Stylized facts are empirical features of financial return data

1. Lack of Autocorrelation in Returns Daily returns typically show little to no correlation with their past values.

2. Heavy Tails Return distributions exhibit more frequent extreme outcomes (both positive and negative) than would be expected under a normal distribution. This property is known as “heavy tails” or “leptokurtosis.” In practice, this means large losses or gains happen more often than simple models assume, which has implications for risk management.

3. Volatility Clustering
   Periods of high volatility tend to follow other high-volatility periods, and the same applies to low-volatility periods. Although returns themselves are not significantly correlated, the magnitude or intensity of returns tends to be. This persistence in volatility is known as volatility clustering, and it suggests that volatility is time-varying rather than constant.

4. Aggregational Gaussianity Although daily returns are not normally distributed, when returns are aggregated over longer time periods (such as weeks or months), their distribution tends to look more like a normal distribution.