QuanTAlib/lib/dynamics/dmx/Dmx.md

DMX: Directional Movement Index (Jurik)

Jurik's directional movement applies adaptive smoothing to DI lines, reducing whipsaws in the classic DMI framework.

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Single series (Dmx)
Output range	Varies (see docs)
Warmup	period bars
PineScript	dmx.pine

• The DMX is Mark Jurik's modernized overhaul of Wilder's Directional Movement system, replacing the sluggish RMA smoothing with the Jurik Moving Ave...
• Parameterized by period.
• Output range: Varies (see docs).
• Requires period bars of warmup before first valid output (IsHot = true).
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

The DMX is Mark Jurik's modernized overhaul of Wilder's Directional Movement system, replacing the sluggish RMA smoothing with the Jurik Moving Average (JMA) to achieve faster trend detection with superior noise rejection. The core directional movement logic (+DM, -DM, True Range) is preserved faithfully from Wilder, but the three parallel smoothing passes use JMA's adaptive bandwidth instead of RMA's fixed \alpha = 1/N. The result is a directional indicator that reacts 3-5 bars earlier to trend changes than standard DMI while filtering out more noise during consolidation. Output is the difference between smoothed directional indicators: DMX = DI^+ - DI^-, positive for uptrends and negative for downtrends.

Historical Context

Wilder's original ADX/DMI system (1978) is foundational but mathematically primitive — its RMA smoothing introduces substantial lag that delays trend detection. Jurik's contribution was recognizing that the directional movement decomposition itself is sound; only the smoothing pipeline needed upgrading. JMA is an adaptive filter that tracks signal closely during transitions (low lag) and smooths aggressively during stable periods (high noise reduction). This dynamic behavior means DMX signals trend changes significantly earlier than DMI without the whipsaw penalty typically associated with faster indicators. DMX is not available in standard TA libraries (TA-Lib, Skender, Tulip) since JMA is a proprietary algorithm. The QuanTAlib implementation uses its own JMA recreation.

Architecture & Physics

1. Directional Movement (Wilder's Original)

\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} -DM = \begin{cases} \text{DownMove} & \text{if DownMove} > \text{UpMove and DownMove} > 0 \\ 0 & \text{otherwise} \end{cases}

2. True Range

TR = \max(H_t - L_t,\; |H_t - C_{t-1}|,\; |L_t - C_{t-1}|)

3. JMA Smoothing (Replaces RMA)

Three parallel JMA filters replace Wilder's three RMA passes:

+DM_{\text{smooth}} = \text{JMA}(+DM, N) -DM_{\text{smooth}} = \text{JMA}(-DM, N) TR_{\text{smooth}} = \text{JMA}(TR, N)

4. Directional Indicators

DI^+ = 100 \times \frac{+DM_{\text{smooth}}}{TR_{\text{smooth}}}, \quad DI^- = 100 \times \frac{-DM_{\text{smooth}}}{TR_{\text{smooth}}}

5. DMX Output

DMX = DI^+ - DI^-

Positive values indicate bullish directional dominance; negative values indicate bearish.

6. Complexity

• Time: O(1) per bar — three JMA updates (each O(1))
• Space: O(1) — JMA maintains fixed-size internal state
• Warmup: \approx N bars (JMA converges faster than RMA)

Mathematical Foundation

Parameters

Symbol	Parameter	Default	Constraint
N	period	14	N \geq 2

DMX vs DMI Comparison

Property	DMI (Wilder)	DMX (Jurik)
Smoothing	RMA (\alpha = 1/N)	JMA (adaptive)
Lag	\approx N bars	\approx N/2 bars
Whipsaw rejection	Moderate	High
Available in TA-Lib	Yes	No
Overshoot	Low	Can overshoot in extreme volatility

Period Selection

Because JMA is more efficient than RMA, slightly longer periods (e.g., 20 instead of 14) can be used without incurring a lag penalty, producing smoother results while maintaining responsiveness.

Performance Profile

Operation Count (Streaming Mode)

DMX (Directional Movement Index) computes +DM and −DM only, without ADX smoothing — a lighter version of ADX.

Post-warmup steady state (per bar):

Operation	Count	Cost (cycles)	Subtotal
SUB × 4 (TR components + DM moves)	4	1	4
ABS × 2 (absolute TR components)	2	1	2
MAX × 2 (TR max)	2	1	2
CMP × 2 (DM directional guards)	2	1	2
FMA × 2 (RMA smooth +DM, −DM)	2	4	8
FMA × 1 (RMA smooth TR)	1	4	4
DIV × 2 (+DI, −DI from smoothed values)	2	15	30
MUL × 2 (scale to 100)	2	3	6
Total	19	—	~58 cycles

DMX skips the DX/ADX second smoothing phase. ~58 cycles per bar vs ~79 for full ADX.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
TR/DM computation	Yes	VSUBPD + VABSPD + VMAXPD + VCMPPD
RMA smoothing × 3	No	Recursive IIR — sequential
DI scaling	Yes	VDIVPD + VMULPD after RMA pass

Same constraint as ADX: the recursive RMA smoothing blocks cross-bar SIMD.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	FMA-precise Wilder smoothing
Timeliness	6/10	N-bar warmup only (vs 2N for ADX); responds faster
Smoothness	7/10	Single RMA layer; less smooth than full ADX
Noise Rejection	7/10	One smoothing pass sufficient for directional signals

Resources

• Wilder, J.W. — New Concepts in Technical Trading Systems (Trend Research, 1978)
• Jurik, M. — JMA adaptive smoothing methodology
• PineScript reference: dmx.pine in indicator directory