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Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et)...

Let {et} denote a white noise process from a normal distribution with E[et] = 0, Var(et) = σe2 and Cov(et, es) = 0 for t ≠ s.

Define a new time series {Yt} by Yt = et + 0.6 et -- 1 – 0.4 et – 2 + 0.2 et – 3.

1. Find E(Yt ) and Var(Yt ).

2. Find Cov(Yt , Yt – k) for k = 1, 2, ...

math   Statistics-And-Probability   
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2 EY t-2 0.2e E(e) 0 6 E (et 0 :ECet) 0 For all tVart Yt) 0 4) Varet (02) Varlet-s) Tf x Xi s are independer Von n dom hen Vam ables, i=l, 2,../ n/ ai Var 2 fow alu 2 156 00 t-3 L-K -3when eov (Yt, Yt-1 ) t- 2 t 0 6 Vare t -20 240 80 2 28 e When k 2 0 4e 0.2e t06et-304-4 0 2 e-5 0 4 Var (et-2) 0. 2 art 2 an ( et-32 0 280 e When K 3 0 4 e-g + 0 2 t- 6 t-4 0 2 Varle) when 4 Cav (Y, Y-A) t 3-4 + 0-6 et-5-0 . 4 e t-6 t 0.2 et-7) 0 aee and So on2 e. for k74

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