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Proving a Time Series is White Noise and Stationary

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Suppose {e_t} and {E_t} are two independent white noise processes with variance sigma^2 and sigma^2_e respectively.

(a) Show that {v_t = e_tE_(t-1)} is also a white noise and calculate its variance.
(b) Show that y_t = v_t - 0.5_(vt-1) + 3e_(t-1) is stationary.

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The solution gives detailed steps on showing how to prove a given time series is white noise and stationary.

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