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I have a time-series of noisy data which occasionally triggers an event, and once that happens, the noise calms down and the cycle repeats itself (until the event is triggered once again). What I want to try and model is essentially the likelihood of the event occurring at any point throughout my univariate time series.

For example, in the picture below, the blue line measures the time to event, with the red line being the actual data. How could I predict when the blue line dips/the event occurs?

I thought Survival analysis would fit the bill, as it deals with modelling time to events, but I have had difficulty locating the right resources, and would appreciate any advice.

enter image description here

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You may be looking for joint models.

These models are a combination of a survival model to consider events and a mixed model to take into account evolution of some factors over time.

There is a R tutorial you can try (never tried myself so I'm no help sorry), and here is what it says you can do (I added bold in what you should be interessed in):

The whole model and its parts can be extended in several ways:

  • To find latent population heterogeneity (latent class joint models).

  • Allow for multiple longitudinal markers.

  • Allow for the analysis of multiple failure times. This is the case of competing risks and recurrent events (for instance, when a child develops asthma attacks, to find the risk of recurrence).

  • Time-Dependent accelerated failure time (AFT) Models.

  • Dynamic predictions when new values are added for the longitudinal variable, using Maximum Likelihood Estimates and empirical Bayes
    estimates.

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  • $\begingroup$ Huh, absolutely never heard of them before. Will take a look, and report back at some point. Thanks! $\endgroup$ – Coolio2654 Feb 28 at 3:30

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