Say what autoregressive conditional heteroskedasticity (ARCH) is and show how ARCH models help forecast a time series' variance
The idea
Autoregressive conditional heteroskedasticity means the variance of a model's error in one period depends on the size of past errors, so calm and turbulent periods cluster. Test for ARCH(1) by regressing the squared residuals on their lagged values: ε²(t) = a0 + a1ε²(t − 1) + u(t). A significant a1 means ARCH is present, making the standard errors of the original model unreliable; they then need a correction for heteroskedasticity, such as robust standard errors. The ARCH equation also predicts next period's variance: a0 + a1 times the square of the latest residual. Common slips are to use the unsquared residual, or to assume that no autocorrelation in the residuals rules out ARCH.
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