Mandelbrot and Volatility Clustering: The Intuition behind GARCH

Large changes tend to be followed by large changes, small changes by small changes, observed Mandelbrot (1963). In other words, you get persistence in the amplitudes of price changes.

Such observations in financial time series have paved the way for models like ARCH (Engle, 1982) and GARCH (Bollerslev, 1986). These aim to describe volatility clustering and kurtosis. GARCH was one of the first models to take into account volatility clustering.

Rama Cont has written a paper on volatility clustering where he proposes an agent-based explanation for clustering based on investor inertia.