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I have a dataset that I am trying to analyse that consists of multiple (~500) time series each with around 25 observations. For each observation I have a large number of covariates, some of which will have predictive power in forecasting the individual time series. The time series exhibit similar behavior so I wish to look into the possibility they can be modeled by a common underlying random process. The problem I have run into is that the individual time series seem to have a notable amount of memory.

Is there a framework (preferably one that is easily implementable, or already implemented in R or python) that captures this memory property as well as taking into account the predictive factors? I would be appreciative of any direction towards literature or suggestions of model architectures.

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You can use the Long-Term-short-Memory neural networks.Take a look at this.

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