analysing time series

I'm analysing time series and have a question related to the dependency between the elements. Lets assume I have a time series and want to extrapolate future values. For this purpose I want to know if the time series can be estimated by using specified patterns or if the upcoming values are mainly influenced by the latest values of the time series.

My idea was to analyze the correlation beween $x_{n}$ and $x_{n-k}$, where k belongs to a specified set of indices.

Honestly I'm not really concinced by this idea. Does somebody know a different methodhelping me with this issue.

Kind regards

Bernhard

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If you do not get an answer here, I would suggest also to try at stats.stackexchange.com –  Artium Jun 20 '12 at 14:34

There are plenty methods of extrapolating time series. Mainly there are a models like MA, AR, ARIMA, that are the cornerstone of timeseries prognosis. These methods are mainly based on lags of the either data or shocks (I mean $x_{t-i}$ or $\varepsilon_{t-i}$). In timeseries analysis people also take in mind a trend and seasonality, because once predicting the further values one have to remove those two (or as it called decompose the timeseries) and make prediction based on what's left.