Plot dimension m of n ValueDimensions in TemporalData: with proper temporal values

I have a TemporalData object that has td["ValueDimensions"] =3. Right now I only have one sample, K=1. So the following example is the simplest case, dim=3 and K=1. To begin with, I just want to plot each dimension separately. Should be trivial but it seems I have to twist the td object into knots to get the time dimension to show correctly...

 ts = {{{0., {1.333999006891247, 12.053810602014542,
87.94618939798545}}, {0.1, {1.3514434090695817,
12.093415930914793,
86.53455823856495}}, {0.2, {1.2484079436257138,
12.25553483931355,
92.89743502043808}}, {0.30000000000000004, \
{1.3781565261854645, 12.184908506564101,
84.45147211241067}}, {0.4, {1.3285491537059095,
12.29338463899116,
87.1154457958651}}, {0.5, {1.353124500190124,
12.328305046121512,
85.38069968635773}}, {0.6000000000000001, {1.4134624696453986,
12.326915095624361,
81.70867228313669}}, {0.7000000000000001, {1.195964818586219,
12.60441567097316,
94.68144692187659}}, {0.8, {1.2736346893937893,
12.587741552453553,
89.29573476671187}}, {0.9, {1.0705151506735828,
12.853307642920917,
103.2366857670525}}, {1., {0.9802798326333646,
13.00862708606569, 110.54583685327417}}}}
tds = TemporalData[ts]
ListLinePlot[td]
(* Pols suggests if "ValuesDimension" returns 3 then this would just work *)
ListLinePlot[td["Values", 1]]
ListLinePlot[td["Values", 2]]
ListLinePlot[td["Values", 3]]

(* The following shows on dimension for the one path, but feels wrong on so many levels, e.g. the time dimension has been lost*)
tds["ValueList"][[1, All, 1]] // ListLinePlot


Once I can do this, I'd like to generate (using ItoProcess) K paths instead of just one, and then I'd like to plot each of these.

Would appreciate any hints or tips about how to do this elegantly.

The following is undocumented:

tds["PathComponents"]


ListLinePlot @ tds["PathComponents"]


Plot component 3 only

ListLinePlot @ tds["PathComponent", 3]
(* or *) ListLinePlot @ tds["PathComponents"][[3]]


The property "PathComponent" and the form tds["PathComponent", componentnumber] are undocumented.

Both "PathComponents" nor PathComponent" work in versions 9.0, 11.3 and 12.0 although neither appear in the property list:

tds["Properties"]


{Components, DateList, DatePath, DatePaths, Dates, FirstDates, FirstTimes, FirstValues, LastDates, LastTimes, LastValues, Part,Path, PathCount, PathFunction, PathFunctions, PathLength, PathLengths, Paths, PathTimes, SliceData, SliceDistribution, TimeList, Times, ValueDimensions, ValueList, Values}

• Many thanks. Could you add "The following is undocumented:" as the first line. This will forewarn others in case wolfram change this behavior to some thing else undocumented. Then I'll accept the answer. I'm the OP and I was annoyed with myself . Its reasonable others think "The lazy so-and-so. Why didn't he just read the docs about this". Any insight into how to elegantly select dimension M of sample/Simulation K. – Hedgehog Dec 31 '17 at 20:02
• @Hedgehog, done. – kglr Dec 31 '17 at 20:06