A Comparison Between Econometric and Machine Learning Approaches to S&P 500 Volatility

We propose a supervised learning approach to predict the 21-day historical volatility of S&P 500 log returns over the past five years. GARCH models are presented, and a GARCH(1, 1) specification is used as a baseline. We consider log returns and squared log returns, along with their lags, as inputs to the machine learning models, and the 21-day historical volatility of S&P 500 log returns as the target variable. More than forty machine learning models are evaluated using the Python library "lazypredict", with ensemble tree-based algorithms emerging as the best-performing models according to several evaluation metrics.