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Has anyone any idea how one could distinguish time series according to certain properties? The only time series properties I know are stationarity/nonstationarity and homoskedasticity/heteroskedasticity. But are there any other possibilities to distinguish time series?

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  • $\begingroup$ Yes, but there really are entire textbooks on this. See stats.stackexchange.com/help/dont-ask for guidance on scope. "Your questions should be reasonably scoped. If you can imagine an entire book that answers your question, you’re asking too much." $\endgroup$ – Nick Cox Jul 11 '13 at 13:04
  • $\begingroup$ maybe you can recommend me one or two good books? $\endgroup$ – DatamineR Jul 11 '13 at 13:11
  • $\begingroup$ Once again, the help explains how you can search for yourself first. stats.stackexchange.com/questions/6275/… is one of several starting points. $\endgroup$ – Nick Cox Jul 11 '13 at 13:15
  • $\begingroup$ There is also this: books-for-self-studying-time-series-analysis. $\endgroup$ – gung - Reinstate Monica Jul 11 '13 at 13:32
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    $\begingroup$ I am not voting to close. Consider this interpretation: "What are the major qualitative properties of time series that one looks at when commencing any analysis/forecast/etc?" Surely our time-series experts would be able to rattle off a half dozen or so characteristics and (I hope) most would agree on them. Offhand, I imagine these would include trend, seasonality, sign of serial correlation, heteroscedasticity, outliers, and any suggestion of changepoints. (It's unclear whether stationarity can be qualitatively apprehended.) A discussion of these could be a useful guide for non-experts. $\endgroup$ – whuber Jul 11 '13 at 14:45
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A very widely used time-series identification scheme is the Box-Jenkins approach. See here. This involves establishing stationarity and decomposing seasonality, then fitting Autoregressive (Integrated) Moving Average (ARIMA) models to the resulting series. The R function ARIMA() in the stats package will do this and chooses the appropriate model and estimates parameters according to AIC.

A point of clarification in your question, however: The concept of stationarity includes the variance (i.e. homoskedasticity vs. heteroskedasticity). A stationary series is, by definition, homoskedastic. See here.

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I think I have found what I have been looking for in the paper of Rob Hyndman:

"...there are nine classical and advanced statistical features describing a time series’ global characteristics. They are: trend, seasonality, periodicity, serial correlation, skewness, kurtosis, non-linearity, self-similarity, and chaos." (Wang/Smith/Hyndman (2006),Characteristic-Based Clustering for Time Series Data)

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