Plotting rescaled time series and temporal data

Question

I am trying to use ListLinePlot to plot three "Components" of my TemporalData in Mathematica. The three components differ widely in the range of the data. So, I want to Rescale each component and plot.

I used the Rescale function on each "Components". This works well if there is no missing data in the Component. However, it does not plot if there is missing data. I know there is a RescaleTimeSeries function to scale the time axis. Is there a corresponding function for the y-axis.

@Gladaed, Here is an example with two components:

r = {11, 13, 2, 7, 17, 8};
s = {2, 1, 6, 5, 7, 4};
t = {1, 2, 5, 10, 12, 15};
td = TemporalData[{r, s}, {t}]

rmissing = {11, 13, Missing["No Data"], 7, 17, 8};
tdmissing = TemporalData[{rmissing, s}, {t}]

grp0 = ListLinePlot[td]
grpmissing = ListLinePlot[tdmissing]

grp1 = ListLinePlot[{Rescale[td["Components"][[1]]], Rescale[td["Components"][[2]]]}]
grprescaledandmissing = ListLinePlot[{Rescale[tdmissing["Components"][[1]]], Rescale[tdmissing["Components"][[2]]]}]

You will see that the Rescaled Plot "grprescaledandmissing" does not plot the Component with missing data. The regular ListLinePlot "grpmissing" that is not Rescaled is fine.

Answer 1

Your issue is caused by the way Mathematica's Plot function handles missing data. It assumes it to be eg. a potentially noisy dataset where interpolating could lead to false assumptions about the dataset.

EG: A vibration/motion sensor gives us information about the quality of a measurement. Less variance the better. It measures tries to measure this:

But since it only can measure once every 10th part of a second it gives us:

which is good. But now the sensor had a loose connection now it gave temporal data with some Missing[] elements. If it assumed it should interpolate it would give this curve below. While it is a little obvious for this example imagine more smaller sections of missing data. This could do serious damage to you project if you don't know about this behaviour.

Now you would think that the data is way less noisy than it actually is instead of noting the lack of data like this:

That's why you have to tell TemporalData via MissingDataMethod what to do in such cases if you want some fixing of missing points. Found using: google search.

Code:

randomList = RandomVariate[NormalDistribution[], 100];
t = Range[-5, 5, 10.0/(100 - 1)];
randomTD = TemporalData[randomList, {t}]
randomList[[40 ;; 60]] = Missing["loose connection"]
randomMissingTD = TemporalData[randomList, {t}]
randomMissingInterpolTD = 
 TemporalData[randomList, {t}, 
  MissingDataMethod -> {"Interpolation"}]
Plot[RandomVariate[NormalDistribution[]], {x, -5, 5}]
ListLinePlot[randomTD]
ListLinePlot[randomMissingTD]
ListLinePlot[randomMissingInterpolTD]