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各位前辈帮帮忙啊~~！！刚学经济学不久，老师出的两道题一点头绪都没有，各位兄弟姐妹知道的帮帮忙，告诉我怎么做啊。给我点提示也可以的啊~~谢谢啦！我怕我翻译的不好，中英文都放在上面了！谢谢谢谢谢谢了！！！！！！！
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1. X为随机变量，关于0对称分布，方差为σ2 。若Xt =(-1)tX .证明随机过程Xt   协方差平稳。
1. Let X be a random variable which is symmetrically distributed about 0, with
variances σ2 . If Xt =(-1)tX , prove that the stochastic process Xt is covariance
stationary.



2.使X，Z为两个独立白噪音过程。试说明时间序列Y=X+Z的性质。若X,Z在滞后一项相关，则Y是什么性质的时间序列？
2. Let X and Z be two independent white noise processes. What can you say about the
time series properties of the process Y = X + Z? How will your answer change if the
processes X and Z are correlated at lag one?

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关键词：Time Series Independent distributed Correlated stationary 请教 前辈

怕大家看的不清楚，
Xt =(-1)tX  里面第一个t是下角标，第二个t是上角标，指数。 谢啦！

不会，帮顶好了。

1,to prove covariance stationarity.you need to show (1)E(Xt)=constant, this is garanteed by X is symmetric dist. (2) Cov(Xt,Xt-j)=gamma(j),this is true, since if j is odd, its negativesigma square,otherwise, it is sigma square; (3) finite varaiance, true by X has variance sigma square.
2, The answer depends on what " X and Z are correlated at lag one" means. I dont know whether it means X t is correlated with Zt-1, or Xt is correlated with Xt-1

thank you! 3# sillymoon

4# cbqywl

X t is correlated with Zt-1

大哥谢啦~~那第二题该怎么做呢？