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I would like to separate a big time series into its components to improve forecasting.

To clarify: I would like to find the different components - maybe it is better to say frequencies which constitute the overall time series. These frequencies will not occur in sequence (one after the other) but are combined / in parallel.

Edit:

Similar to the proposed idea [here](DOI: 10.3233/AIC-2010-0485), I think forecasting the different components separately may improve the overall quality of the prediction.

Think about a smart meter. There one could break up the singular, aggregated time series of the meter into one for the washing machine, one for the fridge, etc., and one more for the remaining noise in order to model and forecast the energy usage separately and improve prediction (cf., nonintrusive load monitoring)?

A similar but different scenario is the history of transactions in a bank account: Here breaking up the cashflow means finding the individual time series of payments (salary, rent, newspapers, etc.) out of the list of discrete transactions. As mentioned, it might be better to talk about seasonality in this case as recurring payments are different seasonal components.

In a more general sense, I would like to find the basic frequencies / periodicities in the data (cf., spectral density estimation) which constitute the overall main time series.

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  • $\begingroup$ Do you mean different temporal segments (eg, 10/2013 - 5/2014; 6/2014 - 1/2015, etc) or different seasonal components (eg, weekly patterns, & annual patterns, etc)? $\endgroup$ – gung Mar 9 '15 at 23:18
  • $\begingroup$ I think of different seasonal components e.g some yearly, & monthly seasonal patterns. I do not think these are temporal segments (one after the other). $\endgroup$ – Georg Heiler Mar 10 '15 at 6:22
  • $\begingroup$ Your question, as written, is unclear. From your comment, it seems you may be asking about seasonality, not clustering. Consider editing your Q to clarify (if correct) that you want to identify seasonality on different time scales in your data. You should probably add the tag [seasonality] & drop [clustering] at least. What are [pca] & [frequency] doing there, are they related to your Q somehow? If your Q can be made clear enough, we can re-open it for you. $\endgroup$ – gung Mar 10 '15 at 15:30
  • $\begingroup$ I hope the question is now clear enough. $\endgroup$ – Georg Heiler Mar 10 '15 at 21:46
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    $\begingroup$ If you want spectral density estimation, you know where to find it. Otherwise with a suitably general definition of components very many time series methods could be phrased in terms of identification and estimation of components and so this seems too broad to answer satisfactorily. $\endgroup$ – Nick Cox Mar 11 '15 at 10:57

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