[問題] 時間序列的問題 weak/strong stationary

[blackie0221 (扁我吧)]

Let Ｚt be strictly stationary white noise process
(t = ..., -2, -1, 0, 1, 2, ...)

(1)Ｘt = a + bＺt + cＺt-1
(2)Ｘt = Ｚ1cos(ct) + Ｚ2sin(ct)

我想知道的是如何判斷Ｘt是weak stationary or strictly stationary?

感恩!!

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推 kvincent:(2)的hint cos(A)cos(B)+sin(A)sin(B) = cos(A-B)
推 blackie0221:感謝樓上 這樣可以得到mu, sigma, cov都是stationary
→ blackie0221:但是光這樣好像還不是strict stationary
→ blackie0221:請教該如何進一步證明他是strict stationary?  謝謝
推 trml:你要算cov(Xt,Xt+h) 假如算出來的東西沒有t  就是stationary