Let {Xt : t ∈ Z} be a covariance stationary process that satisfies: Xt + Xt−1 = Zt , where EZt = 0, EZ 2 t = σ 2 ≥ 0, and EZtZs = 0 for all t, s ∈ Z and t 6= s. Show that the only possible stationary solution of this process is Xt = (−1)sXt−1
Let {Xt : t ∈ Z} be a covariance stationary process that satisfies: Xt + Xt−1 = Zt , where EZt = 0, EZ 2 t = σ 2 ≥ 0, and EZtZs = 0 for all t, s ∈ Z and t 6= s. Show that the only possible stationary solution of this process is Xt = (−1)sXt−1
Let {Xt : t ∈ Z} be a covariance stationary process that satisfies: Xt + Xt−1 = Zt , where EZt = 0, EZ 2 t = σ 2 ≥ 0, and EZtZs = 0 for all t, s ∈ Z and t 6= s. Show that the only possible stationary solution of this process is Xt = (−1)sXt−1
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Let {Xt : t ∈ Z} be a covariance stationary process that satisfies: Xt + Xt−1 = Zt , where EZt = 0, EZ 2 t = σ 2 ≥ 0, and EZtZs = 0 for all t, s ∈ Z and t 6= s. Show that the only possible stationary solution of this process is Xt = (−1)sXt−1
Definition Definition Measure of how two random variables change together. Covariance indicates the joint variability or the directional relationship between two variables. When two variables change in the same direction (i.e., if they either increase or decrease together), they have a positive covariance. When the change is in opposite directions (i.e., if one increases and the other decreases), the two variables have a a negative covariance.
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