feat(dynamics): add PlusDI, MinusDI, PlusDM, MinusDM indicators

Complete thin Dx-composition wrapper indicators with full test coverage:

- PlusDi/MinusDi: Directional Indicator wrappers (DiPlus/DiMinus from Dx)
- PlusDm/MinusDm: Directional Movement wrappers (DmPlus/DmMinus from Dx)
- Individual validation tests per indicator directory (TALib, Skender, bounds)
- Combined unit tests (DiDm.Tests.cs) and validation tests (DiDm.Validation.Tests.cs)
- Quantower wrappers + tests for all 4 indicators
- PineScript v6 implementations with compensated RMA
- Normalized .md documentation for all indicators and categories
- 182 tests passing, 0 failures
This commit is contained in:
Miha Kralj
2026-03-11 20:21:52 -07:00
parent 56b86bebfb
commit 33d20f2a18
437 changed files with 4589 additions and 2792 deletions
+2 -41
View File
@@ -1,5 +1,7 @@
# UBANDS: Ehlers Ultimate Bands
> *Ehlers' ultimate bands apply cycle-aware smoothing to define an envelope that resonates with dominant frequency.*
| Property | Value |
| ---------------- | -------------------------------- |
| **Category** | Channel |
@@ -107,47 +109,6 @@ $$
Cutoff frequency: approximately $f_c \approx 1/(2\pi n)$ cycles per bar. Rolloff: 12 dB/octave.
### Pseudo-code
```
function ubands(source[], period, multiplier):
// precompute USF coefficients
arg = sqrt(2) * pi / period
c2 = 2 * exp(-arg) * cos(arg)
c3 = -exp(-2 * arg)
c1 = (1 + c2 - c3) / 4
usf_prev1 = NaN, usf_prev2 = NaN
for each bar t:
s0 = source[t]
s1 = source[t-1] // or s0 if unavailable
s2 = source[t-2] // or s1 if unavailable
if usf not initialized:
usf = s0
else:
usf = (1 - c1)*s0 + (2*c1 - c2)*s1
- (c1 + c3)*s2 + c2*usf_prev1 + c3*usf_prev2
usf_prev2 = usf_prev1
usf_prev1 = usf
// RMS of residuals over window
sum_sq = 0, count = 0
for i = 0 to period-1:
r = source[t-i] - usf_at[t-i] // residual at bar t-i
if r is valid:
sum_sq += r * r
count += 1
rms = count > 0 ? sqrt(sum_sq / count) : 0
upper = usf + multiplier * rms
lower = usf - multiplier * rms
emit (upper, usf, lower)
```
### RMS vs Standard Deviation
Standard deviation measures dispersion around the mean: $\sigma = \sqrt{E[(X - \mu)^2]}$. RMS measures dispersion around zero: $\text{RMS} = \sqrt{E[X^2]}$. Since the residuals $r_t = P_t - \text{USF}_t$ are already deviations from the smooth centerline, RMS is the correct measure. When the mean of residuals is zero (as it approximately is for a well-fitted filter), RMS equals standard deviation.