What happens if the output time series is a linear combination of the basis time series, and what if it is a nonlinear function of the basis time series? The time series may well be noises.
Dear Laya. I assume that the two "basic" time series are unobservables. If you do not have any information of the Data Generating Process of these original series, obviously you can not "deduct" or estimate the series.
The point is that maybe you can make some assumptions about these series. For example, in time series decomposition methods, see Maravall, you assume that a series is the result of trend, cycle, seasonal, etc.. You have to hypothesize about the model (the DGP) of any component (but not the parameters). Then, you can estimate the parameters of each component and "estimate" these "original" series.
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