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I am searching for an approach that is able to predict a complete time series for a given parameter set.

Imagine a robotic arm which has a starting position and a target position. There is a sensor mounted to the top of the arm. For random start and target positions I can record the sensor values as a time series. Now, I would like to predict the sensor values for a previously unknown start and target position.

Currently, the only approaches I can find try to forecast the next values for a given time series. Other approaches aim for generating new sequences for a given set of sequences, which is close to what I would like, but without the possibility to connect the sequences to parameter sets.

Does anyone have an idea?

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Check the literature on functional data. Your function here comprises the sensor values over a complete path of the robotic arm. From a random sample of such functions you are wanting to predict a new function with specified start and target positions. A good intro is Ramsay and Silverman (2005).

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