Miha Kralj
90d5638008
- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
4.8 KiB
DX: Directional Movement Index
The Directional Movement Index is the raw, unsmoothed measure of trend strength from Wilder's directional movement system. It decomposes price expansion into +DM and -DM, normalizes against True Range using RMA smoothing to produce +DI and -DI, then computes the ratio DX = 100 \times |{+DI - {-DI}}| / ({+DI + {-DI}}). Unlike ADX, which applies a final RMA pass to DX, the raw DX responds immediately to changes in directional dominance — making it noisier but approximately one full period faster. Output ranges from 0 to 100, where high values indicate strong directional movement regardless of up/down direction. DX is the building block from which ADX is derived.
Historical Context
J. Welles Wilder Jr. introduced the complete Directional Movement System in New Concepts in Technical Trading Systems (1978). The system's pipeline produces several intermediate values — +DM, -DM, TR, +DI, -DI, DX — before reaching the final ADX. Most traders skip directly to ADX, but DX occupies a useful middle ground: it contains all the directional normalization logic (the hard part) without the final smoothing layer (which adds lag). For traders who can tolerate more noise in exchange for faster response, DX provides trend strength signals roughly N bars ahead of ADX. The tradeoff is straightforward: DX spikes on volatile bars and can produce false readings during whipsaw, while ADX absorbs these transients through its additional RMA pass.
Architecture & Physics
1. Directional Movement
\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. Wilder Smoothing (RMA)
All three series use Wilder's smoothing with \alpha = 1/N:
+DM_{\text{smooth}} = \text{RMA}(+DM, N)
-DM_{\text{smooth}} = \text{RMA}(-DM, N)
TR_{\text{smooth}} = \text{RMA}(TR, N)
4. Directional Indicators
+DI = 100 \times \frac{+DM_{\text{smooth}}}{TR_{\text{smooth}}}
-DI = 100 \times \frac{-DM_{\text{smooth}}}{TR_{\text{smooth}}}
5. DX (No Final Smoothing)
DX = 100 \times \frac{|+DI - (-DI)|}{+DI + (-DI)}
When +DI + (-DI) = 0 (no directional movement), DX = 0.
6. Complexity
- Time:
O(1)per bar — all RMA updates are recursive - Space:
O(1)— scalar state only - Warmup:
Nbars
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N |
period | 14 | N \geq 2 |
Pseudo-code
Initialize:
α = 1 / period
smoothPlusDM = smoothMinusDM = smoothTR = 0
prevHigh = prevLow = prevClose = NaN
On each bar (high, low, close, isNew):
if !isNew: restore previous state
// True Range
TR = max(high - low, |high - prevClose|, |low - prevClose|)
upMove = high - prevHigh
downMove = prevLow - low
+DM = (upMove > downMove AND upMove > 0) ? upMove : 0
-DM = (downMove > upMove AND downMove > 0) ? downMove : 0
// Wilder smoothing
smoothPlusDM = FMA(smoothPlusDM, 1 - α, α × +DM)
smoothMinusDM = FMA(smoothMinusDM, 1 - α, α × -DM)
smoothTR = FMA(smoothTR, 1 - α, α × TR)
// Directional Indicators
+DI = smoothTR > 0 ? 100 × smoothPlusDM / smoothTR : 0
-DI = smoothTR > 0 ? 100 × smoothMinusDM / smoothTR : 0
// DX (raw, no final RMA)
diSum = +DI + -DI
DX = diSum > 0 ? 100 × |+DI - -DI| / diSum : 0
prevHigh = high
prevLow = low
prevClose = close
output:
DX = DX // trend strength (0-100)
DiPlus = +DI // bullish directional indicator
DiMinus = -DI // bearish directional indicator
DX vs ADX
| Property | DX | ADX |
|---|---|---|
| Smoothing | RMA on components only | RMA on components + RMA on DX |
| Response | Immediate to bar-level changes | Lagged by \approx N bars |
| Noise | High; can spike on volatile bars | Low; smooth, stable signal |
| Use case | Fast trend detection, signal generation | Regime classification, filter |
Interpretation
| DX Value | Trend Strength |
|---|---|
| 0-15 | No meaningful trend |
| 15-25 | Developing trend |
| 25-50 | Strong trend |
| 50-75 | Very strong trend |
| 75-100 | Extreme (rare, usually transient) |
DX measures trend strength, not direction. Direction is determined by comparing +DI vs -DI: if +DI > -DI, the trend is up; if -DI > +DI, the trend is down. DI crossovers signal potential trend reversals.
Resources
- Wilder, J.W. — New Concepts in Technical Trading Systems (Trend Research, 1978)
- PineScript reference:
dx.pinein indicator directory