Editing Colors of noise (section)

=== Lag(m) autocorrelation method (overlapped) ===
This method improves on the accuracy of the previous method and was introduced by Z. Chunlei, Z. Qi, Y. Shuhuana. Instead of using the lag(1) autocorrelation function the lag(m) correlation function is computed instead:<ref>{{Cite book |last1=Zhou Chunlei |last2=Zhang Qi |last3=Yan Shuhua |chapter=Power law noise identification using the LAG 1 autocorrelation by overlapping samples |date=August 2011 |pages=110–113 |title=IEEE 2011 10th International Conference on Electronic Measurement & Instruments |chapter-url=http://dx.doi.org/10.1109/icemi.2011.6037776 |publisher=IEEE |doi=10.1109/icemi.2011.6037776|isbn=978-1-4244-8158-3 }}</ref>

<math>R_m = \frac{\frac{1}{N}\sum_{t=1}^{N-m}(z_t - \bar z)*(z_{t+m} - \bar z)}
{\frac{1}{N}\sum_{t=1}^{N}{(z_t - \bar z)}^{2}}</math>

where <math>m</math> is the "lag" or shift between the time series and the delayed version of itself. A major difference is that <math>z_t </math> are now the averaged values of the original time series computed with a moving window average and averaging factor also equal to <math>m</math>. The value of <math>\delta </math> is computed the same way as in the previous method and <math>\delta < .25 </math> is again the criteria for a stationary process. The other major difference between this and the previous method is that the differencing used to make the time series stationary (<math>\delta < .25 </math>) is done between values that are spaced a distance <math>m</math> apart:

<math>z_1 = z_{1+m}-z_1, z_2 = z_{2+m} - z_2..., z_{N-m} = z_N - z_{N-m} </math>

The value of the power is calculated the same as the previous method as well.