Forecast Time Series like data I have time series like data, 500 data points of (x,y) pairs. Where x = time in seconds and y = signals. Each of this candidates have an additional label (which tells about the nature of the wave source). And this way I have about thousand candidates data.
Now I want to do a forecast analysis, such that the label can be predicted (after a supervised learning). Typical data looks like this,
t1,t2,t3,...,t500, sa1,sa2,sa3,...,sa500,Label1
t1,t2,t3,...,t500, sb1,sb2,sb3,...,sb500,Label2
t1,t2,t3,...,t500, sc1,sc2,sc3,...,sc500,Label3
.
.
.
t1,t2,t3,...,t500, sx1,sx2,sx3,...,sx500,LabelX 

The time array(/values) is same for all candidates.
A typical plot of three random candidates look, as shown below,
I want to know/discuss what algorithms are appropriate (pros and cons, efficiency, optimization etc) for such an analysis, want to know from the experts.


This is a classification problem with functional data. The fact that there is a time index is not really important. Think about each time series as a continuous function that is observed at discrete points.
There was a review of the literature about 10 years ago by Baillo, Cuevas and Fraiman. I'm sure a lot has been done since then. You can track the citations for that paper at https://scholar.google.com.au/scholar?cites=947432642489427396
