Which time series prediction techniques are useful given harmonic properties? I have a time series dataset where events have harmonic properties, and seemingly the nature of the event's early segments can determine the remainder of the event (see example 1's oscillations). Additionally, these early segments might determine the properties/likelihood of some following/associated event (example 2).

Which time series prediction techniques may be suitable for making predictions based on this kind of behaviour? Specifically:


For determining how an event, from appearance, might oscillate and dissipate (forecast/extrapolation). 
For predicting what event may follow (probabilistic model).


I am not very knowledgeable in this, but seemingly dynamic ARIMA may be appropriate for the extrapolation at a given point. Also, the early segment might be suitable as a feature for prediction in some other model (e.g. SVC)?

Example Event 1



Example Event 2





EDIT: I want to avoid fitting a highly specialised/targeted model based on observation - but would be happy for some process to learn this representation. I am interested in learning about existing models/methodologies that could be applied to this problem, references would be great.
I would suggest to make the correlation plot and observe the dependencies. Yes, ARIMA, is so far the best forecasting model for time series and it should work in this data set too. 
For the implementation, in R, there is auto ARIMA, which automatically takes the best suited valued for the parameters( 
    p: The number of lag observations included in the model, also called the lag order.
    d: The number of times that the raw observations are differenced, also called the degree of differencing.
    q: The size of the moving average window, also called the order of moving average.)

But as far as I am concerned, in Python, you have to manually tune the parameters by yourself by analyzing the correlation plot. This is a very well explained beginner level tutorial for the implementation in Python.  
Let me know in the comments if it works (or not).