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Hi,
Time series prediction is a voluminous subject.
The best method with known process is Kalman filtering/prediction. For this the models should be know as accurate as possible. It is possible to get the models by data analysis. Check Maybeck.
In general there are paramateric and non parametric methods. Choose parametric if you know someting about the source else go for non parametric.
Why we can predict a time series? The reason is that every series has enertia. If we could acquir some parameters which can describe enertia, prediction can be done. Correlation is the most important one of parameters which we need. So the methods of AR, MA, LMS, Winner, Kalman filter are all based on it.
Please, be more specific. First: your problem of time series prediction is related with a linear or a non linear system? (the system which is generating such time series).
If it is a linear system, then the AR, ARMA, and others approaches (such as the listed above) are indicated.
If you are working with a nonlinear system, there are (again) a lot of methods. Maybe the more used is a neural network. This network is trained with the data and next you can use it for prediction.
One of the fields where more work is being done in this field is... finance, econometrics. Some links to browse
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