Take the 2-minute tour ×
Quantitative Finance Stack Exchange is a question and answer site for finance professionals and academics. It's 100% free, no registration required.

I have issues with this problem:

Let $\{X_t, t\in \Bbb N\}$ be a 2-state stationary Markov chain, with transition $M$ (and $M(1,2)\neq 0 \neq M(2,1)$), let $\{W_t, t\in \Bbb N\}$ be a strong Gaussian white noise.

Let $$ Y_t = b_{X_t} + \sigma_{X_t} W_t $$ How to prove that $\{Y_t, t\in \Bbb N\}$ is an ARMA(1,1) process?

share|improve this question

migrated from math.stackexchange.com May 8 at 14:17

This question came from our site for people studying math at any level and professionals in related fields.

    
I thought that cross-posting has to be avoided. –  mookid May 7 at 20:12
    
You're right, it should be avoided. We can try try get a moderator to migrate it if you want. –  joebloggs May 7 at 22:10
    
So you have a Markov chain $X_t$ and as you describe the transition matrix $M$ it is possible to go from state $1$ to $2$ and back. Is this really enough info to prove that $Y_t$ solves $Y_t = a Y_{t-1} + b W_{t-1} + W_t$, the ARMA(1,1) representation? –  Richard May 12 at 9:27
    
I think it is enough to prove that it is the stationnary solution of this equation, indeed. One way suggested seems to look at the ACF of $Y$. –  mookid May 13 at 21:20

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Browse other questions tagged or ask your own question.