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I have several time series that are each observations of the same phenomenon, for example:

Observation 1: 10, 25, 36, 72, 80, ....

Observation 2: 32, 46, 78, 90, 100, ....

Observation 3: 12, 27, 34, 75, 36, ...

....

Observation 100: 7, 33, 45, 56, 32, ...

Each of my measurements within each observation are taken at equivalent periods of time. I can use a variety of methods to fit curves to my time series and predict performance for each individual series. However, how do I then combine these curves to create a generalizable model that takes into account all 100 observations?

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It sounds like that you have several time series, such as $\{Y_{1,i}\}_{i=0}^T, \{Y_{2,i}\}_{i=0}^T, \{Y_{3,i}\}_{i=0}^T, \cdots$ that happen to be dependent on each other for observations $i=1,\cdots,T$. In which case, you should look into vector autoregressions (http://en.wikipedia.org/wiki/Vector_autoregression), vector ARMA (http://homepage.univie.ac.at/robert.kunst/var11_iqbal_naveed_nadeem.pdf), and other simultaneous equations models depending on the structure of how your time series are related. For example, if you think that each time series depends on lags of itself and lags of the other variables, and you're willing to impose to same structure lag-variable on each time series, then you should look into vector autoregressions (VARs).

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