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Miha Kralj
109 lines
4.4 KiB
Markdown
109 lines
4.4 KiB
Markdown
# MIDPOINT: Rolling Range Midpoint
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> *The center holds, but only for the window you're watching.*
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| Property | Value |
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| ---------------- | -------------------------------- |
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| **Category** | Core |
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| **Inputs** | Source (close) |
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| **Parameters** | `period` |
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| **Outputs** | Single series (Midpoint) |
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| **Output range** | Varies (see docs) |
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| **Warmup** | `period` bars |
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| **PineScript** | [midpoint.pine](midpoint.pine) |
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- Single-series rolling midpoint: `(Highest(V, N) + Lowest(V, N)) * 0.5`.
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- **Similar:** [MidPrice](../midprice/Midprice.md), [Midbody](../midbody/Midbody.md) | **Trading note:** (Highest+Lowest)/2 over period; simple support/resistance level.
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- Validated against TA-Lib, Skender, and Tulip reference implementations where available.
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Single-series rolling midpoint: `(Highest(V, N) + Lowest(V, N)) * 0.5`. Returns the center of the value range within a lookback window. TA-Lib compatible (`MIDPOINT` function). Unlike MIDPRICE which operates on separate High/Low bar channels, MIDPOINT operates on a single value series.
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## Historical Context
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The midpoint of a rolling range is one of the simplest channel-center calculations in technical analysis. It appears in virtually every charting platform as the baseline for range-based indicators. TA-Lib implements it as `MIDPOINT` (single series) vs `MIDPRICE` (dual H/L series). The distinction matters: MIDPOINT feeds any single-valued series through a rolling window, while MIDPRICE decomposes OHLC bars into separate high/low channels.
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## Architecture and Physics
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### 1. RingBuffer Pattern
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Uses a single `RingBuffer(period)` to store the last N values. On each update, the buffer provides `Max()` and `Min()` for the rolling window. This is self-contained with no external indicator dependencies.
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### 2. Data Flow
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```text
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Input(value) --> NaN guard --> RingBuffer.Add(v, isNew)
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(Max() + Min()) * 0.5
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Output
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```
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### 3. State Synchronization
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Uses the standard `_s` / `_ps` state local copy pattern for bar correction (`isNew = false`). The `RingBuffer.Add(v, isNew)` call handles rollback internally when `isNew` is false.
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## Mathematical Foundation
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### Midpoint Definition
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$$
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\text{MIDPOINT}(N) = \frac{\max(V_0, V_1, \ldots, V_{N-1}) + \min(V_0, V_1, \ldots, V_{N-1})}{2}
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$$
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### Equivalent Formulation
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$$
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\text{MIDPOINT}(N) = \min(V, N) + \frac{\text{range}(V, N)}{2}
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$$
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where $\text{range}(V, N) = \max(V, N) - \min(V, N)$.
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### Properties
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- **Bounded:** Always between the minimum and maximum of the window
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- **Idempotent on constants:** If all values equal $c$, midpoint equals $c$
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- **Lag:** Responds only when the max or min of the window changes
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## Performance Profile
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### Operation Count (Streaming Mode)
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| Operation | Count |
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|-----------|-------|
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| Comparison (Max scan) | $O(N)$ per update |
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| Comparison (Min scan) | $O(N)$ per update |
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| Addition | 1 |
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| Multiplication | 1 |
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| **Total** | $O(N)$ |
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### Batch Mode
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The span-based `Batch` method uses a single `RingBuffer` with linear scan for max/min. For large datasets, amortized cost is $O(N \cdot P)$ where $P$ is the period.
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### Quality Metrics
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| Metric | Score |
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|--------|-------|
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| Simplicity | 9/10 |
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| Responsiveness | 5/10 |
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| Smoothness | 3/10 |
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| SIMD potential | Low (sequential max/min dependency) |
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## Validation
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| Library | Function | Match | Notes |
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|---------|----------|-------|-------|
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| TA-Lib | `MIDPOINT` | Exact (1e-10) | Batch + Streaming + Span validated |
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## Common Pitfalls
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1. **Confusing MIDPOINT with MIDPRICE:** MIDPOINT takes a single value series; MIDPRICE takes separate High/Low channels from bars.
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2. **Window lag:** The midpoint only changes when the rolling max or min changes. It can remain flat for extended periods.
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3. **NaN propagation:** Implementation substitutes last-valid value for NaN/Infinity inputs to prevent corruption.
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4. **Period = 1:** Returns the input value unchanged (max = min = value).
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5. **Warmup:** First `period - 1` values use a partial window (fewer than N values).
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## References
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- TA-Lib `MIDPOINT` function documentation
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- Murphy, J. *Technical Analysis of the Financial Markets* (range-based indicators) |