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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.
124 lines
4.3 KiB
Markdown
124 lines
4.3 KiB
Markdown
# AC: Acceleration Oscillator
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> "Knowing speed is useful. Knowing whether you're speeding up or slowing down is what keeps you alive."
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## Introduction
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The Acceleration Oscillator (AC) is Bill Williams' second-derivative momentum indicator. Where the Awesome Oscillator (AO) measures the speed of market momentum, AC measures whether that momentum is accelerating or decelerating. AC is computed as AO minus a 5-period SMA of AO. Zero crossings and color changes signal shifts in market driving force before price reverses.
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## Historical Context
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Bill Williams introduced AC alongside AO in his "Trading Chaos" methodology. While AO already strips trend by subtracting a slow SMA from a fast SMA (both applied to the bar midpoint), traders found they needed earlier warning of momentum shifts. AC provides exactly that: the rate of change of AO itself. When AC crosses zero from below, the market's driving force is accelerating upward, often preceding AO's own zero crossing by several bars.
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## Calculation
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The AC indicator is calculated in two stages:
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### Stage 1: Awesome Oscillator
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$$\text{Median Price} = \frac{\text{High} + \text{Low}}{2}$$
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$$\text{AO} = \text{SMA}(\text{Median Price}, \text{fast}) - \text{SMA}(\text{Median Price}, \text{slow})$$
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### Stage 2: Acceleration
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$$\text{AC} = \text{AO} - \text{SMA}(\text{AO}, \text{acPeriod})$$
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Default parameters: fast = 5, slow = 34, acPeriod = 5.
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## Interpretation
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- **AC > 0 and rising (green):** Bullish acceleration. Momentum is strengthening.
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- **AC > 0 and falling (red):** Bullish deceleration. Momentum still positive but weakening.
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- **AC < 0 and falling (green to red):** Bearish acceleration. Momentum is weakening further.
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- **AC < 0 and rising (red to green):** Bearish deceleration. Downward momentum is weakening.
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- **Zero crossings:** Often precede AO zero crossings, providing earlier entry/exit signals.
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### Bill Williams' Trading Rules
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1. **Buy signal:** AC is green (rising) for two consecutive bars above zero, or three consecutive green bars below zero.
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2. **Sell signal:** AC is red (falling) for two consecutive bars below zero, or three consecutive red bars above zero.
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## Parameters
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| Parameter | Default | Range | Description |
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| :-------- | :------ | :---- | :---------- |
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| fastPeriod | 5 | > 0 | Fast SMA period for AO calculation |
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| slowPeriod | 34 | > fast | Slow SMA period for AO calculation |
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| acPeriod | 5 | > 0 | SMA period applied to AO values |
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## API
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### Streaming
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```csharp
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var ac = new Ac(fastPeriod: 5, slowPeriod: 34, acPeriod: 5);
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TValue result = ac.Update(bar, isNew: true);
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```
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### Batch (TBarSeries)
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```csharp
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TSeries results = Ac.Batch(barSeries);
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```
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### Batch (Span)
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```csharp
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Ac.Batch(highSpan, lowSpan, outputSpan, fastPeriod: 5, slowPeriod: 34, acPeriod: 5);
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```
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### Calculate
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```csharp
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var (results, indicator) = Ac.Calculate(barSeries, fastPeriod: 5, slowPeriod: 34, acPeriod: 5);
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```
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## Usage
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```csharp
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// Streaming
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var ac = new Ac();
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foreach (var bar in bars)
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{
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var result = ac.Update(bar);
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if (ac.IsHot && result.Value > 0)
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{
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// Bullish momentum accelerating
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}
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}
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// Event-driven chaining
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ac.Pub += (sender, e) => Console.WriteLine($"AC: {e.Value.Value:F4}");
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```
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## Performance
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| Operation | Complexity | Allocations |
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| :-------- | :--------- | :---------- |
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| Update (streaming) | O(1) | Zero |
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| Batch (Span) | O(n) | ArrayPool |
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| Warmup period | slow + ac - 1 | — |
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AC uses three internal SMA instances. Each SMA uses a RingBuffer for O(1) sliding window computation. The Batch path uses SIMD-accelerated subtraction via `SimdExtensions.Subtract`.
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## Validation
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AC is validated via self-consistency (AC = AO - SMA(AO, acPeriod)) and batch/streaming equivalence. No external library implements AC with identical SMA methodology for cross-library validation.
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| Test | Status |
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| :--- | :----- |
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| AC = AO - SMA(AO) identity | Pass |
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| Batch/streaming match | Pass |
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| Span/TBarSeries match | Pass |
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| Determinism | Pass |
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| Constant input convergence | Pass (→ 0) |
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| Large dataset stability | Pass (5000 bars) |
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## Sources
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- Williams, Bill. "Trading Chaos." Wiley, 1995.
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- Williams, Bill. "New Trading Dimensions." Wiley, 1998.
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- [Investopedia: Accelerator Oscillator](https://www.investopedia.com/terms/a/accelerationdeceleration-indicator.asp)
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- [TradingView: AC](https://www.tradingview.com/support/solutions/43000501837-accelerator-oscillator-ac/)
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