= Solution
Two useful features of <autoregressive conditional heteroscedasticity> are \b[persistent changes in conditional scale] and \b[excess unconditional <kurtosis>]. Its time-varying <conditional variance> can explain <volatility clustering>, where large absolute returns occur in groups even when signed returns have little <autocorrelation>. A homoscedastic <autoregressive moving-average model> has a fixed innovation <variance>.
Also, a conditional <normal distribution> with a random scale is a <Gaussian scale mixture>. Its unconditional <kurtosis> can exceed $3$, or its <fourth moment> can be infinite. A Gaussian <autoregressive moving-average model> remains jointly Gaussian and cannot reproduce this effect. In the particular <lag-two ARCH process>, persistence of the squared scale occurs within each parity subsequence; the two parity subsequences are independent.
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