Exercise Solution 4.12

A stochastic process is covariance stationary if every segment of a given length has the same unconditional means, standard deviations and correlations (including autocorrelations and cross correlations) as every other segment of the same length. It is homoskedastic if the unconditional covariance matrix is the same for all terms of the stochastic process. Covariance stationarity implies homoskedasticity—just consider segments of length one and apply the definition of covariance stationarity. It does not imply conditional homoskedasticity—covariance stationarity says nothing about conditional distributions.