Model classes
White noise
A white noise is a sequence of uncorrelated random variables with the same mean and the same vari...
Moving average processes
Given a zero mean white noise $e(t) \sim WN(0,\lambda^2)$ we define the moving average process o...
Auto regressive processes
AR processes Given a zero mean white noise $e(t) \sim WN(0, \lambda^2)$ then the stochastic proce...
Transfer function (digital filter)
A transfer function $W(z)=\frac{C(z)}{A(z)}$ is an operator that given a process $v(t)$ outputs t...
When ARMA is well defined?
Given the steady state output of the recursive equation defined by the transfer function $W(z)$ f...
Non steady state solutions
If we consider a stationary stochastic process $v(t)$ and an assintotically stable transfer func...
Weak (wide sense) characterization of ARMA
Given the ARMA process: $$y(t)=\frac{c_0+c_1z^{-1}+...+c_nz^{-n}}{1-a_1z^{-1}-...-a_mz^{-m}}e(t)=...
Non zero mean ARMA
Consider the ARMA process $y(t)=\frac{C(z)}{A(z)}e(t)$ where is a non zero mean white noise$e(t) ...
Auto regressive processes with exogenous input
With ARMA we model time-series: we analize the output of a system without observing any input. In...