Learning from time-series data to predict time-series (not forecasting) - machine-learning

Question

I have a number of datasets where each of them contains a number of input variables (lets say 3) as time series and an output variable, also as a time series and all over the same time period.
Each of these series has the same number of datapoints (say 1000*10 if 10 second data was gathered at 1000Hz).
I want to learn from this data and given a new dataset with 3 time serieses for input variables, I want to predict the time series for the output variable.
I will write the problem below in some non-English notation. I will avoid using terms like features, sample, target etc because since I haven't formulated the problem for any algorithm, I don't want to speculate what will be what.
Datasets to learn from look like this:
dataset1:{Inputs=(timSeries1,timSeries2,timSeries3), Output=(timSeriesOut)}
dataset2:{Inputs=(timSeries1,timSeries2,timSeries3), Output=(timSeriesOut)}
dataset3:{Inputs=(timSeries1,timSeries2,timSeries3), Output=(timSeriesOut)}
.
.
datasetn:{Inputs=(timSeries1,timSeries2,timSeries3), Output=(timSeriesOut)}
Now, given a new (timSeries1, timSeries2, timSeries3) I want to predict (timSeriesOut)
datasetPredict:{Inputs=(timeSeries1,timSeries2,timSeries3), Output = ?}
What technique should I use and how should the problem be formulated? Should I just break it as separate learning problem for each time stamp with three features and one target (either for that or next timestamp)?
Thank you all!