- #1
Ardla
- 5
- 0
Hi, can someone please provide some guidance on how i should go about finding the stationary distribution of:
[tex]X_t = [/tex] [tex] \rho X_{t-1} + \epsilon_t[/tex], [tex]X_0 = 0 [/tex]and [tex]|\rho|<1[/tex]
where [tex]\epsilon_1, \epsilon_2, \cdots[/tex] are all independent N(0,1)..
i have no idea what to do, so here's my attempt which i know to be completely wrong:
suppose,
[tex]Var(X_1) = \rho \sigma^2 < \infty [/tex]
[tex] Var(X_2) = \rho\sigma^2 + 1 [/tex]
[tex] \vdots [/tex]
[tex]Var(X_{n+1}) = \rho\sigma^2 + t [/tex]
As [tex] t \rightarrow \infty, Var(X_{n+1} = \rho \sigma^2 + t [/tex] ?
yeah I am very sure I am not doing it right... Can someone please help me out?
[tex]X_t = [/tex] [tex] \rho X_{t-1} + \epsilon_t[/tex], [tex]X_0 = 0 [/tex]and [tex]|\rho|<1[/tex]
where [tex]\epsilon_1, \epsilon_2, \cdots[/tex] are all independent N(0,1)..
i have no idea what to do, so here's my attempt which i know to be completely wrong:
suppose,
[tex]Var(X_1) = \rho \sigma^2 < \infty [/tex]
[tex] Var(X_2) = \rho\sigma^2 + 1 [/tex]
[tex] \vdots [/tex]
[tex]Var(X_{n+1}) = \rho\sigma^2 + t [/tex]
As [tex] t \rightarrow \infty, Var(X_{n+1} = \rho \sigma^2 + t [/tex] ?
yeah I am very sure I am not doing it right... Can someone please help me out?
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