Hands-On Machine Learning for Algorithmic Trading

The autoregressive conditional heteroskedasticity (ARCH) model

The ARCH(p) model is simply an AR(p) model applied to the variance of the residuals of a time series model that makes this variance at time t conditional on lagged observations of the variance. More specifically, the error terms, ε_t, are residuals of a linear model, such as ARIMA, on the original time series and are split into a time-dependent standard deviation, σ_t, and a disturbance, z_t, as follows:

An ARCH(p) model can be estimated using OLS. Engle proposed a method to identify the appropriate ARCH order using the Lagrange multiplier test that corresponds to the F-test of the ...