ABM: Stylized Facts of Financial Returns

What does "heavy tails" mean in financial returns?

Large price changes happen more often than predicted by a normal distribution (leptokurtosis).

What mathematical pattern describes heavy tails?

Power-law decay: P(|r| > x) ~ x^(-α), with α ≈ 3.

What is volatility clustering?

Periods of high volatility tend to be followed by more high-volatility periods; volatility is persistent over time.

Do raw returns show autocorrelation?

No, raw returns have near-zero autocorrelation, showing weak-form efficiency.

What shows positive autocorrelation in financial data?

Absolute returns (|rt|) or squared returns (rt²) show positive autocorrelation, decaying slowly.

What is aggregational Gaussianity?

At longer time scales, aggregated returns become closer to Gaussian (normal distribution) due to the Central Limit Theorem.

What are scaling laws in financial markets?

Trading volume, volatility, and returns follow power-law distributions, showing similar patterns across scales.

What is the typical formula for returns?

rt = ln(pt) - ln(p_{t-1}), the log difference between current and previous price.

What does weak-form efficiency mean?

Past returns do not help predict future returns; markets quickly incorporate information.

Why are stylized facts important?

They challenge simple Gaussian models and motivate models like GARCH, stochastic volatility, and agent-based models.