Model prediction

Starting from an $ARMA$ process $y(t)=W(z)e(t)=\frac{C(z)}{A(z)}e(t)$, wehere $e(t) \sim WN(0,\lambda^2)$ (non zero mean case is an easy extension) we assume: $W(z)$ is asymptotically stable, and so…

Starting from an $ARMA$ process $y(t)=W(z)e(t)=\frac{C(z)}{A(z)}e(t)$, wehere $e(t) \sim WN(0,\lambda^2)$ we know that $y(t)$ is a steady state solution and $y(t) \sim MA(\infty)$, so: $$y(t) =…

The steady state solution of an $ARMA$ process can be obtained with a long k-step division of $C(z)$ and $A(z)$ seen as polynomial of $z$ performing only k-steps.…

In the real world we cannot measur the white noise, the only aviable information is the values of the process up to time $t$. We need to construct the white noise underlyning the generation of the…

Starting from an $ARMA$ process $y(t)=W(z)e(t)=\frac{C(z)}{A(z)}e(t)$, wehere $e(t) \sim WN(\mu,\lambda^2)$ that is canonical and minimum phase we need to compute the unbiased processes : $$…

Starting from an $ARMAX$ process $y(t)=\frac{B(z)}{A(z)}u(t-d)+\frac{C(z)}{A(z)}e(t)$, wehere $e(t) \sim WN(0,\lambda^2)$ and $\frac{C(z)}{A(z)}$ is canonical and minimum phase then we assume that…