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
LUNAR: Lunar Phase Indicator
LUNAR calculates the Moon's illumination fraction using precise orbital mechanics from Jean Meeus' Astronomical Algorithms. Output ranges from 0.0 (New Moon) through 0.5 (Quarter) to 1.0 (Full Moon), providing a continuous astronomical cycle for research into potential lunar-correlated market behavior. The indicator is purely time-based, requires no price data, and has zero warmup since the calculation is deterministic from any timestamp.
Historical Context
Lunar cycles have guided human activity for millennia. The hypothesis that lunar phases influence human behavior—and by extension, financial markets—dates to early technical analysis and remains a subject of academic investigation. Some studies (Dichev & Janes, 2001; Yuan, Zheng & Zhu, 2006) find statistically significant correlations between lunar phases and market returns, while others dismiss such findings as data mining artifacts. Regardless of one's position, rigorous testing requires precise phase calculation. This implementation derives from Meeus' (1991) standard reference for computational positional astronomy, accounting for major orbital perturbations including the Moon's elliptical orbit (eccentricity e \approx 0.0549), solar perturbations, and nodal regression, achieving sub-degree accuracy sufficient for financial cycle research.
Architecture & Physics
1. Julian Date Conversion
Convert Unix timestamp to Julian centuries from J2000 epoch:
JD = \frac{UnixMs}{86400000} + 2440587.5
T = \frac{JD - 2451545.0}{36525.0}
2. Mean Orbital Elements
Polynomial series (Horner's method) compute five fundamental arguments:
L' = 218.3164477 + 481267.88123421T - 0.0015786T^2 + \frac{T^3}{538841}
D = 297.8501921 + 445267.1114034T - 0.0018819T^2 + \frac{T^3}{545868}
M = 357.5291092 + 35999.0502909T - 0.0001536T^2
M' = 134.9633964 + 477198.8675055T + 0.0087414T^2
F = 93.2720950 + 483202.0175233T - 0.0036539T^2
where L' = mean lunar longitude, D = mean elongation, M = solar mean anomaly, M' = lunar mean anomaly, F = lunar argument of latitude.
3. Perturbation Corrections
Major periodic terms correct the Moon's true longitude:
\Sigma = 6288.016 \sin M' + 1274.242 \sin(2D - M') + 658.314 \sin 2D + 214.818 \sin 2M' + 186.986 \sin M + 109.154 \sin 2F
\lambda_{Moon} = L' + \frac{\Sigma}{10^6}
4. Phase Angle
The angular separation between Moon and Sun:
\psi = \lambda_{Moon} - \lambda_{Sun}
5. Illumination Fraction
k = \frac{1 - \cos(\psi)}{2}
This gives 0.0 at New Moon (\psi = 0°) and 1.0 at Full Moon (\psi = 180°).
6. Complexity
O(1) per timestamp. No state required (deterministic from time). Zero warmup. The synodic period is approximately 29.53 days.
Mathematical Foundation
Parameters
| Parameter | Description | Default | Constraint |
|---|---|---|---|
| (none) | No user-configurable parameters |
The calculation is entirely determined by the input timestamp.
Pseudo-code
function LUNAR(timestamp):
// Julian date
JD ← timestamp_to_unix_ms / 86400000 + 2440587.5
T ← (JD - 2451545.0) / 36525.0
// Mean orbital elements (Horner evaluation)
Lp ← FMA(T, FMA(T, FMA(T, 1/538841, -0.0015786), 481267.88123421), 218.3164477)
D ← FMA(T, FMA(T, FMA(T, 1/545868, -0.0018819), 445267.1114034), 297.8501921)
M ← FMA(T, FMA(T, -0.0001536, 35999.0502909), 357.5291092)
Mp ← FMA(T, FMA(T, 0.0087414, 477198.8675055), 134.9633964)
F ← FMA(T, FMA(T, -0.0036539, 483202.0175233), 93.2720950)
// Normalize to [0°, 360°)
Lp, D, M, Mp, F ← mod(*, 360)
// Perturbation correction (6 major terms)
Σ ← 6288016·sin(Mp) + 1274242·sin(2D - Mp) + 658314·sin(2D)
+ 214818·sin(2Mp) + 186986·sin(M) + 109154·sin(2F)
λ_moon ← Lp + Σ / 1e6
// Solar longitude (simplified)
L0 ← 280.46646 + 36000.76983·T
M_sun ← 357.52911 + 35999.05029·T
λ_sun ← L0 + 1.9146·sin(M_sun) + 0.02·sin(2·M_sun)
// Phase angle and illumination
ψ ← λ_moon - λ_sun
k ← (1 - cos(ψ)) / 2
emit k // 0.0 = New Moon, 1.0 = Full Moon
Output Interpretation
| Value | Phase |
|---|---|
k \approx 0.0 |
New Moon |
k rising, < 0.5 |
Waxing Crescent |
k \approx 0.5 (rising) |
First Quarter |
k rising, > 0.5 |
Waxing Gibbous |
k \approx 1.0 |
Full Moon |
k falling, > 0.5 |
Waning Gibbous |
k \approx 0.5 (falling) |
Last Quarter |
k falling, < 0.5 |
Waning Crescent |
Resources
- Meeus, J. Astronomical Algorithms. 2nd ed., Willmann-Bell, 1998.
- Dichev, I.D. & Janes, T.D. "Lunar Cycle Effects in Stock Returns." Journal of Private Equity, 2001.
- Yuan, K., Zheng, L. & Zhu, Q. "Are Investors Moonstruck? Lunar Phases and Stock Returns." Journal of Empirical Finance, 2006.