Project Christy ACFs
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[edit] 1 Autocovariance functions
I used Matlab's 'xcorr' function to create the autocovariance functions for these data. I subtracted the mean and chose the 'unbiased' option (ACF = xcorr(data-mean(data),'unbiased'). I then plotted against time.
Image:ACF V1.pngImage:ACF V2.png
Figure 1: Above are the autocovariance functions for the velocity of the two data sets. The left panel is the longer, Roberts and Goldstein set, while the right shows the shorter Set #2. Both ACFs show periodicities of 26 days. The amplitude of the R&G data is greater, but other than that, the ACFs are strikingly similar. They do not show evidence of a 34-day period, and the peaks get larger with time.
Image:ACF B1.pngImage:ACF B2.png
Figure 2: This figure shows the autocovariance functions for the magnetic field of the data sets. R&G's data is again on the left. These ACFs are clearly more complicated than the velocity ACFs, but their main period is still the 26-day cycle. However, these data also show a 34-day period quite clearly, as well as other smaller periods. The peaks again get larger with time, indicative of a system that predicts periodicities better the further they are in time. I cannot explain this at this point.
Image:ACF N1.pngImage:ACF N2.png
Figure 3: The last figure shows the autocovariance functions of the density data with the R&G data on the left. As with the magnetic field data, these data show 26- and 34-day periods (although the 34 day period is small). The peaks also increase in amplitude with time. The R&G data appear to be much noisier than the Set #2 data.
[edit] 2 OMNIweb data analysis
I am not able to explain why the peaks in all of these ACFs are increasing with time. As I stated, it is indicative of a system that is more predictable as time from the present increases. The best way to confirm that this is a true effect and not just a artifact of the data is to find other magnetic field, density, or velocity data from the same time period, but with a different instrument. I looked at OMNIweb data for the 1992-1993 period (R&G data), but there were huge gaps in the time series. The OMNIweb magnetic field and velocity data from the 1996-1997 time period have fewer gaps, so I found the ACF for those data. The results are below:
Image:ACF Vomni.pngImage:ACF Bomni.png
Figure 4: The above autocovariance plots are for velocity (left) and magnetic field (right) data from OMNIweb. They show the same trend as the Ulysses data; the peaks increase with time. The effect is not as pronounced in these data, though.
