Question: (a) Suppose xt is a weakly stationary time series with mean zero and with absolutely summable autocovariance function, (h), such that X h= (h) =

(a) Suppose xt is a weakly stationary time series with mean zero and with absolutely summable autocovariance function, γ(h), such that X∞

h=−∞

γ(h) = 0.

Prove that √n x¯ p

→ 0, where ¯x is the sample mean (1.32).

(b) Give an example of a process that satisfies the conditions of part (a). What is special about this process?

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