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## #1 2016-09-14 00:49:56

Yoghurt
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### Concerning stationary time series

Okay, so I have this assignment in Time Series which I've tried working on for a day now. I really have a hard time grasping what they want us to do. The question is as follows.

" Suppose a person is recording the observations of a stationary time series {X_t} with zero mean and auto-covariance function gamma_x(h), h=1,2,3 ... . At each time t, with a probability p the person erroneously records the value of the process as zero instead of X_t. This happens independently for each time t and the prob. p does not vary over time. If the resulting series is {Y_t} (i.e., Y_t is 0 with prob. p and X_t with prob (1-p) for all t), show that

a) {Y_t} is covariance stationary - and
b) obtain gamma_y(h) in terms of p and gamma_x(h) for h=1,2,3 ..."

So I would assume that there is some sort of white noise in this, and that the proof would have to include that as well. Apart from that I am a little bit lost. Any help here?

PS: Subscript is denoted by _