Market Volatility and Planetary Harmonics #

Research Question #

Can planetary harmonics (aspects) be used as exogenous variables in GARCH models to improve prediction of market volatility?

Hypothesis #

Planetary harmonics, when included as exogenous variables in GARCH models, will not significantly improve out-of-sample volatility forecasting compared to standard GARCH models.

Background #

Financial astrologers claim that planetary aspects correlate with market volatility. This research rigorously tests this claim using GARCH models—the gold standard for volatility modeling—by including planetary aspects as exogenous variables.

Data Sources #

• Tick/Daily OHLC data: S&P 500, Bitcoin from Yahoo Finance or professional data feeds
• Swiss Ephemeris: For precise planetary positions and aspect calculations
• VIX data: For comparison volatility measures

Mathematical Methods #

1. GARCH models: Baseline volatility modeling
2. GARCH-X: GARCH with exogenous planetary variables
3. Model comparison: AIC, BIC, out-of-sample testing
4. Diebold-Mariano tests: Compare forecast accuracy

Implementation Plan #

Step 1: Data Collection #

• Download S&P 500 and Bitcoin daily data (20+ years)
• Calculate daily returns and squared returns
• Generate planetary aspect data for same period

Step 2: Aspect Encoding #

• Calculate all major aspects daily
• Create aspect strength indicators (using orbs)
• Encode as continuous or binary variables
• Generate harmonic strength measures

Step 3: GARCH Modeling #

• Fit baseline GARCH(1,1) model
• Fit GARCH-X with planetary exogenous variables
• Test various aspect combinations
• Compare model fit statistics

Step 4: Out-of-Sample Testing #

• Rolling window forecasting
• Calculate forecast error metrics
• Perform Diebold-Mariano tests
• Assess economic significance

Step 5: Robustness Checks #

• Test different GARCH specifications
• Try different markets/assets
• Vary aspect orb definitions

Expected Outputs #

• Model comparison statistics
• Out-of-sample forecast performance
• Visualization of volatility with aspects
• Economic significance assessment

Required Python Libraries #

pyswisseph
pandas
numpy
arch
statsmodels
yfinance
matplotlib
seaborn

Ethical Considerations #

• Clear disclaimer: not financial advice
• Report all tested specifications
• Honest reporting of negative results

Data Provenance #

Financial Data #

• Source: Yahoo Finance via yfinance API.
• Dataset: S&P 500 Historical Data.
• Link: https://finance.yahoo.com