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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
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1 Answer

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.

Prediction of time series is also based on lags and is quite difficult process since you usually have to choose the order of lags yourself. Of course, there's a lot of automated procedures but in the end it's analyst who decide. Also, not all the timeseries can be predicted since there are some processes like white noise or random walk that are just randomly changing their values and there are tests to check either your timeseries belongs to such kind of processes.

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you wrote: "Also, not all the timeseries can be predicted since there are some processes like white noise or random walk that are just randomly changing their values and there are tests to check either your timeseries belongs to such kind of processes." which kind of test exist for this? do you have some links or further informations? –  Stoecki Jun 21 '12 at 6:25
    
To chech whether timeseries is white noise, we can draw the ACF and PACF graphs and check for certain pattern. Other approach is when you want to check whether timeseries is random walk. Random walk is a simpliest I(1) process you have to do integration test (there are several like Dickey-Fuller, Augmented Dickey-Fuller, KPSS). This is not an easy thing since sometimes tests can be threated differently and under some conditions can be lying. –  user974514 Jun 21 '12 at 7:49
    
If you want to learn this quickly I would skip through the wiki if not there's free book here. –  user974514 Jun 21 '12 at 7:50
    
thanks for the reply –  Stoecki Jun 21 '12 at 9:40
    
Actually if you have a process the is just random noise about a constant value c (c may or may not be zero), there is a best forecast which is to use the sample mean of the observed data. It is possible that when others have claimed that you can't predict in this situation, they meant that recent history is no more helpful than ancient history. –  Michael Chernick Jul 26 '12 at 13:43
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