More on CPS Signal Distortion
Posted by Jeff Id on August 26, 2009
I’ve been playing around with CPS some more and am trying to figure out how to correct for the signal de-amplification created by correlation based proxy sorting. As I have explained here Historic Hockey Stick – Pt 2 Shock and Recovery correlation does not respond linearly to noise. I’ve re-written that post several times to improve it so it reads completely differently than before. This post was created using the same 10000 ARMA simulated proxies as noise and adding a new signal with a square wave in the historic portion. By averaging the square wave which was spread over 200 years we can get a nice calculation of the signal magnitude. Figure 1 is the shape of the signal used.
Now to explore the effects of different noise levels on the ARMA data a multiplier was used from 0 – 1 in 0.01 steps. So each calculation used the Fig 1 signal + proxy * multiplier. This had the effect of adding noise levels from 0 to 1 times the proxy data. Since the proxy data had a standard deviation very close to 1 you can think of the multiplier as the standard deviation of the noise.
Since we have 101 individual CPS reconstructions of varying quality, a surface plot does a good job depicting the shape change in the recovered signal. The RMS axis is noise/signal because the plotting program needed ascending values. Each of the individual reconstructions is plotted on the time axis.
From Figure 2, the non-linearity of the response is apparent. The CPS method with no noise results in a perfect reconstruction and as noise level is increased the values appear to asymptotically drift toward a zero historic signal magnitude. This demonstrates that higher noise levels will result in a ‘more unprecedented’ calibration range signal.
So then I plotted the magnification factor of the signal recovery for each reconstruction in Figure 3.
This again clearly demonstrates the reasons why correlation cannot be used to sort proxy data for validity. All of the proxies used here had equal validity yet there is a serious distortion in both the historic and calibration range signal magnitudes. I’ll have more on this in the near future.
Just for fun, I learned how to make gif movies. Click to play, I think!