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?
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
扫码加好友，拉您进群
全部版块
我的主页
收藏
