What is the difference between irregularly sampled time series and non-linear time series? Also, what are the best methods for the analysis of irregularly sampled time series? Are there any sample data sets for such time series?


A non-linear time series is a time series which is generated by a non-linear process. For an regularly sampled time series $x_0, …, x_n$, this corresponds to a non-linear dependence of $x_t$ on $x_{t-1}, x_{t-2}, …, x_{t-m}$. For irregularly sampled time series, there is no such correspondence.

As a result, there is no general relation between the linearity of a time series and the regularity of the sampling, as the first property is about what you observe and the second property is about how you observe. So, there are

  • regularly sampled linear time series,
  • irregularly sampled linear time series,
  • regularly sampled non-linear time series,
  • irregularly sampled non-linear time series.

Irregularly sampled time series are a rather broad topic, so I can only give you some question you should ask yourself:

It is very crucial what determines your sampling times. They could be:

  • comparably random, e.g., if you can only take samples, if nobody else claimes the laboratory and this is not mainly determined by schedules
  • depending on a complex process, e.g., if you make astronomical observations and can only do so, if the weather is fine and at a specific time of the year
  • strongly depend on the observed process, e.g., if you analyse seismical activity which is only recorded in the temporal vicinity of earth quakes

The latter two options may introduce a strong bias on your data and affect the results of your analysis, if you are not careful. In particular they may cause the time series to appear to be non-linear (if you ignore the sampling), even if the underlying process isn’t.

| cite | improve this answer | |
  • $\begingroup$ Thanks. This was of great help. Are there any sample data sets for irregularly sampled time series that can be worked on? I have only found regularly sampled data. $\endgroup$ – user93 Oct 12 '14 at 15:01
  • $\begingroup$ @user93: I do not know any, but you can always generate yourself some data for a start, e.g., an irregularly sampled sine wave. $\endgroup$ – Wrzlprmft Oct 12 '14 at 16:11

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.