 Autoregressive conditional heteroscedasticity

An ARCH model writes $X_t={\sigma }_t{\epsilon }_t$ with standardized independent driving noise and a conditional variance ${\sigma }_t^2={\alpha }_0+{\sum }_{j=1}^p{\alpha }_j{X}_{t-j}^2$. Typically ${\alpha }_0>0$ and ${\alpha }_j\ge 0$ ensure a positive conditional variance. It allows a changing conditional scale even when $X$ is a stationary process.