How to deal with sparse time series before establishing a unified prediction model for a large number of time series?

[nullgogo]

According to the prediction requirements, the time series is granular in minutes. We first remove all the parts with missing rate exceeding 10% in the time series, but in the remaining time series, there are still some sparse time series.
For example, the time series of consumers paying per minute has a value of 0 at many points in time. If these sequences are directly modeled, the prediction effect of the model may be greatly reduced. So, how do you preprocess these sparse time series before building a predictive model? Have you ever encountered a similar situation and how is it handled? Thank you

The following image is a screenshot of some of the data in the sparse time series (the length of time is one month)