Miha Kralj
4.3 KiB
PLUS_DM: Plus Directional Movement
+DM captures the raw upward price extension, smoothed by Wilder's RMA — the building block before normalization to +DI.
| Property | Value |
|---|---|
| Category | Dynamic |
| Inputs | OHLCV bar (TBar) |
| Parameters | period (default 14) |
| Outputs | Single series |
| Output range | ≥ 0 (price units) |
| Warmup | period bars |
| PineScript | plusdm.pine |
- Plus Directional Movement outputs the Wilder-smoothed upward directional movement in price units.
- Similar: MinusDm, DX | Complementary: ATR for normalization | Trading note: Plus Directional Movement; raw upward price expansion before smoothing.
- Validated against TA-Lib and Dx equivalence.
Plus Directional Movement (+DM) measures the magnitude of upward price movement, smoothed using Wilder's method. Unlike +DI which normalizes by true range to produce a percentage, +DM outputs raw smoothed values in price units. +DM captures when the current bar's high exceeds the previous bar's high by more than the previous bar's low exceeds the current bar's low. It is the raw building block of the Directional Movement System — the unnormalized signal before division by True Range converts it to +DI.
Historical Context
J. Welles Wilder Jr. designed the Directional Movement System as a pipeline in New Concepts in Technical Trading Systems (1978). +DM is the first computational stage: a binary event detector that fires when upward range expansion dominates. Wilder's insight was that direction should be measured by range extension, not by close-to-close returns. A bar that pushes to a new high by more than it pushes to a new low registers as positive directional movement. The smoothed +DM series shows how much upward thrust is being sustained over the lookback period, in absolute price units.
Architecture & Physics
1. Plus Directional Movement (Raw)
\text{UpMove} = H_t - H_{t-1}, \quad \text{DownMove} = L_{t-1} - L_t
+DM = \begin{cases} \text{UpMove} & \text{if UpMove} > \text{DownMove and UpMove} > 0 \\ 0 & \text{otherwise} \end{cases}
Only one of +DM or -DM can be non-zero per bar — the dominant direction wins.
2. Wilder Smoothing (RMA)
+DM_{\text{smooth}} = \text{RMA}(+DM, N), \quad \alpha = 1/N
3. Complexity
- Time:
O(1)per bar — recursive RMA update - Space:
O(1)— scalar state only (delegates to Dx) - Warmup:
Nbars
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N |
period | 14 | N \geq 2 |
Interpretation
| +DM Behavior | Signal |
|---|---|
| Rising +DM | Increasing upward price extension |
| +DM > -DM | Upward movement exceeds downward movement |
| Zero +DM | No upward directional movement on the bar |
| Values scale with instrument | Compare within same instrument only |
+DM values are in price units and scale with the instrument. They cannot be compared across different instruments without normalization (which is what +DI provides).
Performance Profile
Operation Count (Streaming Mode)
+DM is a thin wrapper around Dx. The per-bar cost is identical to Dx (one property extraction after Dx completes its update).
Post-warmup steady state (per bar):
| Operation | Count | Cost (cycles) | Subtotal |
|---|---|---|---|
| Dx.Update (full pipeline) | 1 | 75 | 75 |
| Property extraction | 1 | 1 | 1 |
| Total | 2 | — | ~76 cycles |
Quality Metrics
| Metric | Score | Notes |
|---|---|---|
| Accuracy | 9/10 | Exact Dx delegation; FMA-precise RMA smoothing |
| Timeliness | 7/10 | N-bar warmup; responds to bar-level changes |
| Smoothness | 7/10 | Single RMA layer; moderate noise suppression |
| Noise Rejection | 7/10 | Wilder smoothing filters transient spikes |
Resources
- Wilder, J.W. — New Concepts in Technical Trading Systems (Trend Research, 1978)
- PineScript reference:
plusdm.pinein indicator directory