Returns & Time Series
Log returns aggregate across time, and their fat tails and volatility clustering are the stylized facts every later model must face.
Every pricing model starts by asking how prices change, and the honest answer begins with returns. Simple returns are intuitive percentages; log returns add across time, which is why statistics and models prefer them. Real return series refuse the normal template: autocorrelation is near zero at short lags, yet squared returns are strongly autocorrelated, producing volatility clustering, and the tails are fat, so extreme moves arrive far more often than a bell curve allows. Recognizing these stylized facts disciplines everything downstream, from the stochastic processes chosen next to the risk models built on them.