mirror of
https://github.com/mihakralj/QuanTAlib.git
synced 2026-08-09 14:30:56 +00:00
Miha Kralj
119 lines
4.8 KiB
Markdown
119 lines
4.8 KiB
Markdown
# PIVOTFIB: Fibonacci Pivot Points
|
||
|
||
> *Fibonacci pivots project support and resistance from the golden ratio, blending numerology with price structure.*
|
||
|
||
| Property | Value |
|
||
| ---------------- | -------------------------------- |
|
||
| **Category** | Reversal |
|
||
| **Inputs** | OHLCV bar (TBar) |
|
||
| **Parameters** | None |
|
||
| **Outputs** | Single series (PIVOTFIB) |
|
||
| **Output range** | Varies (see docs) |
|
||
| **Warmup** | `2` bars |
|
||
| **PineScript** | [pivotfib.pine](pivotfib.pine) |
|
||
|
||
- Fibonacci Pivot Points apply Fibonacci retracement ratios (38.2%, 61.8%, 100%) to the standard pivot point formula.
|
||
- No configurable parameters; computation is stateless per bar.
|
||
- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
|
||
|
||
## Overview
|
||
Fibonacci Pivot Points apply Fibonacci retracement ratios (38.2%, 61.8%, 100%) to the standard pivot point formula. The central pivot (PP) uses the classic HLC/3 calculation, while support and resistance levels are derived by adding or subtracting Fibonacci proportions of the previous bar's trading range.
|
||
|
||
## Origin and Sources
|
||
- **Concept**: Adaptation of Leonardo Fibonacci's ratios (derived from the Fibonacci sequence) to traditional pivot point analysis
|
||
- **Foundation**: Standard pivot points combined with Fibonacci retracement levels (0.382, 0.618, 1.000)
|
||
|
||
## Formula
|
||
|
||
Using previous bar's High (H), Low (L), Close (C):
|
||
|
||
```
|
||
PP = (H + L + C) / 3
|
||
range = H - L
|
||
|
||
R1 = PP + 0.382 × range S1 = PP - 0.382 × range
|
||
R2 = PP + 0.618 × range S2 = PP - 0.618 × range
|
||
R3 = PP + 1.000 × range S3 = PP - 1.000 × range
|
||
```
|
||
|
||
### Known Values Example
|
||
For H = 110, L = 90, C = 100:
|
||
- PP = 100.0, range = 20
|
||
- R1 = 107.64, S1 = 92.36
|
||
- R2 = 112.36, S2 = 87.64
|
||
- R3 = 120.00, S3 = 80.00
|
||
|
||
## Key Properties
|
||
- **Symmetry**: R_n - PP = PP - S_n for all levels
|
||
- **Level ordering**: S3 < S2 < S1 < PP < R1 < R2 < R3 (when range > 0)
|
||
- **Fibonacci ratios**: Distances from PP are proportional to 0.382, 0.618, and 1.000 of the range
|
||
- **Golden ratio relationship**: 0.618 ≈ φ - 1, where φ = (1 + √5) / 2; 0.382 = 1 - 0.618
|
||
|
||
## Usage
|
||
```csharp
|
||
// Streaming
|
||
var fib = new Pivotfib();
|
||
var result = fib.Update(bar);
|
||
double pp = fib.PP;
|
||
double r1 = fib.R1; // 38.2% resistance
|
||
double r2 = fib.R2; // 61.8% resistance
|
||
double r3 = fib.R3; // 100% resistance
|
||
double s1 = fib.S1; // 38.2% support
|
||
double s2 = fib.S2; // 61.8% support
|
||
double s3 = fib.S3; // 100% support
|
||
|
||
// Batch
|
||
var results = Pivotfib.Batch(bars);
|
||
|
||
// All 7 levels at once
|
||
Pivotfib.BatchAll(high, low, close, ppOut, r1Out, s1Out, r2Out, s2Out, r3Out, s3Out);
|
||
```
|
||
|
||
## Comparison with Other Pivot Variants
|
||
|
||
| Variant | R/S Formula | Levels | Ratios Used |
|
||
|---------|------------|--------|-------------|
|
||
| **PIVOT** (Classic) | Arithmetic from PP | 7 | 1×, 2× range |
|
||
| **PIVOTFIB** | Fibonacci × range | 7 | 0.382, 0.618, 1.000 |
|
||
| **PIVOTCAM** (Camarilla) | Close ± ratio × range | 9 | 1.1/12 series |
|
||
| **PIVOTEXT** (Extended) | Arithmetic extended | 11 | 1×–4× range |
|
||
| **PIVOTDEM** (DeMark) | Conditional X/4 | 3 | Direction-based |
|
||
|
||
|
||
## Performance Profile
|
||
|
||
### Operation Count (Streaming Mode)
|
||
|
||
PivotFib computes PP and 6 Fibonacci S/R levels from previous bar's HLC — O(1) pure arithmetic.
|
||
|
||
| Operation | Count | Cost (cycles) | Subtotal |
|
||
| :--- | :---: | :---: | :---: |
|
||
| Store prev bar HLC | 3 | 1 cy | ~3 cy |
|
||
| PP = (H + L + C) / 3 | 1 | 2 cy | ~2 cy |
|
||
| range = H - L | 1 | 1 cy | ~1 cy |
|
||
| R1/S1 via FMA (0.382 * range) | 2 | 1 cy | ~2 cy |
|
||
| R2/S2 via FMA (0.618 * range) | 2 | 1 cy | ~2 cy |
|
||
| R3/S3 = PP +/- range | 2 | 1 cy | ~2 cy |
|
||
| NaN guard + state update | 1 | 2 cy | ~2 cy |
|
||
| **Total** | **O(1)** | — | **~14 cy** |
|
||
|
||
Pure O(1) arithmetic on previous-bar data. Fibonacci multipliers 0.382 and 0.618 are precomputed constants; FMA fuses multiply-add into a single instruction.
|
||
|
||
### Batch Mode (SIMD Analysis)
|
||
|
||
| Operation | Vectorizable? | Notes |
|
||
| :--- | :---: | :--- |
|
||
| PP computation | Yes | Vector<double> (H+L+C)/3 across all bars |
|
||
| Range calculation | Yes | Vector subtract H-L |
|
||
| Fibonacci level projection | Yes | FMA with broadcast constants 0.382, 0.618 |
|
||
| All 7 output spans | Yes | Full SIMD pass — no data dependencies |
|
||
|
||
Excellent SIMD candidate — all 7 output levels are independent. BatchAll span overload processes 4 bars per AVX2 cycle. Expected 4× throughput vs scalar.
|
||
|
||
## Implementation Details
|
||
- **WarmupPeriod**: 2 bars (need previous bar's HLC)
|
||
- **Parameters**: None
|
||
- **Outputs**: 7 (PP, R1, R2, R3, S1, S2, S3)
|
||
- **Input**: TBar (OHLCV)
|
||
- **Complexity**: O(1) per bar
|
||
- **Uses FMA**: `Math.FusedMultiplyAdd` for R1/S1/R2/S2 computations |