My Math Forum Problems to find the cross spectrum of a time series system

 April 25th, 2015, 08:52 PM #1 Newbie   Joined: Apr 2015 From: Australia Posts: 1 Thanks: 0 Problems to find the cross spectrum of a time series system I'm looking for some advice to find the cross-spectrum for this system. $$y_t= r_t+\epsilon_t$$ $$r_t=\frac{\theta}{1-\psi z^{-1}}u_t$$ and the input is $$u_t=(1-\gamma z^{-1})w_t$$ $\epsilon_t$ and $w_t$ are both independent white noise signals with zero mean and independent variances and I'm looking for the cross_spectrum $G_{yu}(\omega)$ I've tried two ways, but the system configuration (the fact that there are two WN signals with different variances) confuses me and don't know how to proceed. First I tried to advance calculating the cross covariance, writing $r_t$ as an infinite summation $$r_t=u_t+\psi u_{t-1}+\psi^2 u_{t-2}+...$$ but don't how to include $\epsilon_{t}$ Also tried to use the identity $$G_{yu}=h(e^{-j\omega})G_x(\omega)$$ where $h(z^{-1})$ is the relationship between $y$ and $u$ and $G_u$ is the spectrum of $u$ but here don't know how to account for $w_t$ I would appreciate your advice on how to face this problem.

 Tags cross, find, problems, series, spectrum, system, time, time series

 Thread Tools Display Modes Linear Mode

 Similar Threads Thread Thread Starter Forum Replies Last Post lemgruber Physics 1 April 8th, 2015 04:23 AM omercano Applied Math 0 January 8th, 2015 12:30 PM sosjava Differential Equations 1 December 16th, 2014 04:59 PM Begtostudy Real Analysis 1 August 24th, 2010 02:32 PM FreaKariDunk Calculus 4 February 10th, 2010 09:59 PM

 Contact - Home - Forums - Cryptocurrency Forum - Top