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In the context of time series prediction, I have read that time series is a series of data that taken at successive equally spaced points in time (which means its in order). What if I have a discontinuous time series data, for example:

If I have data that represnt a room temperature within the working hours, specifically from 7:00 am - 3:00 pm. And this data is repeated on the day of the week. So we have something similar to this:

Saturday: [ Time series data from 7:00 am - 3:00 pm]

Sunday: [ Time series data from 7:00 am - 3:00 pm]

Monday: [ Time series data from 7:00 am - 12:00 pm] -- Only up to 12 pm

The first question:

  1. Is that considered as time series data

  2. Now if I want to predict the room temperature on Monday @ 1:00 pm. How can I do this using given this type of datasets?

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  • $\begingroup$ Yes, it is. Try Gaussian process regression. $\endgroup$ – Emre Apr 5 '18 at 17:12
  • $\begingroup$ @Emre, thanks for your prompt answer. But I am wondering how Gaussian process regression is different than Linear regression. and which one is more powerful to handle such case? .... Also if you have any example how to do it in python I would appreciate it $\endgroup$ – Neno M. Apr 5 '18 at 17:51
  • $\begingroup$ Both can extrapolate, but Gaussian process regression gives you prediction intervals, and readily allows you to incorporate things like seasonality; relevant things to your problem. Here's a library: github.com/GPflow/GPflow $\endgroup$ – Emre Apr 5 '18 at 18:23
  • $\begingroup$ @Emre Thank you again, But I think I didn't explain my question well. Let me clarify. My main issue is that since my data is only cover 7 hours of the day. So if I put the days in sequence, there will be a big gap between the days .... For example end of Saturday is @ 3pm and the next point will be the first point of next day which is @ 7am .... Now I am not sure if what you have suggested can address this kind of gaps in my sequence (which is not equally spaced) $\endgroup$ – Neno M. Apr 6 '18 at 4:33
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Yes, it is time series with missing values. In fact you have process $X_t$, which is room temperature in moment $t$, but you have observations in specific time intervals. So your goal is to find out missing values between non-observed intervals. There are several methods and packages for solving problems like this, here is an implementation of some methods in R:

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