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https://github.com/mihakralj/QuanTAlib.git
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Miha Kralj
92709ef2ed
- Implemented Stochastic Oscillator (%K and %D) in Stoch.cs with streaming and batch processing capabilities. - Added validation tests for the Stochastic Oscillator in Stoch.Validation.Tests.cs, ensuring consistency with Skender.Stock.Indicators. - Created documentation for the Stochastic Oscillator in Stoch.md, detailing its mathematical formula, architecture, parameters, and common pitfalls. - Updated project file to include necessary numeric libraries for highest and lowest calculations.
105 lines
3.2 KiB
Markdown
105 lines
3.2 KiB
Markdown
# Detrended Price Oscillator (DPO)
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## Overview
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The **Detrended Price Oscillator (DPO)** removes the trend component from price data by displacing a Simple Moving Average (SMA), isolating short-term price cycles. Unlike most oscillators, DPO is not aligned to the latest price—it references a past SMA value to filter out long-term trends.
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## Formula
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```
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displacement = floor(period / 2) + 1
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DPO = price − SMA(period)[displacement bars ago]
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```
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Where:
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- **period** — SMA lookback window (default: 20)
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- **displacement** — number of bars the SMA is shifted backward
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- **SMA** — Simple Moving Average of the source series
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## Architecture
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```
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Source ──→ RingBuffer(period) ──→ SMA ──→ RingBuffer(displacement+1) ──→ DPO
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[running sum] [O(1)] [stores SMA history]
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```
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### Streaming (O(1) per bar)
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| Component | Role |
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|-----------|------|
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| `_smaBuffer` | `RingBuffer(period)` — maintains running sum for O(1) SMA via `Sum / period` |
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| `_smaHistory` | `RingBuffer(displacement + 1)` — stores past SMA values; `.Oldest` gives the displaced SMA |
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### Bar Correction
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Uses `Snapshot()` / `Restore()` on both RingBuffers for intra-bar updates (`isNew = false`).
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### Warmup
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`WarmupPeriod = period + displacement` — need `period` bars to compute the first SMA, then `displacement` more bars before the displaced SMA is available.
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## Performance Profile
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| Metric | Value |
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|--------|-------|
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| Time complexity | O(1) per bar (streaming) |
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| Space complexity | O(period + displacement) |
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| Allocations | Zero per update |
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| NaN handling | Last valid value substitution |
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| SIMD | Not applicable (displacement dependency) |
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## Usage
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```csharp
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// Streaming
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var dpo = new Dpo(period: 20);
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TValue result = dpo.Update(new TValue(time, price));
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// Event-based
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var source = new TSeries();
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var dpo = new Dpo(source, period: 20);
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// Batch
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TSeries results = Dpo.Batch(source, period: 20);
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// Span
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Dpo.Batch(sourceSpan, outputSpan, period: 20);
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```
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## Interpretation
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* **Zero Line Crossovers:**
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- DPO crosses above zero: Price is above the displaced moving average (short-term bullish)
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- DPO crosses below zero: Price is below the displaced moving average (short-term bearish)
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* **Cycle Identification:**
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- DPO peaks and troughs correspond to short-term price cycles
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- Distance between peaks estimates the dominant cycle period
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- Works best when the dominant cycle length approximates the DPO period
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* **Overbought/Oversold:**
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- Extreme DPO values suggest price has deviated significantly from its trend
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- No fixed bounds; context-dependent interpretation
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* **Divergence:**
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- Bullish: Price makes lower lows while DPO makes higher lows
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- Bearish: Price makes higher highs while DPO makes lower highs
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## Validation
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Cross-validated against:
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- **Tulip Indicators** (`dpo`) — exact match within 1e-9 tolerance
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- **Manual SMA computation** — independent verification of displaced SMA algorithm
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## Parameters
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| Parameter | Type | Default | Range | Description |
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|-----------|------|---------|-------|-------------|
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| `period` | int | 20 | > 0 | SMA lookback period |
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## References
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- William Blau, *Momentum, Direction, and Divergence*, 1995
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- Thomas Dorsey, *Point and Figure Charting*, 2007
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- PineScript reference: `dpo.pine`
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