Methods to extract signal from three very noisy time series of same event I have three time series of same length, all containing magnitude measurements of the same event "A". But each time series is using a different method of measurement.
My goal is to merge the three time series into a single one, so that I can more easily find the "upward" and "downward" phases. (Like a smooth sinus-curve or binary data-set 1=up, 0=down.)
For instance, as you can see the "raw" measurement data is very noisy and looks like this for measurement system number 3:

To get a better understanding of the data I have used a Moving Average (window length 2000) to smooth the time series data for each measurement system 1 - 3, which yields the following figure:

Since they are measurements of the same event, and often have their peaks and valleys at similar times, I would like to merge the three time series into a single time series, with as little noise as possible. What methods should I try? I'm open to try anything!
I have tried using Fourier analysis (FFT in the SciPy package), but I cannot find any significant frequencies in any part of the data.
[edit for Whuber's comment] I unfortunately only have access to the MA smoothed data for all three, which has the following statistics (using DataFrame.describe() function):

*

*MA_measurement 1: mean 0.991957, std 0.156941

*MA_measurement 2: mean -0.000003, std 0.000016

*MA_measurement 3: mean -0.000800, std 0.000856

And using DataFrame.corr() to get the correlations between the (smoothed) measurement systems:
$$\begin{array}{c|c|c|c|} 
 & \text{MA_meas3} & \text{MA_meas2} & \text{MA_meas1} \\ \hline
\text{MA_meas3} & 1.000000 & 0.337050 & 0.297922\\ \hline
\text{MA_meas2} & 0.337050 & 1.000000 & 0.807282 \\ \hline
\text{MA_meas1} & 0.297922 & 0.807282 & 1.000000 \\ \hline
\end{array}$$
For the unsmoothed (i.e. "raw") data I only have data for time series number 2 and 3:

*

*measurement 2: mean -0.000003, std 0.000747

*measurement 3: mean -0.000812, std 0.022399

And they have a correlation of Corr(meas2,meas3)=0.027199.
[edit 2] I have been able to get hold of the the MA data shown in the second graph (i.e. 3 subplots), hope this can be of use!
MA data measurement 1
MA data measurement 2
MA data measurement 3
[edit 3] To elaborate on Matt F.'s comment: I hope to find around 33 upward and downward phases in total (peaks + troughs) in each MA measurement series (see edit 2) of event A. In theory it should be cyclical, i.e. up -> down -> up -> down... etc.

I would apply PCA to three series, then assess how much variance is explained by the first principal component. If it is very high, then use the PC1 as your signal. The PCA transforms your three signals into three orthogonal linear combinations of signals in decreasing order of variance. So, your first principal component can be seen as an average level of three signals. If PCA works very well, then PC1 will explain the most variance in the data
You may need to mess with phase differences, depending on how the measurements were done. For instance, if it's three microphones picking up the source, then sound waves reach with a lag. This can easily be taken care of with coherence/phase shift analysis. Once you identify the phase shifts, it's still the same PCA but with appropriate lags
