Stylized Facts of Financial Time Series

"Stylized Facts" are empirical properties that are consistent across different markets, assets, and time periods. Any good financial model must account for these facts.

1. Absence of Autocorrelation in Returns

• Fact: Linear autocorrelation of asset returns is often insignificant (near zero).
• Implication: You cannot predict tomorrow's return based only on today's return. Markets are efficiently priced.

2. Heavy Tails (Fat Tails)

• Fact: The distribution of returns has fatter tails (high Kurtosis) than a Normal distribution.
• Implication: Crashes happen more often than you think.

3. Gain/Loss Asymmetry

• Fact: Large drawdowns (crashes) are more common than equally large upward rallies. The distribution is negatively skewed.

4. Aggregational Gaussianity

• Fact: As you increase the time scale (from daily to monthly to yearly), returns distribution looks more "Normal".
• Implication: Normal distribution is okay for long-term (annual) modeling, but bad for short-term (daily) risk.

5. Volatility Clustering

• Fact: Periods of high volatility are followed by high volatility; periods of low by low.
• Implication: Volatility is predictable, even if returns are not.

6. Leverage Effect

• Fact: Volatility increases more after negative returns than positive returns.

7. Volume/Volatility Correlation

• Fact: Trading volume is positively correlated with volatility. High volume days are usually high volatility days.

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