrum/ (LuxAlgo Library). Free to use with attribution: https://www.luxalgo.com/library/license/