Results 1 to 1 of 1

Thread: Stationary process of time series

  1. #1
    Newbie
    Joined
    May 2010
    Posts
    3

    Stationary process of time series

    Say we have $\displaystyle X_t$ = $\displaystyle \sum_{j=1}^{q}(A_j cos\lambda_jt + B_j sin\lambda_jt)$ for t = 0,1,2...

    where $\displaystyle \lambda_1,....\lambda_q$ are constants and $\displaystyle A_1,...A_q,B_1,...B_q$ are independent, zero mean r.v's all with variance $\displaystyle \sigma^2$.

    I need to show that $\displaystyle X_t$ is a stationary process. I've already worked out the mean, but now I just need to show that Cov($\displaystyle X_t,X_{t+k}$) depends only on k, and is independent of t.

    Any help would be much appreciated.
    Attached Thumbnails Attached Thumbnails Stationary process of time series-untitled.bmp  
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Time Series weakly stationary
    Posted in the Advanced Math Topics Forum
    Replies: 0
    Last Post: Oct 18th 2010, 06:39 AM
  2. Testing an AR process to see if it's stationary
    Posted in the Advanced Statistics Forum
    Replies: 1
    Last Post: Feb 23rd 2010, 07:26 AM
  3. Replies: 0
    Last Post: Feb 18th 2010, 02:15 PM
  4. Stationary process
    Posted in the Business Math Forum
    Replies: 1
    Last Post: Sep 7th 2009, 07:33 PM
  5. Non-stationary time series
    Posted in the Advanced Statistics Forum
    Replies: 0
    Last Post: May 25th 2009, 07:21 AM

Search Tags


/mathhelpforum @mathhelpforum