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fix(docs): correct .md documentation across errors, dynamics, filters, forecasts, momentum, numerics, oscillators, reversals, statistics, trends, volatility, volume

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Deep review of all indicator categories verified .md headers against .cs WarmupPeriod, parameters, inputs, and outputs. Fixes include warmup corrections, parameter documentation, output type accuracy, and Pine Script alignment.
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Miha Kralj
2026-03-10 18:38:23 -07:00
parent 8906c62dcf
commit 35a6702b06
178 changed files with 2579 additions and 998 deletions
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lib/filters/agc/Agc.md
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| **Inputs** | Source (close) |
| **Parameters** | `decay` (default 0.991) |
| **Outputs** | Single series (AGC) |
| **Output range** | Tracks input |
| **Output range** | [-1, +1] (normalized) |
| **Warmup** | `1` bars |
### TL;DR
- The Automatic Gain Control normalizes any oscillating signal to the \[-1, +1\] range through exponential peak tracking.
- Parameterized by `decay` (default 0.991).
- Output range: Tracks input.
- Requires `1` bars of warmup before first valid output (IsHot = true).
- Output range: [-1, +1] (normalized amplitude).
- Requires `1` bar of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The purpose of the AGC is to normalize the amplitude of any indicator to unity." — John F. Ehlers, TASC January 2015
@@ -86,26 +86,25 @@ Peak initializes to $10^{-10}$ (tiny positive) to avoid division by zero on the
### Operation Count (Streaming Mode)
AGC (Adaptive Gain Control) applies a slow EMA to estimate signal level, then scales the signal by the inverse of that level. O(1) per bar.
AGC uses exponential peak decay with a ratchet-up mechanism, then divides the signal by the tracked peak. O(1) per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Level EMA (FMA) | 1 | ~4 cy | ~4 cy |
| Gain = 1 / level (division) | 1 | ~10 cy | ~10 cy |
| Output multiply | 1 | ~3 cy | ~3 cy |
| **Total** | **3** | — | **~17 cycles** |
| Peak decay (multiply) | 1 | ~3 cy | ~3 cy |
| Abs + compare (ratchet) | 1 | ~2 cy | ~2 cy |
| Normalize (division) | 1 | ~10 cy | ~10 cy |
| **Total** | **3** | — | **~15 cycles** |
O(1) per bar. The division dominates; precomputing gain incrementally saves it but adds state. ~17 cycles/bar.
O(1) per bar. The division dominates. ~15 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Level EMA recursion | No | Sequential IIR dependency |
| Gain division | No | Depends on current EMA |
| Output multiply | N/A | Single scalar multiply |
| Peak decay + ratchet | No | Data-dependent branching (max of decay vs abs) |
| Normalize (division) | No | Depends on current peak |
Fully recursive. Batch throughput: ~17 cy/bar.
Fully sequential due to data-dependent peak tracking. Batch throughput: ~15 cy/bar.
| Metric | Value |
|---|---|
lib/filters/alaguerre/ALaguerre.md
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| **Parameters** | `length` (default 20), `medianLength` (default 5) |
| **Outputs** | Single series (ALaguerre) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Warmup** | `max(4, length)` bars |
| **Signature** | [alaguerre_signature](alaguerre_signature.md) |
### TL;DR
@@ -15,7 +15,7 @@
- The Adaptive Laguerre Filter extends Ehlers' four-element all-pass cascade by replacing the fixed damping factor with a per-bar adaptive alpha deri...
- Parameterized by `length` (default 20), `medianlength` (default 5).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `max(4, length)` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The best filter is one that knows when to listen closely and when to smooth aggressively." -- John F. Ehlers (paraphrased)
@@ -111,24 +111,28 @@ The filter requires $\max(4, N)$ bars before producing reliable output. The firs
### Operation Count (Streaming Mode)
Laguerre filter uses 4 cascaded Laguerre stages L0..L3, each an O(1) gamma-parameterized FMA, plus a final weighted combination.
Adaptive Laguerre combines HH/LL tracking error normalization (O(N) scan), median smoothing (O(M log M) sort), and 4-stage Laguerre cascade (O(1)).
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Tracking error computation | 1 | ~3 cy | ~3 cy |
| HH/LL scan over N-element buffer | N | ~2 cy | ~40 cy (N=20) |
| Median via insertion sort (M elements) | M log M | ~3 cy | ~25 cy (M=5) |
| Laguerre state update x4 (each: 2 FMA) | 8 | ~4 cy | ~32 cy |
| Weighted output combination (3 adds) | 3 | ~2 cy | ~6 cy |
| **Total** | **11** | — | **~38 cycles** |
| Weighted output combination | 3 | ~2 cy | ~6 cy |
| **Total** | — | — | **~106 cycles** (N=20, M=5) |
O(1) per bar. Four recursive stages with precomputed gamma constant. ~38 cycles/bar.
O(N + M log M) per bar due to HH/LL scan and median sort. Dominated by the lookback scan for large N.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Laguerre stage recursion | No | Each stage `L[k][n]` depends on `L[k-1][n]` and `L[k][n-1]` |
| Weighted combination | No | Only 4 terms; SIMD overhead not worthwhile |
| HH/LL scan | Partial | Min/max over contiguous buffer amenable to `Vector<double>` |
| Median sort | No | Comparison-based sort, data-dependent |
| Laguerre cascade | No | Each stage depends on previous stage and previous bar |
Cascaded IIR stages cannot be vectorized. Batch throughput: ~38 cy/bar.
Adaptive overhead limits SIMD gains. Batch throughput: ~106 cy/bar (N=20, M=5).
| Metric | Value | Notes |
|--------|-------|-------|
lib/filters/baxterking/BaxterKing.md
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| **Inputs** | Source (close) |
| **Parameters** | `pLow` (default 6), `pHigh` (default 32), `k` (default 12) |
| **Outputs** | Single series (BaxterKing) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Output range** | Oscillates around zero |
| **Warmup** | `2K+1` bars (default 25) |
| **Signature** | [baxterking_signature](baxterking_signature.md) |
### TL;DR
- The **Baxter-King Band-Pass Filter** is a symmetric finite impulse response (FIR) filter that approximates the ideal spectral band-pass by truncati...
- Parameterized by `plow` (default 6), `phigh` (default 32), `k` (default 12).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Output range: Oscillates around zero (extracts cyclical component).
- Requires `2K+1` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The business cycle is whatever remains after you strip away the trend and the noise. Baxter and King figured out the stripping."
lib/filters/bessel/Bessel.md
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| **Parameters** | `length` |
| **Outputs** | Single series (Bessel) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Warmup** | `length` bars |
| **Signature** | [bessel_signature](bessel_signature.md) |
### TL;DR
@@ -15,7 +15,7 @@
- The Bessel Filter is a 2nd-order low-pass IIR filter designed to preserve the **shape** and **timing** of price moves.
- Parameterized by `length`.
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `length` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> When you care more about *when* the market turns than how aggressively you can torture the noise, you reach for a Bessel.
lib/filters/bpf/Bpf.md
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| **Inputs** | Source (close) |
| **Parameters** | `lowerPeriod`, `upperPeriod` |
| **Outputs** | Single series (BPF) |
| **Output range** | Tracks input |
| **Output range** | Oscillates around zero |
| **Warmup** | `Math.Max(lowerPeriod, upperPeriod)` bars |
| **Signature** | [bpf_signature](bpf_signature.md) |
@@ -14,7 +14,7 @@
- The **BPF** (BandPass Filter) is a second-order IIR architecture designed to surgically excise specific frequency components from a time series.
- Parameterized by `lowerperiod`, `upperperiod`.
- Output range: Tracks input.
- Output range: Oscillates around zero (bandpass extracts cyclic component).
- Requires `Math.Max(lowerPeriod, upperPeriod)` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
lib/filters/cfitz/Cfitz.md
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| **Inputs** | Source (close) |
| **Parameters** | `pLow` (default 6), `pHigh` (default 32) |
| **Outputs** | Single series (Cfitz) |
| **Output range** | Tracks input |
| **Output range** | Oscillates around zero |
| **Warmup** | `2` bars |
| **Signature** | [cfitz_signature](cfitz_signature.md) |
@@ -14,7 +14,7 @@
- The **Christiano-Fitzgerald Band-Pass Filter** is an asymmetric full-sample filter that approximates the ideal spectral band-pass by using time-var...
- Parameterized by `plow` (default 6), `phigh` (default 32).
- Output range: Tracks input.
- Output range: Oscillates around zero (extracts cyclical component).
- Requires `2` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
lib/filters/edcf/Edcf.md
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| **Parameters** | `length` (default 15) |
| **Outputs** | Single series (Edcf) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Warmup** | `length` bars |
| **Signature** | [edcf_signature](edcf_signature.md) |
### TL;DR
@@ -15,7 +15,7 @@
- The **Ehlers Distance Coefficient Filter (EDCF)** is a nonlinear adaptive FIR filter created by John F.
- Parameterized by `length` (default 15).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `length` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
## Overview
lib/filters/gauss/Gauss.md
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- Gauss (Gaussian Filter) is a smoothing filter that applies a Gaussian kernel to time series data.
- Parameterized by `sigma` (default 1.0).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `2⌈3σ⌉+1` bars of warmup before first valid output (IsHot = true). Default: **7 bars** (σ=1.0).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "SMA smears data like cheap paint. Gaussian filtering respects the signal's soul."
lib/filters/hann/Hann.md
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- Hann (Hann Filter) is a Finite Impulse Response (FIR) smoothing filter that applies a Hann window to time series data.
- Parameterized by `length`.
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `length` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The Hanning window whispers where the Boxcar screams. Smoothness is not just an aesthetic; it's a mathematical necessity."
lib/filters/hp/Hp.md
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- The Hodrick-Prescott (HP) filter is a widely used tool in macroeconomics for separating the cyclical component of a time series from raw data.
- Parameterized by `lambda` (default 1600.0).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `⌈2√λ⌉` bars of warmup before first valid output (IsHot = true). Default: **~80 bars** (λ=1600).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "Trends are not lines; they are curves that we simplify for our sanity, often at the cost of reality."
lib/filters/hpf/Hpf.md
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- The 2-Pole Highpass Filter (HPF) is designed to separate high-frequency components (like cycles and noise) from the underlying trend.
- Parameterized by `length` (default 40).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Output range: Oscillates around zero (detrended signal).
- Requires `length` bars of warmup before first valid output (IsHot = true). Default: **40 bars**.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "Noise is just signal you haven't figured out how to filter yet. Or maybe, it's the only signal that matters."
lib/filters/rmed/Rmed.md
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| **Parameters** | `period` (default 12) |
| **Outputs** | Single series (Rmed) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Warmup** | 5 bars (MedianWindow) |
| **Signature** | [rmed_signature](rmed_signature.md) |
### TL;DR
@@ -15,7 +15,7 @@
- RMED applies exponential smoothing to a 5-bar running median, creating a nonlinear IIR filter that rejects impulsive spike noise while providing sm...
- Parameterized by `period` (default 12).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires **5 bars** of warmup (MedianWindow) before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "John Ehlers combined two tools that rarely meet: the median (nonlinear, spike-resistant) and the EMA (smooth, recursive). The median kills the spikes, the EMA smooths the survivors. Together they produce a filter that is both resistant and smooth."
lib/filters/roofing/Roofing.md
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| **Inputs** | Source (close) |
| **Parameters** | `hpLength` (default 48), `ssLength` (default 10) |
| **Outputs** | Single series (ROOFING) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Output range** | Oscillates around zero |
| **Warmup** | `hpLength` bars (default 48) |
### TL;DR
- The **Roofing Filter** is John Ehlers' bandpass architecture designed specifically for oscillator construction.
- Parameterized by `hplength` (default 48), `sslength` (default 10).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Output range: Oscillates around zero (bandpass behavior).
- Requires `hpLength` bars of warmup before first valid output (IsHot = true). Default: **48 bars**.
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The trend is your friend until it overwhelms the signal. The noise is your enemy until you mistake it for alpha."
lib/filters/spbf/Spbf.md
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| **Inputs** | Source (close) |
| **Parameters** | `shortPeriod` (default 40), `longPeriod` (default 60), `rmsPeriod` (default 50) |
| **Outputs** | Single series (SPBF) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Output range** | Oscillates around zero |
| **Warmup** | `max(longPeriod, rmsPeriod)` bars (default 60) |
### TL;DR
- The **Super Passband Filter** is John Ehlers' wide-band bandpass constructed by differencing two z-transformed EMAs with Ehlers-style smoothing ($\...
- Parameterized by `shortperiod` (default 40), `longperiod` (default 60), `rmsperiod` (default 50).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Output range: Oscillates around zero.
- Requires `max(longPeriod, rmsPeriod)` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "Two EMAs walk into a frequency domain. The difference between them is the only thing worth trading."
lib/filters/ssf2/ssf2.pine
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@@ -26,7 +26,7 @@ ssf2(series float src, simple int length) =>
float ssrc = nz(src, src[1])
float src1 = nz(src[1], ssrc)
float src2 = nz(src[2], src1)
ssf_internal := c1 * ssrc + c2 * nz(ssf_internal[1], src1) + c3 * nz(ssf_internal[2], src2)
ssf_internal := c1 * (ssrc + src1) * 0.5 + c2 * nz(ssf_internal[1], src1) + c3 * nz(ssf_internal[2], src2)
ssf_internal
// ---------- Main loop ----------
lib/filters/usf/Usf.md
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### Operation Count (Streaming Mode)
Universal Smooth Filter: adaptive-weight FIR that adjusts taps based on signal characteristics. O(N) per bar.
Ehlers Ultimate Smoother Filter (USF): 2-pole IIR low-pass filter with high-pass subtraction for zero-lag smoothing. Five FMA operations per bar.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Adaptive weight derivation | N | ~8 cy | ~240 cy (N=30) |
| Weighted sum FMA | N | ~5 cy | ~150 cy |
| Normalization | 1 | ~3 cy | ~3 cy |
| **Total (N=30)** | **2N+1** | — | **~393 cycles** |
| Input combination (3 taps) | 3 | ~4 cy | ~12 cy |
| Feedback (2 taps) | 2 | ~4 cy | ~8 cy |
| State update | 4 | ~1 cy | ~4 cy |
| **Total** | **9** | — | **~24 cycles** |
O(N) per bar. Adaptive weights computed per bar (no precomputation) because they depend on current signal level. ~393 cycles for N=30.
O(1) per bar. Coefficients derived from period parameter; precomputed. ~24 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Adaptive weight computation | Partial | Independent per element; vectorizable if no data dependency |
| Weighted sum FMA | Yes | Standard dot product |
| USF recursion | No | y[n] depends on y[n-1] and y[n-2] |
SIMD potential: ~100 cy for N=30 if adaptive weights vectorized.
Batch throughput: ~24 cy/bar.
| Metric | Score | Notes |
| :--- | :--- | :--- |
lib/filters/voss/Voss.md
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@@ -6,7 +6,7 @@
| **Inputs** | Source (close) |
| **Parameters** | `period` (default 20), `predict` (default 3), `bandwidth` (default 0.25) |
| **Outputs** | Single series (VOSS) |
| **Output range** | Tracks input |
| **Output range** | Oscillates around zero |
| **Warmup** | `period` bars |
| **Signature** | [voss_signature](voss_signature.md) |
@@ -86,25 +86,26 @@ The Voss predictor stage is an IIR filter with `Order` feedback taps, each weigh
### Operation Count (Streaming Mode)
Voss-McCartney 1/f noise filter: octave-cascade of N random sources, each updated probabilistically. O(N) per bar worst-case, O(1) amortized.
Ehlers Voss Predictive Filter: two-stage pipeline — 2-pole bandpass filter (Stage 1) + weighted feedback predictor (Stage 2). O(Order) per bar where Order = 3 × Predict.
| Operation | Count | Cost (cycles) | Subtotal |
| :--- | :---: | :---: | :---: |
| Bit-scan (which octave to update) | 1 | ~3 cy | ~3 cy |
| RNG sample + accumulate | 1 | ~8 cy | ~8 cy |
| Running sum update | 1 | ~2 cy | ~2 cy |
| **Total (amortized)** | **3** | — | **~13 cycles** |
| BPF: diff + 3-term FMA | 3 | ~4 cy | ~12 cy |
| Voss: weighted sum loop | Order | ~5 cy | ~45 cy (Order=9) |
| Voss: gain × filt − sumC | 2 | ~4 cy | ~8 cy |
| State update (shifts) | 4 | ~1 cy | ~4 cy |
| **Total (Order=9)** | **Order+9** | — | **~69 cycles** |
O(1) amortized per bar. Each bar updates exactly 1 octave source on average. ~13 cycles/bar amortized.
O(Order) per bar. Order = 3 × Predict; at defaults (Predict=3), Order=9. ~69 cycles/bar.
### Batch Mode (SIMD Analysis)
| Operation | Vectorizable? | Notes |
| :--- | :---: | :--- |
| Octave update scheduling | No | Bit-count branching; data-dependent |
| RNG generation | Partial | SIMD RNG (e.g., xoshiro SIMD) available but niche |
| BPF recursion | No | y[n] depends on y[n-1] and y[n-2] |
| Voss weighted sum | Partial | Inner loop vectorizable but short (Order=9) |
Amortized O(1) makes SIMD gains minimal. Batch throughput: ~13 cy/bar.
Batch throughput: ~69 cy/bar at defaults.
| Metric | Value |
|--------|-------|
lib/filters/wavelet/Wavelet.md
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@@ -7,14 +7,14 @@
| **Parameters** | `levels` (default 4), `threshMult` (default 1.0) |
| **Outputs** | Single series (Wavelet) |
| **Output range** | Tracks input |
| **Warmup** | 1 bar |
| **Warmup** | `2^levels` bars (default 16) |
### TL;DR
- The Wavelet Denoising Filter applies an *à trous* (with holes) Haar wavelet decomposition with soft thresholding to remove high-frequency noise fro...
- Parameterized by `levels` (default 4), `threshmult` (default 1.0).
- Output range: Tracks input.
- Requires 1 bar of warmup before first valid output (IsHot = true).
- Requires `2^levels` bars of warmup before first valid output (IsHot = true).
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
> "The wavelet transform is to the Fourier transform what a microscope is to a telescope: same math, different scale."