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I'm attempting to devise a strategy to make time series forecasts based on costs accumulated over time. My dataset contains about 7500 time-series sequences (call it an instance for now), each having accumulated cost values over time. Four random instances have been sampled (out of the 7500 instances) and their individual time series sequences have been plotted below (note these are points and not continuous lines). I've dealt with time series forecasting before, but not in this sense where I have multiple time series sequences that are not in sync. Also the events don't have constant periodicity, that is, one instance can have a cost observation in 7 days, and then the next observation will be in 3 days.

Time series of 4 arbitrary instances in dataset

What would be an appropriate strategy to make the next forecast of the cost value for each instance given its unique prior history?

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