Big moves tend to be followed by big moves (in either direction), and quiet periods tend to be followed by quiet periods. If you plot the S&P 500 or Bitcoin returns, you don’t see random scatter. You see pockets of chaos and pockets of calm.
But an ARCH model recognizes a pattern: Large errors tend to be followed by large errors of either sign. At its core, an ARCH(q) model says: Today's variance depends on the squared "shocks" (unexpected returns) from the previous q days. In simple terms: If the market has been crazy for the last week, tomorrow will probably also be crazy. arch models
[ \sigma_t^2 = \omega + \alpha_1 \epsilon_t-1^2 + \alpha_2 \epsilon_t-2^2 + ... + \alpha_q \epsilon_t-q^2 ] Big moves tend to be followed by big