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Disclaimer: I am pretty new to time series prediction. I hope my questions are not stupid. If so, or they should be changed, give me a friendly nudge.

Tasks

I have a system that gives me status messages. Receiving those I end up with a time series. These messages/events have a time stamp, but they do not come with equi-distance, like

(12:00am, Message1), (12:02am, Message2), (12:05am, Message2), (12:20am, Message1), (12:21am, Message3)

(thanks to @Igor)

For some messages the time stamp is identical. So one could consider them either messages which just happen to have the same time stamp, or on could consider the time stamps to have multivariate messages of varying length.

I would like to

  1. Find out which messages appear together. E.g. a message "door was unexpectedly opened" might appear often together with "door was unexpectedly closed". In this case they most likely also come in this order. Thus the second task is:
  2. Be able to predict which message comes usually after which messages (correlation, not causation), so basically want to predict

    Prob{ message[t] = X | message[t-1] = Y },

for all message types X and Y.

  1. Be able to predict which message will come next and when, based on the previous messages and their timestamps, so basically

    Prob{ message(t_1 > t_0) = X | messages(t < t_0) },

    Prob{ t_1 | messages(t < t_0) },

for all message types X.

Approaches

  1. Task

For the first task we could use a sliding window and thus have groups of which messages are close to each other. So I would have a list (of windows) of lists (of messages that came in this window), but then what? How do I do modelling after that?

  1. Task

I considered using hidden markov models, but I am not sue if this is the right way to go as they they would not consider the time stamp in any way, or are they? How could I use HMM with the time stamp? What method could I use instead - maybe considering more than the last event?

  1. Task

Hidden markov models might be of some use here, but they are not considering the time stamp and they can' tell be when the next event will come. What is an alternative?

In any case: I could calculate the time differences between the events as a feature - but that would not help for a hidden markov model, would it?

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  • $\begingroup$ So your data looks something like: (12:00am, Message1), (12:02am, Message2), (12:05am, Message2), (12:20am, Message1), (12:21am, Message3), ... etc? What does it mean for messages to "come together"? For 2., you want to predict Prob[message(t) = X | message(t-1) = Y], for all message types X and Y? If you aren't conditioning on anything else, then this should just be the transition matrix I think. For 3, what are you thinking of using for your predictors? $\endgroup$ – Igor May 8 '17 at 22:02
  • $\begingroup$ @Igor: Thank you. I updated the "Tasks" part of my question accordingly. Regarding 3: As predictors I wanted to use the previous messages and their timestamps. $\endgroup$ – Make42 May 9 '17 at 7:45

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