QuanTAlib/lib/cycles/solar/Solar.md

SOLAR: Solar Cycle Indicator

Solar cycles encode the Sun's rhythmic activity into a tradeable signal, bridging astrophysics and price action.

Property	Value
Category	Cycle
Inputs	Source (close)
Parameters	None
Outputs	Single series (SOLAR)
Output range	Varies (see docs)
Warmup	0 bars
PineScript	solar.pine

• SOLAR models Earth's seasonal position relative to the Sun using astronomical ephemeris calculations.
• No configurable parameters; computation is stateless per bar.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

SOLAR models Earth's seasonal position relative to the Sun using astronomical ephemeris calculations. Output oscillates continuously from -1.0 (Winter Solstice) through 0.0 (Equinoxes) to +1.0 (Summer Solstice), providing a smooth, mathematically precise seasonal phase for econometric modeling. Like LUNAR, the indicator is purely time-based, requires no price data, and has zero warmup since the calculation is deterministic from any timestamp.

Historical Context

Seasonal adjustments are fundamental to econometric analysis. Agricultural commodities, retail sales, energy consumption, and tourism all exhibit strong annual patterns. Traditional approaches use monthly dummy variables or calendar-based lookup tables, creating discontinuities at month boundaries. Astronomical seasonality offers a continuous, smooth alternative: the Sun's ecliptic longitude provides an exact phase position within the annual cycle at any time resolution. The implementation derives from Jean Meeus' Astronomical Algorithms (1998), computing the Sun's geometric mean longitude, mean anomaly, and equation of center with sufficient precision (\pm 0.01°) for financial applications. Unlike lunar cycles, the tropical year's length varies by only seconds over centuries, making solar seasonality highly predictable.

Architecture & Physics

1. Julian Date Conversion

JD = \frac{UnixMs}{86400000} + 2440587.5 T = \frac{JD - 2451545.0}{36525.0}

where T is Julian centuries from the J2000.0 epoch.

2. Geometric Mean Longitude

The Sun's mean position in its apparent orbit:

L_0 = 280.46646 + 36000.76983T + 0.0003032T^2

3. Mean Anomaly

Angular distance from perihelion:

M = 357.52911 + 35999.05029T - 0.0001537T^2

4. Equation of Center

Correction for orbital eccentricity (e \approx 0.0167):

C = (1.914602 - 0.004817T - 0.000014T^2) \sin M + (0.019993 - 0.000101T) \sin 2M + 0.000289 \sin 3M

5. True Ecliptic Longitude

\lambda_{Sun} = L_0 + C

6. Seasonal Index

Solar = \sin(\lambda_{Sun})

This maps: Vernal Equinox (\lambda = 0°) \to 0, Summer Solstice (\lambda = 90°) \to +1, Autumnal Equinox (\lambda = 180°) \to 0, Winter Solstice (\lambda = 270°) \to -1.

7. Complexity

O(1) per timestamp. No state required. Zero warmup. The tropical year is approximately 365.242 days.

Mathematical Foundation

Parameters

Parameter	Description	Default	Constraint
(none)	No user-configurable parameters

The calculation is entirely determined by the input timestamp.

Seasonal Correspondence (Northern Hemisphere)

Date (approx.)	\lambda_{Sun}	Solar Value	Season
March 20	0°	0.0	Vernal Equinox
June 21	90°	+1.0	Summer Solstice
September 22	180°	0.0	Autumnal Equinox
December 21	270°	-1.0	Winter Solstice

Output Interpretation

Condition	Meaning
Solar \approx +1	Peak summer (Northern Hemisphere)
Solar \approx -1	Peak winter (Northern Hemisphere)
Solar = 0 (rising)	Spring equinox crossing
Solar = 0 (falling)	Autumn equinox crossing
Southern Hemisphere	Negate the output

Performance Profile

Operation Count (Streaming Mode)

Operation	Count per bar	Notes
Julian date conversion	~4	1 DIV + 1 ADD + 1 SUB + 1 DIV
Horner polynomial (L0)	~5	2 FMA + 1 mod
Horner polynomial (M)	~5	2 FMA + 1 mod
SIN evaluations (equation of center)	~24	3 Math.Sin calls (~8 cycles each)
Equation of center arithmetic	~8	3 FMA chains + 2 ADD
True longitude addition	~1	1 ADD
Final SIN (seasonal index)	~10	1 degree-to-radian MUL + 1 Math.Sin
Total	~57	O(1) pure arithmetic; simpler than LUNAR

Batch Mode (SIMD Analysis)

Aspect	Assessment
SIMD vectorizable	Yes: fully stateless; each timestamp independent; Vector<double> applicable
Bottleneck	4 transcendental calls (3 SIN for equation of center + 1 final SIN); ~32 cycles
Parallelism	Full: no inter-bar dependencies; ideal for Vector<double> batch processing
Memory	O(0): zero state; pure function of timestamp
Throughput	Fastest cycle indicator; ~2× faster than LUNAR (fewer perturbation terms)

Resources

• Meeus, J. Astronomical Algorithms. 2nd ed., Willmann-Bell, 1998.
• USNO Astronomical Almanac. U.S. Government Publishing Office (annual reference for solstice/equinox verification).