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102 lines
4.7 KiB
Markdown
102 lines
4.7 KiB
Markdown
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# PCHANNEL: Price Channel
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## Overview and Purpose
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The Price Channel is a simple volatility-based indicator that plots the highest high and the lowest low over a user-defined lookback period. It is very similar in concept and application to Donchian Channels. The channel visually represents the trading range of an asset over the specified period.
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A middle line, typically the average of the upper and lower channel lines, can also be plotted to serve as a mean reference.
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## Core Concepts
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* **Highest High:** The upper band represents the highest price reached during the lookback period.
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* **Lowest Low:** The lower band represents the lowest price reached during thelookback period.
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* **Trading Range:** The channel effectively shows the price extremes for the chosen period.
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* **Breakout Indication:** Prices moving above the upper channel or below the lower channel can signal potential breakouts and the start of new trends.
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## Common Settings and Parameters
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| Parameter | Default | Function | When to Adjust |
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| :-------- | :------ | :------- | :------------- |
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| Length | 20 | Lookback period for determining the highest high and lowest low. | Shorter lengths make the channel more reactive to recent price action; longer lengths create a wider, smoother channel representing longer-term ranges. |
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## Calculation and Mathematical Foundation
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**Simplified explanation:**
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1. For each bar, look back over the specified `Length`.
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2. Identify the absolute highest `high` price during that period. This forms the Upper Channel line.
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3. Identify the absolute lowest `low` price during that period. This forms the Lower Channel line.
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4. (Optional) The Middle Channel line is the average of the Upper and Lower Channel lines: `(Upper Channel + Lower Channel) / 2`.
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**Technical formula:**
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1. **Upper Channel:**
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`UpperChannel = Highest(High, Length)`
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2. **Lower Channel:**
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`LowerChannel = Lowest(Low, Length)`
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3. **Middle Channel (optional):**
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`MiddleChannel = (UpperChannel + LowerChannel) / 2`
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## Performance Profile
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### Operation Count (Streaming Mode, Scalar)
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Per-bar cost using monotonic deque optimization:
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| Operation | Count | Cost (cycles) | Subtotal |
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| :--- | :---: | :---: | :---: |
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| CMP | 4 | 1 | 4 |
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| ADD | 1 | 1 | 1 |
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| MUL | 1 | 3 | 3 |
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| **Total** | **6** | | **~8 cycles** |
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**Complexity**: O(1) amortized per bar monotonic deque maintains max/min efficiently.
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### Batch Mode (SIMD/FMA Analysis)
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Finding max/min over sliding windows has limited SIMD benefit:
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| Operation | Scalar Ops | SIMD Benefit | Notes |
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| :--- | :---: | :---: | :--- |
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| Max/Min update | 4 | 1× | Deque-based, sequential |
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| Middle band | 2 | 2× | ADD + MUL parallelizable |
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**Batch efficiency (512 bars):**
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| Mode | Cycles/bar | Total (512 bars) | Improvement |
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| :--- | :---: | :---: | :---: |
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| Scalar streaming | 8 | 4,096 | |
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| Partial SIMD | ~7 | ~3,584 | **~12%** |
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### Quality Metrics
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| Metric | Score | Notes |
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| :--- | :---: | :--- |
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| **Accuracy** | 10/10 | Exact max/min calculation |
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| **Timeliness** | 6/10 | Tracks past extremes, inherently lagging |
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| **Overshoot** | 10/10 | No overshootbands are actual price levels |
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| **Smoothness** | 5/10 | Bands move in discrete steps |
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## Interpretation Details
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* **Support and Resistance:** The upper band can act as resistance, and the lower band as support.
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* **Breakouts:**
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* A close above the Upper Channel suggests bullish strength and a potential upside breakout.
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* A close below the Lower Channel suggests bearish pressure and a potential downside breakout.
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* **Trend Identification:**
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* In an uptrend, prices may consistently touch or "ride" the Upper Channel.
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* In a downtrend, prices may consistently touch or "ride" the Lower Channel.
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* **Volatility:** The width of the channel can give an indication of volatility. Wider channels suggest higher volatility over the lookback period.
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* **"Turtle Trading" Strategy:** Price Channels (like Donchian Channels) were famously used in the "Turtle Trading" system, where breakouts from the channel were used as entry signals.
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## Limitations and Considerations
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* **Lag:** Like all indicators based on lookback periods, there's an inherent lag. The channel reflects past price action.
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* **Whipsaws:** In choppy, non-trending markets, breakouts can be false, leading to whipsaws.
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* **Parameter Choice:** The `Length` parameter is crucial. A length too short may generate many false signals, while one too long may miss timely entries.
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* **Not a Standalone System:** Best used in conjunction with other indicators (e.g., volume, trend indicators) or price action analysis for confirmation.
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## References
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* Donchian, R. D. (Various). (Conceptual basis for channel breakouts).
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* Faith, C. (2007). *Way of the Turtle*. McGraw-Hill. (Describes trading systems using similar channels).
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