Editing Autoregressive model (section)

===AR(1)===
For AR(1)
: <math>S(f) = \frac{\sigma_Z^2}{| 1- \varphi_1 e^{-2 \pi i f} |^2}
     = \frac{\sigma_Z^2}{ 1 + \varphi_1^2 - 2 \varphi_1 \cos 2 \pi f }</math>
*If <math>\varphi_1 > 0</math>  there is a single spectral peak at <math>f=0</math>, often referred to as [[red noise]]. As <math>\varphi_1 </math>  becomes nearer 1, there is stronger power at low frequencies, i.e. larger time lags. This is then a low-pass filter, when applied to full spectrum light, everything except for the red light will be filtered.
*If <math>\varphi_1 < 0</math> there is a minimum at <math>f=0</math>, often referred to as [[blue noise]]. This similarly acts as a high-pass filter, everything except for blue light will be filtered.